Daily Papers

Large Language Model (LLM) Agents exhibit inherent reasoning abilities through the collaboration of multiple tools. However, during agent inference, existing methods often suffer from (i) locally myopic generation, due to the absence of lookahead, and (ii) trajectory instability, where minor early errors can escalate into divergent reasoning paths. These issues make it difficult to balance global effectiveness and computational efficiency. To address these two issues, we propose meta-adaptive exploration with LLM agents https://github.com/exoskeletonzj/MAXS, a meta-adaptive reasoning framework based on LLM Agents that flexibly integrates tool execution and reasoning planning. MAXS employs a lookahead strategy to extend reasoning paths a few steps ahead, estimating the advantage value of tool usage, and combines step consistency variance and inter-step trend slopes to jointly select stable, consistent, and high-value reasoning steps. Additionally, we introduce a trajectory convergence mechanism that controls computational cost by halting further rollouts once path consistency is achieved, enabling a balance between resource efficiency and global effectiveness in multi-tool reasoning. We conduct extensive empirical studies across three base models (MiMo-VL-7B, Qwen2.5-VL-7B, Qwen2.5-VL-32B) and five datasets, demonstrating that MAXS consistently outperforms existing methods in both performance and inference efficiency. Further analysis confirms the effectiveness of our lookahead strategy and tool usage.

Despite recent advances in inversion-based editing, text-guided image manipulation remains challenging for diffusion models. The primary bottlenecks include 1) the time-consuming nature of the inversion process; 2) the struggle to balance consistency with accuracy; 3) the lack of compatibility with efficient consistency sampling methods used in consistency models. To address the above issues, we start by asking ourselves if the inversion process can be eliminated for editing. We show that when the initial sample is known, a special variance schedule reduces the denoising step to the same form as the multi-step consistency sampling. We name this Denoising Diffusion Consistent Model (DDCM), and note that it implies a virtual inversion strategy without explicit inversion in sampling. We further unify the attention control mechanisms in a tuning-free framework for text-guided editing. Combining them, we present inversion-free editing (InfEdit), which allows for consistent and faithful editing for both rigid and non-rigid semantic changes, catering to intricate modifications without compromising on the image's integrity and explicit inversion. Through extensive experiments, InfEdit shows strong performance in various editing tasks and also maintains a seamless workflow (less than 3 seconds on one single A40), demonstrating the potential for real-time applications. Project Page: https://sled-group.github.io/InfEdit/

Run the same LLM agent on the same task twice: do you get the same behavior? We find the answer is often no. In a study of 3,000 agent runs across three models (Llama 3.1 70B, GPT-4o, and Claude Sonnet 4.5) on HotpotQA, we observe that ReAct-style agents produce 2.0--4.2 distinct action sequences per 10 runs on average, even with identical inputs. More importantly, this variance predicts failure: tasks with consistent behavior (leq2 unique paths) achieve 80--92% accuracy, while highly inconsistent tasks (geq6 unique paths) achieve only 25--60%, a 32--55 percentage point gap depending on model. We trace variance to early decisions: 69% of divergence occurs at step 2, the first search query. Our results suggest that monitoring behavioral consistency during execution could enable early error detection and improve agent reliability.

Diffusion models are relatively easy to train but require many steps to generate samples. Consistency models are far more difficult to train, but generate samples in a single step. In this paper we propose Multistep Consistency Models: A unification between Consistency Models (Song et al., 2023) and TRACT (Berthelot et al., 2023) that can interpolate between a consistency model and a diffusion model: a trade-off between sampling speed and sampling quality. Specifically, a 1-step consistency model is a conventional consistency model whereas we show that a infty-step consistency model is a diffusion model. Multistep Consistency Models work really well in practice. By increasing the sample budget from a single step to 2-8 steps, we can train models more easily that generate higher quality samples, while retaining much of the sampling speed benefits. Notable results are 1.4 FID on Imagenet 64 in 8 step and 2.1 FID on Imagenet128 in 8 steps with consistency distillation. We also show that our method scales to a text-to-image diffusion model, generating samples that are very close to the quality of the original model.

Benchmarks measure whether a model is correct. They do not measure whether a model is reliable. This distinction is largely academic for single-shot inference, but becomes critical for agentic AI systems, where a single rephrased prompt can trigger cascading failures in multi-step execution. Yet this form of instability is not captured by existing evaluations. Hallucinations live in variance: they arise when semantically equivalent prompts activate inconsistent internal pathways, producing divergent outputs. Consistent but incorrect outputs reflect bias or missing knowledge; confident guessing reflects calibration failure. Neither constitutes hallucination under this definition. When error is variance-dominated, reducing redundant pathways improves reliability without adding knowledge. We formalize this through Semantic Stability (SS), measured via Paraphrase Consistency (PC@k): generate k paraphrases, greedy decode each, compute mode agreement. SS is a diagnostic for variance-driven unreliability, not a method for improving correctness. We show that a dense Qwen3-0.6B agrees with itself only 23.8% of the time; at 32% sparsity, agreement jumps to 55.9%. A phase diagram reveals the sweet spot where variance reduction outpaces bias accumulation, and regimes where stability collapses onto wrong answers.

Agentic systems are evaluated on benchmarks where agents interact with environments to solve tasks. Most papers report a pass@1 score computed from a single run per task, assuming this gives a reliable performance estimate. We test this assumption by collecting 60,000 agentic trajectories on SWE-Bench-Verified, spanning three models and two scaffolds. We find substantial variance: single-run pass@1 estimates vary by 2.2 to 6.0 percentage points depending on which run is selected, with standard deviations exceeding 1.5 percentage points even at temperature 0. This variance has critical implications: reported improvements of 2--3 percentage points may reflect evaluation noise rather than genuine algorithmic progress. Through token-level analysis, we show that trajectories diverge early, often within the first few percent of tokens, and that these small differences cascade into different solution strategies. To enable reliable evaluation of agentic systems, we recommend three concrete practices: (1) estimate pass@1 from multiple independent runs per task, especially when measuring small improvements, (2) use statistical power analysis to determine the number of runs needed to detect expected effect sizes, and (3) consider metrics like pass@k (optimistic bound) and pass^k (pessimistic bound) with k>1 to better characterize the full performance envelope. While these practices increase evaluation cost, they are essential for distinguishing genuine scientific progress from statistical noise.

Consistency models are a nascent family of generative models that can sample high quality data in one step without the need for adversarial training. Current consistency models achieve optimal sample quality by distilling from pre-trained diffusion models and employing learned metrics such as LPIPS. However, distillation limits the quality of consistency models to that of the pre-trained diffusion model, and LPIPS causes undesirable bias in evaluation. To tackle these challenges, we present improved techniques for consistency training, where consistency models learn directly from data without distillation. We delve into the theory behind consistency training and identify a previously overlooked flaw, which we address by eliminating Exponential Moving Average from the teacher consistency model. To replace learned metrics like LPIPS, we adopt Pseudo-Huber losses from robust statistics. Additionally, we introduce a lognormal noise schedule for the consistency training objective, and propose to double total discretization steps every set number of training iterations. Combined with better hyperparameter tuning, these modifications enable consistency models to achieve FID scores of 2.51 and 3.25 on CIFAR-10 and ImageNet 64times 64 respectively in a single sampling step. These scores mark a 3.5times and 4times improvement compared to prior consistency training approaches. Through two-step sampling, we further reduce FID scores to 2.24 and 2.77 on these two datasets, surpassing those obtained via distillation in both one-step and two-step settings, while narrowing the gap between consistency models and other state-of-the-art generative models.

Diffusion models achieve superior generation quality but suffer from slow generation speed due to the iterative nature of denoising. In contrast, consistency models, a new generative family, achieve competitive performance with significantly faster sampling. These models are trained either through consistency distillation, which leverages pretrained diffusion models, or consistency training/tuning directly from raw data. In this work, we propose a novel framework for understanding consistency models by modeling the denoising process of the diffusion model as a Markov Decision Process (MDP) and framing consistency model training as the value estimation through Temporal Difference~(TD) Learning. More importantly, this framework allows us to analyze the limitations of current consistency training/tuning strategies. Built upon Easy Consistency Tuning (ECT), we propose Stable Consistency Tuning (SCT), which incorporates variance-reduced learning using the score identity. SCT leads to significant performance improvements on benchmarks such as CIFAR-10 and ImageNet-64. On ImageNet-64, SCT achieves 1-step FID 2.42 and 2-step FID 1.55, a new SoTA for consistency models.

Evaluation benchmarks are the cornerstone of measuring capabilities of large language models (LLMs), as well as driving progress in said capabilities. Originally designed to make claims about capabilities (or lack thereof) in fully pretrained models, evaluation benchmarks are now also extensively used to decide between various training choices. Despite this widespread usage, we rarely quantify the variance in our evaluation benchmarks, which dictates whether differences in performance are meaningful. Here, we define and measure a range of metrics geared towards measuring variance in evaluation benchmarks, including seed variance across initialisations, and monotonicity during training. By studying a large number of models -- both openly available and pretrained from scratch -- we provide empirical estimates for a variety of variance metrics, with considerations and recommendations for practitioners. We also evaluate the utility and tradeoffs of continuous versus discrete performance measures and explore options for better understanding and reducing this variance. We find that simple changes, such as framing choice tasks (like MMLU) as completion tasks, can often reduce variance for smaller scale (sim7B) models, while more involved methods inspired from human testing literature (such as item analysis and item response theory) struggle to meaningfully reduce variance. Overall, our work provides insights into variance in evaluation benchmarks, suggests LM-specific techniques to reduce variance, and more generally encourages practitioners to carefully factor in variance when comparing models.

Diffusion models deliver high-fidelity synthesis but remain slow due to iterative sampling. We empirically observe there exists feature invariance in deterministic sampling, and present InvarDiff, a training-free acceleration method that exploits the relative temporal invariance across timestep-scale and layer-scale. From a few deterministic runs, we compute a per-timestep, per-layer, per-module binary cache plan matrix and use a re-sampling correction to avoid drift when consecutive caches occur. Using quantile-based change metrics, this matrix specifies which module at which step is reused rather than recomputed. The same invariance criterion is applied at the step scale to enable cross-timestep caching, deciding whether an entire step can reuse cached results. During inference, InvarDiff performs step-first and layer-wise caching guided by this matrix. When applied to DiT and FLUX, our approach reduces redundant compute while preserving fidelity. Experiments show that InvarDiff achieves 2-3times end-to-end speed-ups with minimal impact on standard quality metrics. Qualitatively, we observe almost no degradation in visual quality compared with full computations.

Consistency models are a new family of generative models capable of producing high-quality samples in either a single step or multiple steps. Recently, consistency models have demonstrated impressive performance, achieving results on par with diffusion models in the pixel space. However, the success of scaling consistency training to large-scale datasets, particularly for text-to-image and video generation tasks, is determined by performance in the latent space. In this work, we analyze the statistical differences between pixel and latent spaces, discovering that latent data often contains highly impulsive outliers, which significantly degrade the performance of iCT in the latent space. To address this, we replace Pseudo-Huber losses with Cauchy losses, effectively mitigating the impact of outliers. Additionally, we introduce a diffusion loss at early timesteps and employ optimal transport (OT) coupling to further enhance performance. Lastly, we introduce the adaptive scaling-c scheduler to manage the robust training process and adopt Non-scaling LayerNorm in the architecture to better capture the statistics of the features and reduce outlier impact. With these strategies, we successfully train latent consistency models capable of high-quality sampling with one or two steps, significantly narrowing the performance gap between latent consistency and diffusion models. The implementation is released here: https://github.com/quandao10/sLCT/

Timestep distillation is an effective approach for improving the generation efficiency of diffusion models. The Consistency Model (CM), as a trajectory-based framework, demonstrates significant potential due to its strong theoretical foundation and high-quality few-step generation. Nevertheless, current continuous-time consistency distillation methods still rely heavily on training data and computational resources, hindering their deployment in resource-constrained scenarios and limiting their scalability to diverse domains. To address this issue, we propose Trajectory-Backward Consistency Model (TBCM), which eliminates the dependence on external training data by extracting latent representations directly from the teacher model's generation trajectory. Unlike conventional methods that require VAE encoding and large-scale datasets, our self-contained distillation paradigm significantly improves both efficiency and simplicity. Moreover, the trajectory-extracted samples naturally bridge the distribution gap between training and inference, thereby enabling more effective knowledge transfer. Empirically, TBCM achieves 6.52 FID and 28.08 CLIP scores on MJHQ-30k under one-step generation, while reducing training time by approximately 40% compared to Sana-Sprint and saving a substantial amount of GPU memory, demonstrating superior efficiency without sacrificing quality. We further reveal the diffusion-generation space discrepancy in continuous-time consistency distillation and analyze how sampling strategies affect distillation performance, offering insights for future distillation research. GitHub Link: https://github.com/hustvl/TBCM.

Flow matching (FM) is a general framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Recent approaches attempt to straighten these flow trajectories to generate high-quality samples with fewer function evaluations, typically through iterative rectification methods or optimal transport solutions. In this paper, we introduce Consistency Flow Matching (Consistency-FM), a novel FM method that explicitly enforces self-consistency in the velocity field. Consistency-FM directly defines straight flows starting from different times to the same endpoint, imposing constraints on their velocity values. Additionally, we propose a multi-segment training approach for Consistency-FM to enhance expressiveness, achieving a better trade-off between sampling quality and speed. Preliminary experiments demonstrate that our Consistency-FM significantly improves training efficiency by converging 4.4x faster than consistency models and 1.7x faster than rectified flow models while achieving better generation quality. Our code is available at: https://github.com/YangLing0818/consistency_flow_matching

The consistency model (CM) has recently made significant progress in accelerating the generation of diffusion models. However, its application to high-resolution, text-conditioned image generation in the latent space (a.k.a., LCM) remains unsatisfactory. In this paper, we identify three key flaws in the current design of LCM. We investigate the reasons behind these limitations and propose the Phased Consistency Model (PCM), which generalizes the design space and addresses all identified limitations. Our evaluations demonstrate that PCM significantly outperforms LCM across 1--16 step generation settings. While PCM is specifically designed for multi-step refinement, it achieves even superior or comparable 1-step generation results to previously state-of-the-art specifically designed 1-step methods. Furthermore, we show that PCM's methodology is versatile and applicable to video generation, enabling us to train the state-of-the-art few-step text-to-video generator. More details are available at https://g-u-n.github.io/projects/pcm/.

Recent innovations on hardware (e.g. Nvidia A100) have motivated learning N:M structured sparsity masks from scratch for fast model inference. However, state-of-the-art learning recipes in this regime (e.g. SR-STE) are proposed for non-adaptive optimizers like momentum SGD, while incurring non-trivial accuracy drop for Adam-trained models like attention-based LLMs. In this paper, we first demonstrate such gap origins from poorly estimated second moment (i.e. variance) in Adam states given by the masked weights. We conjecture that learning N:M masks with Adam should take the critical regime of variance estimation into account. In light of this, we propose STEP, an Adam-aware recipe that learns N:M masks with two phases: first, STEP calculates a reliable variance estimate (precondition phase) and subsequently, the variance remains fixed and is used as a precondition to learn N:M masks (mask-learning phase). STEP automatically identifies the switching point of two phases by dynamically sampling variance changes over the training trajectory and testing the sample concentration. Empirically, we evaluate STEP and other baselines such as ASP and SR-STE on multiple tasks including CIFAR classification, machine translation and LLM fine-tuning (BERT-Base, GPT-2). We show STEP mitigates the accuracy drop of baseline recipes and is robust to aggressive structured sparsity ratios.

Diffusion models have made significant breakthroughs in image, audio, and video generation, but they depend on an iterative generation process that causes slow sampling speed and caps their potential for real-time applications. To overcome this limitation, we propose consistency models, a new family of generative models that achieve high sample quality without adversarial training. They support fast one-step generation by design, while still allowing for few-step sampling to trade compute for sample quality. They also support zero-shot data editing, like image inpainting, colorization, and super-resolution, without requiring explicit training on these tasks. Consistency models can be trained either as a way to distill pre-trained diffusion models, or as standalone generative models. Through extensive experiments, we demonstrate that they outperform existing distillation techniques for diffusion models in one- and few-step generation. For example, we achieve the new state-of-the-art FID of 3.55 on CIFAR-10 and 6.20 on ImageNet 64x64 for one-step generation. When trained as standalone generative models, consistency models also outperform single-step, non-adversarial generative models on standard benchmarks like CIFAR-10, ImageNet 64x64 and LSUN 256x256.

Visual Autoregressive (VAR) modeling departs from the next-token prediction paradigm of traditional Autoregressive (AR) models through next-scale prediction, enabling high-quality image generation. However, the VAR paradigm suffers from sharply increased computational complexity and running time at large-scale steps. Although existing acceleration methods reduce runtime for large-scale steps, but rely on manual step selection and overlook the varying importance of different stages in the generation process. To address this challenge, we present StageVAR, a systematic study and stage-aware acceleration framework for VAR models. Our analysis shows that early steps are critical for preserving semantic and structural consistency and should remain intact, while later steps mainly refine details and can be pruned or approximated for acceleration. Building on these insights, StageVAR introduces a plug-and-play acceleration strategy that exploits semantic irrelevance and low-rank properties in late-stage computations, without requiring additional training. Our proposed StageVAR achieves up to 3.4x speedup with only a 0.01 drop on GenEval and a 0.26 decrease on DPG, consistently outperforming existing acceleration baselines. These results highlight stage-aware design as a powerful principle for efficient visual autoregressive image generation.

We introduce an approach aimed at enhancing the reasoning capabilities of Large Language Models (LLMs) through an iterative preference learning process inspired by the successful strategy employed by AlphaZero. Our work leverages Monte Carlo Tree Search (MCTS) to iteratively collect preference data, utilizing its look-ahead ability to break down instance-level rewards into more granular step-level signals. To enhance consistency in intermediate steps, we combine outcome validation and stepwise self-evaluation, continually updating the quality assessment of newly generated data. The proposed algorithm employs Direct Preference Optimization (DPO) to update the LLM policy using this newly generated step-level preference data. Theoretical analysis reveals the importance of using on-policy sampled data for successful self-improving. Extensive evaluations on various arithmetic and commonsense reasoning tasks demonstrate remarkable performance improvements over existing models. For instance, our approach outperforms the Mistral-7B Supervised Fine-Tuning (SFT) baseline on GSM8K, MATH, and ARC-C, with substantial increases in accuracy to 81.8% (+5.9%), 34.7% (+5.8%), and 76.4% (+15.8%), respectively. Additionally, our research delves into the training and inference compute tradeoff, providing insights into how our method effectively maximizes performance gains. Our code is publicly available at https://github.com/YuxiXie/MCTS-DPO.

Consistency models (CMs) are a powerful class of diffusion-based generative models optimized for fast sampling. Most existing CMs are trained using discretized timesteps, which introduce additional hyperparameters and are prone to discretization errors. While continuous-time formulations can mitigate these issues, their success has been limited by training instability. To address this, we propose a simplified theoretical framework that unifies previous parameterizations of diffusion models and CMs, identifying the root causes of instability. Based on this analysis, we introduce key improvements in diffusion process parameterization, network architecture, and training objectives. These changes enable us to train continuous-time CMs at an unprecedented scale, reaching 1.5B parameters on ImageNet 512x512. Our proposed training algorithm, using only two sampling steps, achieves FID scores of 2.06 on CIFAR-10, 1.48 on ImageNet 64x64, and 1.88 on ImageNet 512x512, narrowing the gap in FID scores with the best existing diffusion models to within 10%.

Typical neural network trainings have substantial variance in test-set performance between repeated runs, impeding hyperparameter comparison and training reproducibility. We present the following results towards understanding this variation. (1) Despite having significant variance on their test-sets, we demonstrate that standard CIFAR-10 and ImageNet trainings have very little variance in their performance on the test-distributions from which those test-sets are sampled, suggesting that variance is less of a practical issue than previously thought. (2) We present a simplifying statistical assumption which closely approximates the structure of the test-set accuracy distribution. (3) We argue that test-set variance is inevitable in the following two senses. First, we show that variance is largely caused by high sensitivity of the training process to initial conditions, rather than by specific sources of randomness like the data order and augmentations. Second, we prove that variance is unavoidable given the observation that ensembles of trained networks are well-calibrated. (4) We conduct preliminary studies of distribution-shift, fine-tuning, data augmentation and learning rate through the lens of variance between runs.

In modern recommendation systems, the standard pipeline involves training machine learning models on historical data to predict user behaviors and improve recommendations continuously. However, these data training loops can introduce interference in A/B tests, where data generated by control and treatment algorithms, potentially with different distributions, are combined. To address these challenges, we introduce a novel approach called weighted training. This approach entails training a model to predict the probability of each data point appearing in either the treatment or control data and subsequently applying weighted losses during model training. We demonstrate that this approach achieves the least variance among all estimators that do not cause shifts in the training distributions. Through simulation studies, we demonstrate the lower bias and variance of our approach compared to other methods.

Federated learning algorithms, such as FedAvg, are negatively affected by data heterogeneity and partial client participation. To mitigate the latter problem, global variance reduction methods, like FedVARP, leverage stale model updates for non-participating clients. These methods are effective under homogeneous client participation. Yet, this paper shows that, when some clients participate much less than others, aggregating updates with different levels of staleness can detrimentally affect the training process. Motivated by this observation, we introduce FedStale, a novel algorithm that updates the global model in each round through a convex combination of "fresh" updates from participating clients and "stale" updates from non-participating ones. By adjusting the weight in the convex combination, FedStale interpolates between FedAvg, which only uses fresh updates, and FedVARP, which treats fresh and stale updates equally. Our analysis of FedStale convergence yields the following novel findings: i) it integrates and extends previous FedAvg and FedVARP analyses to heterogeneous client participation; ii) it underscores how the least participating client influences convergence error; iii) it provides practical guidelines to best exploit stale updates, showing that their usefulness diminishes as data heterogeneity decreases and participation heterogeneity increases. Extensive experiments featuring diverse levels of client data and participation heterogeneity not only confirm these findings but also show that FedStale outperforms both FedAvg and FedVARP in many settings.

Self-tuning algorithms that adapt the learning process online encourage more effective and robust learning. Among all the methods available, meta-gradients have emerged as a promising approach. They leverage the differentiability of the learning rule with respect to some hyper-parameters to adapt them in an online fashion. Although meta-gradients can be accumulated over multiple learning steps to avoid myopic updates, this is rarely used in practice. In this work, we demonstrate that whilst multi-step meta-gradients do provide a better learning signal in expectation, this comes at the cost of a significant increase in variance, hindering performance. In the light of this analysis, we introduce a novel method mixing multiple inner steps that enjoys a more accurate and robust meta-gradient signal, essentially trading off bias and variance in meta-gradient estimation. When applied to the Snake game, the mixing meta-gradient algorithm can cut the variance by a factor of 3 while achieving similar or higher performance.

Diffusion models have revolutionized generative modeling in continuous domains like image, audio, and video synthesis. However, their iterative sampling process leads to slow generation and inefficient training, challenges that are further exacerbated when incorporating Reinforcement Learning from Human Feedback (RLHF) due to sparse rewards and long time horizons. Consistency models address these issues by enabling single-step or efficient multi-step generation, significantly reducing computational costs. In this work, we propose a direct reward optimization framework for applying RLHF to consistency models, incorporating distributional regularization to enhance training stability and prevent reward hacking. We investigate various f-divergences as regularization strategies, striking a balance between reward maximization and model consistency. Unlike policy gradient methods, our approach leverages first-order gradients, making it more efficient and less sensitive to hyperparameter tuning. Empirical results show that our method achieves competitive or superior performance compared to policy gradient based RLHF methods, across various automatic metrics and human evaluation. Additionally, our analysis demonstrates the impact of different regularization techniques in improving model generalization and preventing overfitting.

Asynchronous reinforcement learning has become increasingly central to scaling LLM post-training, delivering major throughput gains by decoupling rollout generation from policy updates. However, widely used policy-gradient objectives such as REINFORCE and GRPO suffer under high asynchrony: stale rollouts produce heavy-tailed importance weights, so a small number of trajectories dominate updates and the policy-gradient estimator becomes markedly higher variance. Through systematic analysis on math, reasoning, and tool-use benchmarks, we find that this increasing variance is reliably predicted by collapsing effective sample size (ESS), which prior stabilization methods largely fail to address. Motivated by this diagnosis, we introduce Variance Controlled Policy Optimization (VCPO), a method that (i) dynamically scales the learning rate with ESS to dampen unreliable updates and (ii) applies a closed-form minimum-variance baseline for off-policy settings, without a critic model and adding minimal overhead. Empirically, across math and general reasoning benchmarks, this enables robustly stable asynchronous training compared to previous stabilization and algorithmic methods, even in highly off-policy regimes (128 steps off-policy). In a long-horizon, tool-use task, VCPO matches synchronous performance while delivering a 2.5times speedup in training time. Code is available at: https://github.com/mit-han-lab/vcpo

In this article, we study the consistency of the template estimation with the Fr\'echet mean in quotient spaces. The Fr\'echet mean in quotient spaces is often used when the observations are deformed or transformed by a group action. We show that in most cases this estimator is actually inconsistent. We exhibit a sufficient condition for this inconsistency, which amounts to the folding of the distribution of the noisy template when it is projected to the quotient space. This condition appears to be fulfilled as soon as the support of the noise is large enough. To quantify this inconsistency we provide lower and upper bounds of the bias as a function of the variability (the noise level). This shows that the consistency bias cannot be neglected when the variability increases.

Standard practice within Reinforcement Learning from Human Feedback (RLHF) involves optimizing against a Reward Model (RM), which itself is trained to reflect human preferences for desirable generations. A notable subject that is understudied is the (in-)consistency of RMs -- whether they can recognize the semantic changes to different prompts and appropriately adapt their reward assignments -- and their impact on the downstream RLHF model. In this paper, we visit a series of research questions relevant to RM inconsistency: (1) How can we measure the consistency of reward models? (2) How consistent are the existing RMs and how can we improve them? (3) In what ways does reward inconsistency influence the chatbots resulting from the RLHF model training? We propose Contrast Instructions -- a benchmarking strategy for the consistency of RM. Each example in Contrast Instructions features a pair of lexically similar instructions with different ground truth responses. A consistent RM is expected to rank the corresponding instruction and response higher than other combinations. We observe that current RMs trained with the standard ranking objective fail miserably on Contrast Instructions compared to average humans. To show that RM consistency can be improved efficiently without using extra training budget, we propose two techniques ConvexDA and RewardFusion, which enhance reward consistency through extrapolation during the RM training and inference stage, respectively. We show that RLHF models trained with a more consistent RM yield more useful responses, suggesting that reward inconsistency exhibits a trickle-down effect on the downstream RLHF process.

While flow matching is elegant, its reliance on single-sample conditional velocities leads to high-variance training targets that destabilize optimization and slow convergence. By explicitly characterizing this variance, we identify 1) a high-variance regime near the prior, where optimization is challenging, and 2) a low-variance regime near the data distribution, where conditional and marginal velocities nearly coincide. Leveraging this insight, we propose Stable Velocity, a unified framework that improves both training and sampling. For training, we introduce Stable Velocity Matching (StableVM), an unbiased variance-reduction objective, along with Variance-Aware Representation Alignment (VA-REPA), which adaptively strengthen auxiliary supervision in the low-variance regime. For inference, we show that dynamics in the low-variance regime admit closed-form simplifications, enabling Stable Velocity Sampling (StableVS), a finetuning-free acceleration. Extensive experiments on ImageNet 256times256 and large pretrained text-to-image and text-to-video models, including SD3.5, Flux, Qwen-Image, and Wan2.2, demonstrate consistent improvements in training efficiency and more than 2times faster sampling within the low-variance regime without degrading sample quality. Our code is available at https://github.com/linYDTHU/StableVelocity.

Latent Consistency Model (LCM) extends the Consistency Model to the latent space and leverages the guided consistency distillation technique to achieve impressive performance in accelerating text-to-image synthesis. However, we observed that LCM struggles to generate images with both clarity and detailed intricacy. To address this limitation, we initially delve into and elucidate the underlying causes. Our investigation identifies that the primary issue stems from errors in three distinct areas. Consequently, we introduce Trajectory Consistency Distillation (TCD), which encompasses trajectory consistency function and strategic stochastic sampling. The trajectory consistency function diminishes the distillation errors by broadening the scope of the self-consistency boundary condition and endowing the TCD with the ability to accurately trace the entire trajectory of the Probability Flow ODE. Additionally, strategic stochastic sampling is specifically designed to circumvent the accumulated errors inherent in multi-step consistency sampling, which is meticulously tailored to complement the TCD model. Experiments demonstrate that TCD not only significantly enhances image quality at low NFEs but also yields more detailed results compared to the teacher model at high NFEs.

Recent progress in flow-based generative models and reinforcement learning (RL) has improved text-image alignment and visual quality. However, current RL training for flow models still has two main problems: (i) GRPO-style fixed per-prompt group sizes ignore variation in sampling importance across prompts, which leads to inefficient sampling and slower training; and (ii) trajectory-level advantages are reused as per-step estimates, which biases credit assignment along the flow. We propose SuperFlow, an RL training framework for flow-based models that adjusts group sizes with variance-aware sampling and computes step-level advantages in a way that is consistent with continuous-time flow dynamics. Empirically, SuperFlow reaches promising performance while using only 5.4% to 56.3% of the original training steps and reduces training time by 5.2% to 16.7% without any architectural changes. On standard text-to-image (T2I) tasks, including text rendering, compositional image generation, and human preference alignment, SuperFlow improves over SD3.5-M by 4.6% to 47.2%, and over Flow-GRPO by 1.7% to 16.0%.

Diffusion- and flow-based models have emerged as state-of-the-art generative modeling approaches, but they require many sampling steps. Consistency models can distill these models into efficient one-step generators; however, unlike flow- and diffusion-based methods, their performance inevitably degrades when increasing the number of steps, which we show both analytically and empirically. Flow maps generalize these approaches by connecting any two noise levels in a single step and remain effective across all step counts. In this paper, we introduce two new continuous-time objectives for training flow maps, along with additional novel training techniques, generalizing existing consistency and flow matching objectives. We further demonstrate that autoguidance can improve performance, using a low-quality model for guidance during distillation, and an additional boost can be achieved by adversarial finetuning, with minimal loss in sample diversity. We extensively validate our flow map models, called Align Your Flow, on challenging image generation benchmarks and achieve state-of-the-art few-step generation performance on both ImageNet 64x64 and 512x512, using small and efficient neural networks. Finally, we show text-to-image flow map models that outperform all existing non-adversarially trained few-step samplers in text-conditioned synthesis.

Based on the weight-sharing mechanism, one-shot NAS methods train a supernet and then inherit the pre-trained weights to evaluate sub-models, largely reducing the search cost. However, several works have pointed out that the shared weights suffer from different gradient descent directions during training. And we further find that large gradient variance occurs during supernet training, which degrades the supernet ranking consistency. To mitigate this issue, we propose to explicitly minimize the gradient variance of the supernet training by jointly optimizing the sampling distributions of PAth and DAta (PA&DA). We theoretically derive the relationship between the gradient variance and the sampling distributions, and reveal that the optimal sampling probability is proportional to the normalized gradient norm of path and training data. Hence, we use the normalized gradient norm as the importance indicator for path and training data, and adopt an importance sampling strategy for the supernet training. Our method only requires negligible computation cost for optimizing the sampling distributions of path and data, but achieves lower gradient variance during supernet training and better generalization performance for the supernet, resulting in a more consistent NAS. We conduct comprehensive comparisons with other improved approaches in various search spaces. Results show that our method surpasses others with more reliable ranking performance and higher accuracy of searched architectures, showing the effectiveness of our method. Code is available at https://github.com/ShunLu91/PA-DA.

In this paper, we propose a dimensionless anomaly detection method for multivariate streams. Our method is independent of the unit of measurement for the different stream channels, therefore dimensionless. We first propose the variance norm, a generalisation of Mahalanobis distance to handle infinite-dimensional feature space and singular empirical covariance matrix rigorously. We then combine the variance norm with the path signature, an infinite collection of iterated integrals that provide global features of streams, to propose SigMahaKNN, a method for anomaly detection on (multivariate) streams. We show that SigMahaKNN is invariant to stream reparametrisation, stream concatenation and has a graded discrimination power depending on the truncation level of the path signature. We implement SigMahaKNN as an open-source software, and perform extensive numerical experiments, showing significantly improved anomaly detection on streams compared to isolation forest and local outlier factors in applications ranging from language analysis, hand-writing analysis, ship movement paths analysis and univariate time-series analysis.

Consistency Training (CT) has recently emerged as a promising alternative to diffusion models, achieving competitive performance in image generation tasks. However, non-distillation consistency training often suffers from high variance and instability, and analyzing and improving its training dynamics is an active area of research. In this work, we propose a novel CT training approach based on the Flow Matching framework. Our main contribution is a trained noise-coupling scheme inspired by the architecture of Variational Autoencoders (VAE). By training a data-dependent noise emission model implemented as an encoder architecture, our method can indirectly learn the geometry of the noise-to-data mapping, which is instead fixed by the choice of the forward process in classical CT. Empirical results across diverse image datasets show significant generative improvements, with our model outperforming baselines and achieving the state-of-the-art (SoTA) non-distillation CT FID on CIFAR-10, and attaining FID on par with SoTA on ImageNet at 64 times 64 resolution in 2-step generation. Our code is available at https://github.com/sony/vct .

With diffusion and flow matching models achieving state-of-the-art generating performance, the interest of the community now turned to reducing the inference time without sacrificing sample quality. Consistency Models (CMs), which are trained to be consistent on diffusion or probability flow ordinary differential equation (PF-ODE) trajectories, enable one or two-step flow or diffusion sampling. However, CMs typically require prolonged training with large batch sizes to obtain competitive sample quality. In this paper, we examine the training dynamics of CMs near convergence and discover that CM tangents -- CM output update directions -- are quite oscillatory, in the sense that they move parallel to the data manifold, not towards the manifold. To mitigate oscillatory tangents, we propose a new loss function, called the manifold feature distance (MFD), which provides manifold-aligned tangents that point toward the data manifold. Consequently, our method -- dubbed Align Your Tangent (AYT) -- can accelerate CM training by orders of magnitude and even out-perform the learned perceptual image patch similarity metric (LPIPS). Furthermore, we find that our loss enables training with extremely small batch sizes without compromising sample quality. Code: https://github.com/1202kbs/AYT

Consistency Models (CM) (Song et al., 2023) accelerate score-based diffusion model sampling at the cost of sample quality but lack a natural way to trade-off quality for speed. To address this limitation, we propose Consistency Trajectory Model (CTM), a generalization encompassing CM and score-based models as special cases. CTM trains a single neural network that can -- in a single forward pass -- output scores (i.e., gradients of log-density) and enables unrestricted traversal between any initial and final time along the Probability Flow Ordinary Differential Equation (ODE) in a diffusion process. CTM enables the efficient combination of adversarial training and denoising score matching loss to enhance performance and achieves new state-of-the-art FIDs for single-step diffusion model sampling on CIFAR-10 (FID 1.73) and ImageNet at 64x64 resolution (FID 1.92). CTM also enables a new family of sampling schemes, both deterministic and stochastic, involving long jumps along the ODE solution trajectories. It consistently improves sample quality as computational budgets increase, avoiding the degradation seen in CM. Furthermore, unlike CM, CTM's access to the score function can streamline the adoption of established controllable/conditional generation methods from the diffusion community. This access also enables the computation of likelihood. The code is available at https://github.com/sony/ctm.

Self-consistency (SC) is a widely used test-time inference technique for improving performance in chain-of-thought reasoning. It involves generating multiple responses, or samples from a large language model (LLM) and selecting the most frequent answer. This procedure can naturally be viewed as a majority vote or empirical mode estimation. Despite its effectiveness, SC is prohibitively expensive at scale when naively applied to datasets, and it lacks a unified theoretical treatment of sample efficiency and scaling behavior. In this paper, we provide the first comprehensive analysis of SC's scaling behavior and its variants, drawing on mode estimation and voting theory. We derive and empirically validate power law scaling for self-consistency across datasets, and analyze the sample efficiency for fixed-allocation and dynamic-allocation sampling schemes. From these insights, we introduce Blend-ASC, a novel variant of self-consistency that dynamically allocates samples to questions during inference, achieving state-of-the-art sample efficiency. Our approach uses 6.8x fewer samples than vanilla SC on average, outperforming both fixed- and dynamic-allocation SC baselines, thereby demonstrating the superiority of our approach in terms of efficiency. In contrast to existing variants, Blend-ASC is hyperparameter-free and can fit an arbitrary sample budget, ensuring it can be easily applied to any self-consistency application.

Recent advances in continuous generative models, including multi-step approaches like diffusion and flow-matching (typically requiring 8-1000 sampling steps) and few-step methods such as consistency models (typically 1-8 steps), have demonstrated impressive generative performance. However, existing work often treats these approaches as distinct paradigms, resulting in separate training and sampling methodologies. We introduce a unified framework for training, sampling, and analyzing these models. Our implementation, the Unified Continuous Generative Models Trainer and Sampler (UCGM-{T,S}), achieves state-of-the-art (SOTA) performance. For example, on ImageNet 256x256 using a 675M diffusion transformer, UCGM-T trains a multi-step model achieving 1.30 FID in 20 steps and a few-step model reaching 1.42 FID in just 2 steps. Additionally, applying UCGM-S to a pre-trained model (previously 1.26 FID at 250 steps) improves performance to 1.06 FID in only 40 steps. Code is available at: https://github.com/LINs-lab/UCGM.

Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization trick is applicable when we can simulate a random variable by applying a differentiable deterministic function on an auxiliary random variable whose distribution is fixed. For many distributions of interest (such as the gamma or Dirichlet), simulation of random variables relies on acceptance-rejection sampling. The discontinuity introduced by the accept-reject step means that standard reparameterization tricks are not applicable. We propose a new method that lets us leverage reparameterization gradients even when variables are outputs of a acceptance-rejection sampling algorithm. Our approach enables reparameterization on a larger class of variational distributions. In several studies of real and synthetic data, we show that the variance of the estimator of the gradient is significantly lower than other state-of-the-art methods. This leads to faster convergence of stochastic gradient variational inference.

Diffusion models offer a physically grounded framework for probabilistic weather forecasting, but their typical reliance on slow, iterative solvers during inference makes them impractical for subseasonal-to-seasonal (S2S) applications where long lead-times and domain-driven calibration are essential. To address this, we introduce Swift, a single-step consistency model that, for the first time, enables autoregressive finetuning of a probability flow model with a continuous ranked probability score (CRPS) objective. This eliminates the need for multi-model ensembling or parameter perturbations. Results show that Swift produces skillful 6-hourly forecasts that remain stable for up to 75 days, running 39times faster than state-of-the-art diffusion baselines while achieving forecast skill competitive with the numerical-based, operational IFS ENS. This marks a step toward efficient and reliable ensemble forecasting from medium-range to seasonal-scales.

Variance reduction (VR) techniques have contributed significantly to accelerating learning with massive datasets in the smooth and strongly convex setting (Schmidt et al., 2017; Johnson & Zhang, 2013; Roux et al., 2012). However, such techniques have not yet met the same success in the realm of large-scale deep learning due to various factors such as the use of data augmentation or regularization methods like dropout (Defazio & Bottou, 2019). This challenge has recently motivated the design of novel variance reduction techniques tailored explicitly for deep learning (Arnold et al., 2019; Ma & Yarats, 2018). This work is an additional step in this direction. In particular, we exploit the ubiquitous clustering structure of rich datasets used in deep learning to design a family of scalable variance reduced optimization procedures by combining existing optimizers (e.g., SGD+Momentum, Quasi Hyperbolic Momentum, Implicit Gradient Transport) with a multi-momentum strategy (Yuan et al., 2019). Our proposal leads to faster convergence than vanilla methods on standard benchmark datasets (e.g., CIFAR and ImageNet). It is robust to label noise and amenable to distributed optimization. We provide a parallel implementation in JAX.

LLM-judged benchmarks are increasingly used to evaluate complex model behaviors, yet their design introduces failure modes absent in conventional ground-truth based benchmarks. We argue that without tight objectives and verifiable constructions, benchmark rankings can produce high-confidence rankings that are in fact largely noise. We introduce two mechanisms to diagnose these issues. Schematic adherence quantifies how much of a judge's overall verdict is explained by the explicit evaluation schema, revealing unexplained variance when judges deviate from their own rubric. Psychometric validity aggregates internal consistency and discriminant validity signals to quantify irreducible uncertainty in any benchmarking run. Applying these tools to Arena-Hard Auto, we find severe schema incoherence and factor collapse across popular judges: for example, unexplained variance exceeding 90 percent for DeepSeek-R1-32B and factor correlations above 0.93 for most criteria. We also show that the ELO-style aggregation used by Arena-Hard Auto collapses and masks genuine ranking uncertainty. Our results highlight design failures that undermine validity and offer actionable principles for building better-scoped, reliability-aware LLM-judged benchmarks. We release our code at https://anonymous.4open.science/r/judgment-to-noise-947D/README.md

Large multimodal reasoning models have achieved rapid progress, but their advancement is constrained by two major limitations: the absence of open, large-scale, high-quality long chain-of-thought (CoT) data, and the instability of reinforcement learning (RL) algorithms in post-training. Group Relative Policy Optimization (GRPO), the standard framework for RL fine-tuning, is prone to gradient vanishing when reward variance is low, which weakens optimization signals and impairs convergence. This work makes three contributions: (1) We propose Variance-Aware Sampling (VAS), a data selection strategy guided by Variance Promotion Score (VPS) that combines outcome variance and trajectory diversity to promote reward variance and stabilize policy optimization. (2) We release large-scale, carefully curated resources containing ~1.6M long CoT cold-start data and ~15k RL QA pairs, designed to ensure quality, difficulty, and diversity, along with a fully reproducible end-to-end training codebase. (3) We open-source a family of multimodal reasoning models in multiple scales, establishing standardized baselines for the community. Experiments across mathematical reasoning benchmarks demonstrate the effectiveness of both the curated data and the proposed VAS. Comprehensive ablation studies and analyses provide further insight into the contributions of each component. In addition, we theoretically establish that reward variance lower-bounds the expected policy gradient magnitude, with VAS serving as a practical mechanism to realize this guarantee. Our code, data, and checkpoints are available at https://github.com/LengSicong/MMR1.

Continuous-time Consistency Models (CMs) promise efficient few-step generation but face significant challenges with training instability. We argue this instability stems from a fundamental conflict: by training a network to learn only a shortcut across a probability flow, the model loses its grasp on the instantaneous velocity field that defines the flow. Our solution is to explicitly anchor the model in the underlying flow during training. We introduce the Flow-Anchored Consistency Model (FACM), a simple but effective training strategy that uses a Flow Matching (FM) task as an anchor for the primary CM shortcut objective. This Flow-Anchoring approach requires no architectural modifications and is broadly compatible with standard model architectures. By distilling a pre-trained LightningDiT model, our method achieves a state-of-the-art FID of 1.32 with two steps (NFE=2) and 1.76 with just one step (NFE=1) on ImageNet 256x256, significantly outperforming previous methods. This provides a general and effective recipe for building high-performance, few-step generative models. Our code and pretrained models: https://github.com/ali-vilab/FACM.

Continuous-time generative models, such as diffusion models, flow matching, and rectified flow, learn time-dependent vector fields but are typically trained with objectives that treat timesteps independently, leading to high estimator variance and inefficient sampling. Prior approaches mitigate this via explicit smoothness penalties, trajectory regularization, or modified probability paths and solvers. We introduce Temporal Pair Consistency (TPC), a lightweight variance-reduction principle that couples velocity predictions at paired timesteps along the same probability path, operating entirely at the estimator level without modifying the model architecture, probability path, or solver. We provide a theoretical analysis showing that TPC induces a quadratic, trajectory-coupled regularization that provably reduces gradient variance while preserving the underlying flow-matching objective. Instantiated within flow matching, TPC improves sample quality and efficiency across CIFAR-10 and ImageNet at multiple resolutions, achieving lower FID at identical or lower computational cost than prior methods, and extends seamlessly to modern SOTA-style pipelines with noise-augmented training, score-based denoising, and rectified flow.

Normalization techniques are a boon for modern deep learning. They let weights converge more quickly with often better generalization performances. It has been argued that the normalization-induced scale invariance among the weights provides an advantageous ground for gradient descent (GD) optimizers: the effective step sizes are automatically reduced over time, stabilizing the overall training procedure. It is often overlooked, however, that the additional introduction of momentum in GD optimizers results in a far more rapid reduction in effective step sizes for scale-invariant weights, a phenomenon that has not yet been studied and may have caused unwanted side effects in the current practice. This is a crucial issue because arguably the vast majority of modern deep neural networks consist of (1) momentum-based GD (e.g. SGD or Adam) and (2) scale-invariant parameters. In this paper, we verify that the widely-adopted combination of the two ingredients lead to the premature decay of effective step sizes and sub-optimal model performances. We propose a simple and effective remedy, SGDP and AdamP: get rid of the radial component, or the norm-increasing direction, at each optimizer step. Because of the scale invariance, this modification only alters the effective step sizes without changing the effective update directions, thus enjoying the original convergence properties of GD optimizers. Given the ubiquity of momentum GD and scale invariance in machine learning, we have evaluated our methods against the baselines on 13 benchmarks. They range from vision tasks like classification (e.g. ImageNet), retrieval (e.g. CUB and SOP), and detection (e.g. COCO) to language modelling (e.g. WikiText) and audio classification (e.g. DCASE) tasks. We verify that our solution brings about uniform gains in those benchmarks. Source code is available at https://github.com/clovaai/AdamP.

Diffusion-based stylization methods typically denoise from a specific partial noise state for image-to-image and video-to-video tasks. This multi-step diffusion process is computationally expensive and hinders real-world application. A promising solution to speed up the process is to obtain few-step consistency models through trajectory distillation. However, current consistency models only force the initial-step alignment between the probability flow ODE (PF-ODE) trajectories of the student and the imperfect teacher models. This training strategy can not ensure the consistency of whole trajectories. To address this issue, we propose single trajectory distillation (STD) starting from a specific partial noise state. We introduce a trajectory bank to store the teacher model's trajectory states, mitigating the time cost during training. Besides, we use an asymmetric adversarial loss to enhance the style and quality of the generated images. Extensive experiments on image and video stylization demonstrate that our method surpasses existing acceleration models in terms of style similarity and aesthetic evaluations. Our code and results will be available on the project page: https://single-trajectory-distillation.github.io.

As AI becomes more capable, we entrust it with more general and consequential tasks. The risks from failure grow more severe with increasing task scope. It is therefore important to understand how extremely capable AI models will fail: Will they fail by systematically pursuing goals we do not intend? Or will they fail by being a hot mess, and taking nonsensical actions that do not further any goal? We operationalize this question using a bias-variance decomposition of the errors made by AI models: An AI's incoherence on a task is measured over test-time randomness as the fraction of its error that stems from variance rather than bias in task outcome. Across all tasks and frontier models we measure, the longer models spend reasoning and taking actions, the more incoherent their failures become. Incoherence changes with model scale in a way that is experiment dependent. However, in several settings, larger, more capable models are more incoherent than smaller models. Consequently, scale alone seems unlikely to eliminate incoherence. Instead, as more capable AIs pursue harder tasks, requiring more sequential action and thought, our results predict failures to be accompanied by more incoherent behavior. This suggests a future where AIs sometimes cause industrial accidents (due to unpredictable misbehavior), but are less likely to exhibit consistent pursuit of a misaligned goal. This increases the relative importance of alignment research targeting reward hacking or goal misspecification.

Existing losses used in deep metric learning (DML) for image retrieval often lead to highly non-uniform intra-class and inter-class representation structures across test classes and data distributions. When combined with the common practice of using a fixed threshold to declare a match, this gives rise to significant performance variations in terms of false accept rate (FAR) and false reject rate (FRR) across test classes and data distributions. We define this issue in DML as threshold inconsistency. In real-world applications, such inconsistency often complicates the threshold selection process when deploying commercial image retrieval systems. To measure this inconsistency, we propose a novel variance-based metric called Operating-Point-Inconsistency-Score (OPIS) that quantifies the variance in the operating characteristics across classes. Using the OPIS metric, we find that achieving high accuracy levels in a DML model does not automatically guarantee threshold consistency. In fact, our investigation reveals a Pareto frontier in the high-accuracy regime, where existing methods to improve accuracy often lead to degradation in threshold consistency. To address this trade-off, we introduce the Threshold-Consistent Margin (TCM) loss, a simple yet effective regularization technique that promotes uniformity in representation structures across classes by selectively penalizing hard sample pairs. Extensive experiments demonstrate TCM's effectiveness in enhancing threshold consistency while preserving accuracy, simplifying the threshold selection process in practical DML settings.

This paper first answers the question "why do the two most powerful techniques Dropout and Batch Normalization (BN) often lead to a worse performance when they are combined together?" in both theoretical and statistical aspects. Theoretically, we find that Dropout would shift the variance of a specific neural unit when we transfer the state of that network from train to test. However, BN would maintain its statistical variance, which is accumulated from the entire learning procedure, in the test phase. The inconsistency of that variance (we name this scheme as "variance shift") causes the unstable numerical behavior in inference that leads to more erroneous predictions finally, when applying Dropout before BN. Thorough experiments on DenseNet, ResNet, ResNeXt and Wide ResNet confirm our findings. According to the uncovered mechanism, we next explore several strategies that modifies Dropout and try to overcome the limitations of their combination by avoiding the variance shift risks.

Accurate uncertainty measurement is a key step to building robust and reliable machine learning systems. Conformal prediction is a distribution-free uncertainty quantification algorithm popular for its ease of implementation, statistical coverage guarantees, and versatility for underlying forecasters. However, existing conformal prediction algorithms for time series are limited to single-step prediction without considering the temporal dependency. In this paper, we propose a Copula Conformal Prediction algorithm for multivariate, multi-step Time Series forecasting, CopulaCPTS. We prove that CopulaCPTS has finite sample validity guarantee. On several synthetic and real-world multivariate time series datasets, we show that CopulaCPTS produces more calibrated and sharp confidence intervals for multi-step prediction tasks than existing techniques.

Training large language models to reason with search engines via reinforcement learning is hindered by a fundamental credit assignment problem: existing methods such as Search-R1 provide only a sparse outcome reward after an entire multi-step trajectory, making it infeasible to attribute success or failure to individual reasoning and retrieval decisions. Process-reward methods like StepSearch alleviate this by introducing step-level supervision, but rely on heuristic rewards such as TF-IDF overlap with gold documents, and still sample k complete trajectories per example, retaining high gradient variance. We propose SLATE, a framework built on two complementary ideas: (1) truncated step-level sampling, which generates k trajectories that share a common prefix and differ only at the next step, and (2) dense LLM-as-judge rewards, which replace heuristic scoring with a capable LLM evaluator that assesses the quality of each reasoning step, search query, and answer, providing richer and more reliable supervision. We theoretically prove that under the same dense reward structure, truncated sampling reduces the variance of advantage estimates by up to a factor of T compared to full-trajectory sampling for T-step trajectories, yielding lower-variance, better-targeted policy gradients. Experiments on seven QA benchmarks confirm that SLATE consistently outperforms both sparse-reward and process-reward baselines, with the largest gains on harder multi-hop tasks and smaller models.

In this work, we propose a novel Trajectory Score Matching (TSM) method that aims to solve the pseudo ground truth inconsistency problem caused by the accumulated error in Interval Score Matching (ISM) when using the Denoising Diffusion Implicit Models (DDIM) inversion process. Unlike ISM which adopts the inversion process of DDIM to calculate on a single path, our TSM method leverages the inversion process of DDIM to generate two paths from the same starting point for calculation. Since both paths start from the same starting point, TSM can reduce the accumulated error compared to ISM, thus alleviating the problem of pseudo ground truth inconsistency. TSM enhances the stability and consistency of the model's generated paths during the distillation process. We demonstrate this experimentally and further show that ISM is a special case of TSM. Furthermore, to optimize the current multi-stage optimization process from high-resolution text to 3D generation, we adopt Stable Diffusion XL for guidance. In response to the issues of abnormal replication and splitting caused by unstable gradients during the 3D Gaussian splatting process when using Stable Diffusion XL, we propose a pixel-by-pixel gradient clipping method. Extensive experiments show that our model significantly surpasses the state-of-the-art models in terms of visual quality and performance. Code: https://github.com/xingy038/Dreamer-XL.

Most bandit algorithms assume that the reward variances or their upper bounds are known, and that they are the same for all arms. This naturally leads to suboptimal performance and higher regret due to variance overestimation. On the other hand, underestimated reward variances may lead to linear regret due to committing early to a suboptimal arm. This motivated prior works on variance-adaptive frequentist algorithms, which have strong instance-dependent regret bounds but cannot incorporate prior knowledge on reward variances. We lay foundations for the Bayesian setting, which incorporates prior knowledge. This results in lower regret in practice, due to using the prior in the algorithm design, and also improved regret guarantees. Specifically, we study Gaussian bandits with {unknown heterogeneous reward variances}, and develop a Thompson sampling algorithm with prior-dependent Bayes regret bounds. We achieve lower regret with lower reward variances and more informative priors on them, which is precisely why we pay only for what is uncertain. This is the first result of its kind. Finally, we corroborate our theory with extensive experiments, which show the superiority of our variance-adaptive Bayesian algorithm over prior frequentist approaches. We also show that our approach is robust to model misspecification and can be applied with estimated priors.

Plateaus, where an agent's performance stagnates at a suboptimal level, are a common problem in deep on-policy RL. Focusing on PPO due to its widespread adoption, we show that plateaus in certain regimes arise not because of known exploration, capacity, or optimization challenges, but because sample-based estimates of the loss eventually become poor proxies for the true objective over the course of training. As a recap, PPO switches between sampling rollouts from several parallel environments online using the current policy (which we call the outer loop) and performing repeated minibatch SGD steps against this offline dataset (the inner loop). In our work we consider only the outer loop, and conceptually model it as stochastic optimization. The step size is then controlled by the regularization strength towards the previous policy and the gradient noise by the number of samples collected between policy update steps. This model predicts that performance will plateau at a suboptimal level if the outer step size is too large relative to the noise. Recasting PPO in this light makes it clear that there are two ways to address this particular type of learning stagnation: either reduce the step size or increase the number of samples collected between updates. We first validate the predictions of our model and investigate how hyperparameter choices influence the step size and update noise, concluding that increasing the number of parallel environments is a simple and robust way to reduce both factors. Next, we propose a recipe for how to co-scale the other hyperparameters when increasing parallelization, and show that incorrectly doing so can lead to severe performance degradation. Finally, we vastly outperform prior baselines in a complex open-ended domain by scaling PPO to more than 1M parallel environments, thereby enabling monotonic performance improvement up to one trillion transitions.

In trajectory forecasting tasks for traffic, future output trajectories can be computed by advancing the ego vehicle's state with predicted actions according to a kinematics model. By unrolling predicted trajectories via time integration and models of kinematic dynamics, predicted trajectories should not only be kinematically feasible but also relate uncertainty from one timestep to the next. While current works in probabilistic prediction do incorporate kinematic priors for mean trajectory prediction, variance is often left as a learnable parameter, despite uncertainty in one time step being inextricably tied to uncertainty in the previous time step. In this paper, we show simple and differentiable analytical approximations describing the relationship between variance at one timestep and that at the next with the kinematic bicycle model. These approximations can be easily incorporated with negligible additional overhead into any existing trajectory forecasting framework utilizing probabilistic predictions, whether it is autoregressive or one-shot prediction. In our results, we find that encoding the relationship between variance across timesteps works especially well in unoptimal settings, such as with small or noisy datasets. We observe up to a 50% performance boost in partial dataset settings and up to an 8% performance boost in large-scale learning compared to previous kinematic prediction methods on SOTA trajectory forecasting architectures out-of-the-box, with no fine-tuning. In this paper, we show four analytical formulations of probabilistic kinematic priors which can be used for any Gaussian Mixture Model (GMM)-based deep learning models, quantify the error bound on linear approximations applied during trajectory unrolling, and show results to evaluate each formulation in trajectory forecasting.

We study variance-dependent regret bounds for Markov decision processes (MDPs). Algorithms with variance-dependent regret guarantees can automatically exploit environments with low variance (e.g., enjoying constant regret on deterministic MDPs). The existing algorithms are either variance-independent or suboptimal. We first propose two new environment norms to characterize the fine-grained variance properties of the environment. For model-based methods, we design a variant of the MVP algorithm (Zhang et al., 2021a). We apply new analysis techniques to demonstrate that this algorithm enjoys variance-dependent bounds with respect to the norms we propose. In particular, this bound is simultaneously minimax optimal for both stochastic and deterministic MDPs, the first result of its kind. We further initiate the study on model-free algorithms with variance-dependent regret bounds by designing a reference-function-based algorithm with a novel capped-doubling reference update schedule. Lastly, we also provide lower bounds to complement our upper bounds.

Recently, diffusion models have made remarkable progress in text-to-image (T2I) generation, synthesizing images with high fidelity and diverse contents. Despite this advancement, latent space smoothness within diffusion models remains largely unexplored. Smooth latent spaces ensure that a perturbation on an input latent corresponds to a steady change in the output image. This property proves beneficial in downstream tasks, including image interpolation, inversion, and editing. In this work, we expose the non-smoothness of diffusion latent spaces by observing noticeable visual fluctuations resulting from minor latent variations. To tackle this issue, we propose Smooth Diffusion, a new category of diffusion models that can be simultaneously high-performing and smooth. Specifically, we introduce Step-wise Variation Regularization to enforce the proportion between the variations of an arbitrary input latent and that of the output image is a constant at any diffusion training step. In addition, we devise an interpolation standard deviation (ISTD) metric to effectively assess the latent space smoothness of a diffusion model. Extensive quantitative and qualitative experiments demonstrate that Smooth Diffusion stands out as a more desirable solution not only in T2I generation but also across various downstream tasks. Smooth Diffusion is implemented as a plug-and-play Smooth-LoRA to work with various community models. Code is available at https://github.com/SHI-Labs/Smooth-Diffusion.

Group-based reinforcement learning (RL), such as GRPO, has advanced the capabilities of large language models on long-horizon agentic tasks. To enable more fine-grained policy updates, recent research has increasingly shifted toward stepwise group-based policy optimization, which treats each step in a rollout trajectory independently while using a memory module to retain historical context. However, we find a key issue in estimating stepwise relative advantages, namely context inconsistency, where steps within the same group may differ in their historical contexts. Empirically, we reveal that this issue can lead to severely biased advantage estimation, thereby degrading policy optimization significantly. To address the issue, in this paper, we propose Hierarchy-of-Groups Policy Optimization (HGPO) for long-horizon agentic tasks. Specifically, within a group of rollout trajectories, HGPO assigns each step to multiple hierarchical groups according to the consistency of historical contexts. Then, for each step, HGPO computes distinct advantages within each group and aggregates them with an adaptive weighting scheme. In this way, HGPO can achieve a favorable bias-variance trade-off in stepwise advantage estimation, without extra models or rollouts. Evaluations on two challenging agentic tasks, ALFWorld and WebShop with Qwen2.5-1.5B-Instruct and Qwen2.5-7B-Instruct, show that HGPO significantly outperforms existing agentic RL methods under the same computational constraints. Code is available at https://github.com/langfengQ/verl-agent/tree/master/recipe/hgpo.

As hyperparameter tuning becomes increasingly costly at scale, efficient tuning methods are essential. Yet principles for guiding hyperparameter tuning remain limited. In this work, we seek to establish such principles by considering a broad range of hyperparameters, including batch size, learning rate, and weight decay. We identify a phenomenon we call trajectory invariance, where pre-training loss curves, gradient noise, and gradient norm exhibit invariance--closely overlapping--with respect to a quantity that combines learning rate and weight decay. This phenomenon effectively reduces the original two-dimensional hyperparameter space to one dimension, yielding an efficient tuning rule: follow the salient direction revealed by trajectory invariance. Furthermore, we refine previous scaling laws and challenge several existing viewpoints. Overall, our work proposes new principles for efficient tuning and inspires future research on scaling laws.

Large reasoning models (LRMs) generate intermediate reasoning traces before producing final answers, yielding strong gains on multi-step and mathematical tasks. Yet aligning LRMs with human preferences, a crucial prerequisite for model deployment, remains underexplored. The statistically correct objective for preference alignment requires marginalizing over reasoning traces, but this computation is intractable in practice. A common workaround optimizes a single sampled trajectory, which introduces substantial gradient variance from stochastic trace sampling. To address this challenge, we frame preference optimization for LRMs through the lens of the bias--variance trade-off and propose Bias--Variance Optimized Preference Optimization (BVPO), a simple, drop-in method that mixes two gradient estimators: a high-variance trace-based estimator and a low-variance empty-trace estimator obtained by disabling reasoning trace generation. Our theory shows that BVPO strictly reduces trace-induced variance for any nontrivial mixture, provides a closed-form choice of the mixing weight that minimizes mean-squared error relative to the true marginal gradient, and under standard smoothness and step-size conditions, tightens classical convergence bounds for stochastic gradient descent. Empirically, BVPO improves alignment over the best baseline by up to 7.8 points on AlpacaEval~2 and 6.8 points on Arena-Hard. Despite being trained only on general conversational data, BVPO also boosts reasoning performance for base models by up to 4.0 points on the average of six math reasoning benchmarks. These results identify variance from trace sampling as a key bottleneck and demonstrate that directly optimizing the bias--variance trade-off yields more stable training and stronger overall performance.

Current preference learning methods achieve high accuracy on standard benchmarks but exhibit significant performance degradation when objective quality signals are removed. We introduce WritingPreferenceBench, a dataset of 1,800 human-annotated preference pairs (1,200 English, 600 Chinese) across 8 creative writing genres, where responses are matched for objective correctness, factual accuracy, and length. On this benchmark, sequence-based reward models--the standard architecture for RLHF--achieve only 52.7% mean accuracy, while zero-shot language model judges perform at 53.9%. In contrast, generative reward models that produce explicit reasoning chains achieve 81.8% accuracy. We observe high within-model variance across genres: individual models range from 18.2% to 81.8% accuracy across different writing categories, with standard deviations averaging 10.1%. This variance persists regardless of model scale, with 27B parameter models showing no consistent improvement over 8B variants. Our results suggest that current RLHF methods primarily learn to detect objective errors rather than capture subjective quality preferences (e.g., creativity, stylistic flair, and emotional resonance), and that successful preference modeling may require intermediate reasoning representations rather than direct classification.

In physics and engineering literature, the distribution of the excursion-above-zero time distribution (exceedance distribution) for a stationary Gaussian process has been approximated by a stationary switching process with independently distributed switching times. The approach matched the covariance of the clipped Gaussian process with the one for the stationary switching process and the distribution of the latter was used as the so-called independent interval approximation (IIA). The approach successfully assessed the persistency exponent for many physically important processes but left an unanswered question when such an approach leads to a mathematically meaningful and proper exceedance distribution. Here we address this question by proposing an alternative matching of the expected values of the clipped Slepian process and the corresponding switched process initiated at the origin. The method has allowed resolving the mathematical correctness of the matching method for a large subclass of the Gaussian processes with monotonic covariance, for which we provide a sufficient condition for the validity of the IIA. Within this class, the IIA produces a valid distribution for the excursion time and is represented in an explicit stochastic form that connects directly to the covariance of the underlying Gaussian process. We compare the excursion level distributions as well as the corresponding persistency exponents obtained through the IIA method with numerically computed exact distributions, and the simulated distribution for several important Gaussian models. We also argue that for stationary Gaussian processes with a non-monotonic covariance, the IIA fails and should not be used.

Understanding the gradient variance of black-box variational inference (BBVI) is a crucial step for establishing its convergence and developing algorithmic improvements. However, existing studies have yet to show that the gradient variance of BBVI satisfies the conditions used to study the convergence of stochastic gradient descent (SGD), the workhorse of BBVI. In this work, we show that BBVI satisfies a matching bound corresponding to the ABC condition used in the SGD literature when applied to smooth and quadratically-growing log-likelihoods. Our results generalize to nonlinear covariance parameterizations widely used in the practice of BBVI. Furthermore, we show that the variance of the mean-field parameterization has provably superior dimensional dependence.

Flow map models such as Consistency Models (CM) and Mean Flow (MF) enable few-step generation by learning the long jump of the ODE solution of diffusion models, yet training remains unstable, sensitive to hyperparameters, and costly. Initializing from a pre-trained diffusion model helps, but still requires converting infinitesimal steps into a long-jump map, leaving instability unresolved. We introduce mid-training, the first concept and practical method that inserts a lightweight intermediate stage between the (diffusion) pre-training and the final flow map training (i.e., post-training) for vision generation. Concretely, Consistency Mid-Training (CMT) is a compact and principled stage that trains a model to map points along a solver trajectory from a pre-trained model, starting from a prior sample, directly to the solver-generated clean sample. It yields a trajectory-consistent and stable initialization. This initializer outperforms random and diffusion-based baselines and enables fast, robust convergence without heuristics. Initializing post-training with CMT weights further simplifies flow map learning. Empirically, CMT achieves state of the art two step FIDs: 1.97 on CIFAR-10, 1.32 on ImageNet 64x64, and 1.84 on ImageNet 512x512, while using up to 98% less training data and GPU time, compared to CMs. On ImageNet 256x256, CMT reaches 1-step FID 3.34 while cutting total training time by about 50% compared to MF from scratch (FID 3.43). This establishes CMT as a principled, efficient, and general framework for training flow map models.

Financial institutions deploy Large Language Models (LLMs) for reconciliations, regulatory reporting, and client communications, but nondeterministic outputs (output drift) undermine auditability and trust. We quantify drift across five model architectures (7B-120B parameters) on regulated financial tasks, revealing a stark inverse relationship: smaller models (Granite-3-8B, Qwen2.5-7B) achieve 100% output consistency at T=0.0, while GPT-OSS-120B exhibits only 12.5% consistency (95% CI: 3.5-36.0%) regardless of configuration (p<0.0001, Fisher's exact test). This finding challenges conventional assumptions that larger models are universally superior for production deployment. Our contributions include: (i) a finance-calibrated deterministic test harness combining greedy decoding (T=0.0), fixed seeds, and SEC 10-K structure-aware retrieval ordering; (ii) task-specific invariant checking for RAG, JSON, and SQL outputs using finance-calibrated materiality thresholds (plus or minus 5%) and SEC citation validation; (iii) a three-tier model classification system enabling risk-appropriate deployment decisions; and (iv) an audit-ready attestation system with dual-provider validation. We evaluated five models (Qwen2.5-7B via Ollama, Granite-3-8B via IBM watsonx.ai, Llama-3.3-70B, Mistral-Medium-2505, and GPT-OSS-120B) across three regulated financial tasks. Across 480 runs (n=16 per condition), structured tasks (SQL) remain stable even at T=0.2, while RAG tasks show drift (25-75%), revealing task-dependent sensitivity. Cross-provider validation confirms deterministic behavior transfers between local and cloud deployments. We map our framework to Financial Stability Board (FSB), Bank for International Settlements (BIS), and Commodity Futures Trading Commission (CFTC) requirements, demonstrating practical pathways for compliance-ready AI deployments.

This work studies training instabilities of behavior cloning with deep neural networks. We observe that minibatch SGD updates to the policy network during training result in sharp oscillations in long-horizon rewards, despite negligibly affecting the behavior cloning loss. We empirically disentangle the statistical and computational causes of these oscillations, and find them to stem from the chaotic propagation of minibatch SGD noise through unstable closed-loop dynamics. While SGD noise is benign in the single-step action prediction objective, it results in catastrophic error accumulation over long horizons, an effect we term gradient variance amplification (GVA). We show that many standard mitigation techniques do not alleviate GVA, but find an exponential moving average (EMA) of iterates to be surprisingly effective at doing so. We illustrate the generality of this phenomenon by showing the existence of GVA and its amelioration by EMA in both continuous control and autoregressive language generation. Finally, we provide theoretical vignettes that highlight the benefits of EMA in alleviating GVA and shed light on the extent to which classical convex models can help in understanding the benefits of iterate averaging in deep learning.

Majorities of distillation methods on pre-trained diffusion models or on pre-trained rectified flow, focus on either the distillation outputs or the trajectories between random noises and clean images to speed up sample generations from pre-trained models. In those trajectory-based distillation methods, consistency distillation requires the self-consistent trajectory projection to regulate the trajectory, which might avoid the common ODE approximation error {while still be concerning about sampling efficiencies}. At the same time, rectified flow distillations enforce straight trajectory for fast sampling, although an ODE solver is still required. In this work, we propose a trajectory distillation method, \modelname, that enjoys the benefits of both and enables few-step generations. TraFlow adopts the settings of consistency trajectory models, and further enforces the properties of self-consistency and straightness throughout the entire trajectory. These two properties are pursued by reaching a balance with following three targets: (1) reconstruct the output from pre-trained models; (2) learn the amount of changes by pre-trained models; (3) satisfy the self-consistency over its trajectory. Extensive experimental results have shown the effectiveness of our proposed method.

Consistency-based generative models like Shortcut and MeanFlow achieve impressive results via a target-aware design for solving the Probability Flow ODE (PF-ODE). Typically, such methods introduce a target time r alongside the current time t to modulate outputs between a local multi-step derivative (r = t) and a global few-step integral (r = 0). However, the conventional "one input, one output" paradigm enforces a partition of the training budget, often allocating a significant portion (e.g., 75% in MeanFlow) solely to the multi-step objective for stability. This separation forces a trade-off: allocating sufficient samples to the multi-step objective leaves the few-step generation undertrained, which harms convergence and limits scalability. To this end, we propose Duality Models (DuMo) via a "one input, dual output" paradigm. Using a shared backbone with dual heads, DuMo simultaneously predicts velocity v_t and flow-map u_t from a single input x_t. This applies geometric constraints from the multi-step objective to every sample, bounding the few-step estimation without separating training objectives, thereby significantly improving stability and efficiency. On ImageNet 256 times 256, a 679M Diffusion Transformer with SD-VAE achieves a state-of-the-art (SOTA) FID of 1.79 in just 2 steps. Code is available at: https://github.com/LINs-lab/DuMo

Diffusion models have become a popular choice for human motion synthesis due to their powerful generative capabilities. However, their high computational complexity and large sampling steps pose challenges for real-time applications. Fortunately, the Consistency Model (CM) provides a solution to greatly reduce the number of sampling steps from hundreds to a few, typically fewer than four, significantly accelerating the synthesis of diffusion models. However, applying CM to text-conditioned human motion synthesis in latent space yields unsatisfactory generation results. In this paper, we introduce MotionPCM, a phased consistency model-based approach designed to improve the quality and efficiency for real-time motion synthesis in latent space. Experimental results on the HumanML3D dataset show that our model achieves real-time inference at over 30 frames per second in a single sampling step while outperforming the previous state-of-the-art with a 38.9\% improvement in FID. The code will be available for reproduction.

Denoising Diffusion Probabilistic Models (DDPMs) have garnered popularity for data generation across various domains. However, a significant bottleneck is the necessity for whole-network computation during every step of the generative process, leading to high computational overheads. This paper presents a novel framework, Denoising Diffusion Step-aware Models (DDSM), to address this challenge. Unlike conventional approaches, DDSM employs a spectrum of neural networks whose sizes are adapted according to the importance of each generative step, as determined through evolutionary search. This step-wise network variation effectively circumvents redundant computational efforts, particularly in less critical steps, thereby enhancing the efficiency of the diffusion model. Furthermore, the step-aware design can be seamlessly integrated with other efficiency-geared diffusion models such as DDIMs and latent diffusion, thus broadening the scope of computational savings. Empirical evaluations demonstrate that DDSM achieves computational savings of 49% for CIFAR-10, 61% for CelebA-HQ, 59% for LSUN-bedroom, 71% for AFHQ, and 76% for ImageNet, all without compromising the generation quality. Our code and models will be publicly available.

Score distillation sampling (SDS), the methodology in which the score from pretrained 2D diffusion models is distilled into 3D representation, has recently brought significant advancements in text-to-3D generation task. However, this approach is still confronted with critical geometric inconsistency problems such as the Janus problem. Starting from a hypothesis that such inconsistency problems may be induced by multiview inconsistencies between 2D scores predicted from various viewpoints, we introduce GSD, a simple and general plug-and-play framework for incorporating 3D consistency and therefore geometry awareness into the SDS process. Our methodology is composed of three components: 3D consistent noising, designed to produce 3D consistent noise maps that perfectly follow the standard Gaussian distribution, geometry-based gradient warping for identifying correspondences between predicted gradients of different viewpoints, and novel gradient consistency loss to optimize the scene geometry toward producing more consistent gradients. We demonstrate that our method significantly improves performance, successfully addressing the geometric inconsistency problems in text-to-3D generation task with minimal computation cost and being compatible with existing score distillation-based models. Our project page is available at https://ku-cvlab.github.io/GSD/.

In machine learning applications, it is well known that carefully designed learning rate (step size) schedules can significantly improve the convergence of commonly used first-order optimization algorithms. Therefore how to set step size adaptively becomes an important research question. A popular and effective method is the Polyak step size, which sets step size adaptively for gradient descent or stochastic gradient descent without the need to estimate the smoothness parameter of the objective function. However, there has not been a principled way to generalize the Polyak step size for algorithms with momentum accelerations. This paper presents a general framework to set the learning rate adaptively for first-order optimization methods with momentum, motivated by the derivation of Polyak step size. It is shown that the resulting methods are much less sensitive to the choice of momentum parameter and may avoid the oscillation of the heavy-ball method on ill-conditioned problems. These adaptive step sizes are further extended to the stochastic settings, which are attractive choices for stochastic gradient descent with momentum. Our methods are demonstrated to be more effective for stochastic gradient methods than prior adaptive step size algorithms in large-scale machine learning tasks.

Recently, Direct Preference Optimization (DPO) has extended its success from aligning large language models (LLMs) to aligning text-to-image diffusion models with human preferences. Unlike most existing DPO methods that assume all diffusion steps share a consistent preference order with the final generated images, we argue that this assumption neglects step-specific denoising performance and that preference labels should be tailored to each step's contribution. To address this limitation, we propose Step-aware Preference Optimization (SPO), a novel post-training approach that independently evaluates and adjusts the denoising performance at each step, using a step-aware preference model and a step-wise resampler to ensure accurate step-aware supervision. Specifically, at each denoising step, we sample a pool of images, find a suitable win-lose pair, and, most importantly, randomly select a single image from the pool to initialize the next denoising step. This step-wise resampler process ensures the next win-lose image pair comes from the same image, making the win-lose comparison independent of the previous step. To assess the preferences at each step, we train a separate step-aware preference model that can be applied to both noisy and clean images. Our experiments with Stable Diffusion v1.5 and SDXL demonstrate that SPO significantly outperforms the latest Diffusion-DPO in aligning generated images with complex, detailed prompts and enhancing aesthetics, while also achieving more than 20x times faster in training efficiency. Code and model: https://rockeycoss.github.io/spo.github.io/

Benchmark quality is critical for meaningful evaluation and sustained progress in time series forecasting, particularly given the recent rise of pretrained models. Existing benchmarks often have narrow domain coverage or overlook important real-world settings, such as tasks with covariates. Additionally, their aggregation procedures often lack statistical rigor, making it unclear whether observed performance differences reflect true improvements or random variation. Many benchmarks also fail to provide infrastructure for consistent evaluation or are too rigid to integrate into existing pipelines. To address these gaps, we propose fev-bench, a benchmark comprising 100 forecasting tasks across seven domains, including 46 tasks with covariates. Supporting the benchmark, we introduce fev, a lightweight Python library for benchmarking forecasting models that emphasizes reproducibility and seamless integration with existing workflows. Usingfev, fev-bench employs principled aggregation methods with bootstrapped confidence intervals to report model performance along two complementary dimensions: win rates and skill scores. We report results on fev-bench for various pretrained, statistical and baseline models, and identify promising directions for future research.

The iterative sampling procedure employed by diffusion models (DMs) often leads to significant inference latency. To address this, we propose Stochastic Consistency Distillation (SCott) to enable accelerated text-to-image generation, where high-quality generations can be achieved with just 1-2 sampling steps, and further improvements can be obtained by adding additional steps. In contrast to vanilla consistency distillation (CD) which distills the ordinary differential equation solvers-based sampling process of a pretrained teacher model into a student, SCott explores the possibility and validates the efficacy of integrating stochastic differential equation (SDE) solvers into CD to fully unleash the potential of the teacher. SCott is augmented with elaborate strategies to control the noise strength and sampling process of the SDE solver. An adversarial loss is further incorporated to strengthen the sample quality with rare sampling steps. Empirically, on the MSCOCO-2017 5K dataset with a Stable Diffusion-V1.5 teacher, SCott achieves an FID (Frechet Inceptio Distance) of 22.1, surpassing that (23.4) of the 1-step InstaFlow (Liu et al., 2023) and matching that of 4-step UFOGen (Xue et al., 2023b). Moreover, SCott can yield more diverse samples than other consistency models for high-resolution image generation (Luo et al., 2023a), with up to 16% improvement in a qualified metric. The code and checkpoints are coming soon.

In this paper, we focus on quantifying model stability as a function of random seed by investigating the effects of the induced randomness on model performance and the robustness of the model in general. We specifically perform a controlled study on the effect of random seeds on the behaviour of attention, gradient-based and surrogate model based (LIME) interpretations. Our analysis suggests that random seeds can adversely affect the consistency of models resulting in counterfactual interpretations. We propose a technique called Aggressive Stochastic Weight Averaging (ASWA)and an extension called Norm-filtered Aggressive Stochastic Weight Averaging (NASWA) which improves the stability of models over random seeds. With our ASWA and NASWA based optimization, we are able to improve the robustness of the original model, on average reducing the standard deviation of the model's performance by 72%.

MeanFlow (MF) is a diffusion-motivated generative model that enables efficient few-step generation by learning long jumps directly from noise to data. In practice, it is often used as a latent MF by leveraging the pre-trained Stable Diffusion variational autoencoder (SD-VAE) for high-dimensional data modeling. However, MF training remains computationally demanding and is often unstable. During inference, the SD-VAE decoder dominates the generation cost, and MF depends on complex guidance hyperparameters for class-conditional generation. In this work, we develop an efficient training and sampling scheme for MF in the latent space of a Representation Autoencoder (RAE), where a pre-trained vision encoder (e.g., DINO) provides semantically rich latents paired with a lightweight decoder. We observe that naive MF training in the RAE latent space suffers from severe gradient explosion. To stabilize and accelerate training, we adopt Consistency Mid-Training for trajectory-aware initialization and use a two-stage scheme: distillation from a pre-trained flow matching teacher to speed convergence and reduce variance, followed by an optional bootstrapping stage with a one-point velocity estimator to further reduce deviation from the oracle mean flow. This design removes the need for guidance, simplifies training configurations, and reduces computation in both training and sampling. Empirically, our method achieves a 1-step FID of 2.03, outperforming vanilla MF's 3.43, while reducing sampling GFLOPS by 38% and total training cost by 83% on ImageNet 256. We further scale our approach to ImageNet 512, achieving a competitive 1-step FID of 3.23 with the lowest GFLOPS among all baselines. Code is available at https://github.com/sony/mf-rae.

In recent years, diffusion models have emerged as powerful tools for generating ensemble members in meteorology. In this work, we demonstrate that a Denoising Diffusion Implicit Model (DDIM) can effectively control ensemble variance by varying the number of diffusion steps. Introducing a theoretical framework, we relate diffusion steps to the variance expressed by the reverse diffusion process. Focusing on reanalysis downscaling, we propose an ensemble diffusion model for the full ERA5-to-CERRA domain, generating variance-calibrated ensemble members for wind speed at full spatial and temporal resolution. Our method aligns global mean variance with a reference ensemble dataset and ensures spatial variance is distributed in accordance with observed meteorological variability. Additionally, we address the lack of ensemble information in the CARRA dataset, showcasing the utility of our approach for efficient, high-resolution ensemble generation.

Federated learning and gossip learning are emerging methodologies designed to mitigate data privacy concerns by retaining training data on client devices and exclusively sharing locally-trained machine learning (ML) models with others. The primary distinction between the two lies in their approach to model aggregation: federated learning employs a centralized parameter server, whereas gossip learning adopts a fully decentralized mechanism, enabling direct model exchanges among nodes. This decentralized nature often positions gossip learning as less efficient compared to federated learning. Both methodologies involve a critical step: computing a representation of received ML models and integrating this representation into the existing model. Conventionally, this representation is derived by averaging the received models, exemplified by the FedAVG algorithm. Our findings suggest that this averaging approach inherently introduces a potential delay in model convergence. We identify the underlying cause and refer to it as the "vanishing variance" problem, where averaging across uncorrelated ML models undermines the optimal variance established by the Xavier weight initialization. Unlike federated learning where the central server ensures model correlation, and unlike traditional gossip learning which circumvents this problem through model partitioning and sampling, our research introduces a variance-corrected model averaging algorithm. This novel algorithm preserves the optimal variance needed during model averaging, irrespective of network topology or non-IID data distributions. Our extensive simulation results demonstrate that our approach enables gossip learning to achieve convergence efficiency comparable to that of federated learning.

One technique to visualize the training of neural networks is to perform PCA on the parameters over the course of training and to project to the subspace spanned by the first few PCA components. In this paper we compare this technique to the PCA of a high dimensional random walk. We compute the eigenvalues and eigenvectors of the covariance of the trajectory and prove that in the long trajectory and high dimensional limit most of the variance is in the first few PCA components, and that the projection of the trajectory onto any subspace spanned by PCA components is a Lissajous curve. We generalize these results to a random walk with momentum and to an Ornstein-Uhlenbeck processes (i.e., a random walk in a quadratic potential) and show that in high dimensions the walk is not mean reverting, but will instead be trapped at a fixed distance from the minimum. We finally compare the distribution of PCA variances and the PCA projected training trajectories of a linear model trained on CIFAR-10 and ResNet-50-v2 trained on Imagenet and find that the distribution of PCA variances resembles a random walk with drift.

Test-time scaling can improve model performance by aggregating stochastic reasoning trajectories. However, achieving sample-efficient test-time self-consistency under a limited budget remains an open challenge. We introduce PETS (Principled and Efficient Test-TimeSelf-Consistency), which initiates a principled study of trajectory allocation through an optimization framework. Central to our approach is the self-consistency rate, a new measure defined as agreement with the infinite-budget majority vote. This formulation makes sample-efficient test-time allocation theoretically grounded and amenable to rigorous analysis. We study both offline and online settings. In the offline regime, where all questions are known in advance, we connect trajectory allocation to crowdsourcing, a classic and well-developed area, by modeling reasoning traces as workers. This perspective allows us to leverage rich existing theory, yielding theoretical guarantees and an efficient majority-voting-based allocation algorithm. In the online streaming regime, where questions arrive sequentially and allocations must be made on the fly, we propose a novel method inspired by the offline framework. Our approach adapts budgets to question difficulty while preserving strong theoretical guarantees and computational efficiency. Experiments show that PETS consistently outperforms uniform allocation. On GPQA, PETS achieves perfect self-consistency in both settings while reducing the sampling budget by up to 75% (offline) and 55% (online) relative to uniform allocation. Code is available at https://github.com/ZDCSlab/PETS.

As of September 2023, ChatGPT correctly answers "what is 7+8" with 15, but when asked "7+8=15, True or False" it responds with "False". This inconsistency between generating and validating an answer is prevalent in language models (LMs) and erodes trust. In this paper, we propose a framework for measuring the consistency between generation and validation (which we call generator-validator consistency, or GV-consistency), finding that even GPT-4, a state-of-the-art LM, is GV-consistent only 76% of the time. To improve the consistency of LMs, we propose to finetune on the filtered generator and validator responses that are GV-consistent, and call this approach consistency fine-tuning. We find that this approach improves GV-consistency of Alpaca-30B from 60% to 93%, and the improvement extrapolates to unseen tasks and domains (e.g., GV-consistency for positive style transfers extrapolates to unseen styles like humor). In addition to improving consistency, consistency fine-tuning improves both generator quality and validator accuracy without using any labeled data. Evaluated across 6 tasks, including math questions, knowledge-intensive QA, and instruction following, our method improves the generator quality by 16% and the validator accuracy by 6.3% across all tasks.

Latent Diffusion Models (LDMs) are known to have an unstable generation process, where even small perturbations or shifts in the input noise can lead to significantly different outputs. This hinders their applicability in applications requiring consistent results. In this work, we redesign LDMs to enhance consistency by making them shift-equivariant. While introducing anti-aliasing operations can partially improve shift-equivariance, significant aliasing and inconsistency persist due to the unique challenges in LDMs, including 1) aliasing amplification during VAE training and multiple U-Net inferences, and 2) self-attention modules that inherently lack shift-equivariance. To address these issues, we redesign the attention modules to be shift-equivariant and propose an equivariance loss that effectively suppresses the frequency bandwidth of the features in the continuous domain. The resulting alias-free LDM (AF-LDM) achieves strong shift-equivariance and is also robust to irregular warping. Extensive experiments demonstrate that AF-LDM produces significantly more consistent results than vanilla LDM across various applications, including video editing and image-to-image translation. Code is available at: https://github.com/SingleZombie/AFLDM

We present a straightforward statistical test to detect certain violations of the assumption that the data are Independent and Identically Distributed (IID). The specific form of violation considered is common across real-world applications: whether the examples are ordered in the dataset such that almost adjacent examples tend to have more similar feature values (e.g. due to distributional drift, or attractive interactions between datapoints). Based on a k-Nearest Neighbors estimate, our approach can be used to audit any multivariate numeric data as well as other data types (image, text, audio, etc.) that can be numerically represented, perhaps with model embeddings. Compared with existing methods to detect drift or auto-correlation, our approach is both applicable to more types of data and also able to detect a wider variety of IID violations in practice. Code: https://github.com/cleanlab/cleanlab

Large language models (LLMs) appear to bias their survey answers toward certain values. Nonetheless, some argue that LLMs are too inconsistent to simulate particular values. Are they? To answer, we first define value consistency as the similarity of answers across (1) paraphrases of one question, (2) related questions under one topic, (3) multiple-choice and open-ended use-cases of one question, and (4) multilingual translations of a question to English, Chinese, German, and Japanese. We apply these measures to a few large (>=34b), open LLMs including llama-3, as well as gpt-4o, using eight thousand questions spanning more than 300 topics. Unlike prior work, we find that models are relatively consistent across paraphrases, use-cases, translations, and within a topic. Still, some inconsistencies remain. Models are more consistent on uncontroversial topics (e.g., in the U.S., "Thanksgiving") than on controversial ones ("euthanasia"). Base models are both more consistent compared to fine-tuned models and are uniform in their consistency across topics, while fine-tuned models are more inconsistent about some topics ("euthanasia") than others ("women's rights") like our human subjects (n=165).

Diffusion Models (DM) and Consistency Models (CM) are two types of popular generative models with good generation quality on various tasks. When training DM and CM, intermediate weight checkpoints are not fully utilized and only the last converged checkpoint is used. In this work, we find that high-quality model weights often lie in a basin which cannot be reached by SGD but can be obtained by proper checkpoint averaging. Based on these observations, we propose LCSC, a simple but effective and efficient method to enhance the performance of DM and CM, by combining checkpoints along the training trajectory with coefficients deduced from evolutionary search. We demonstrate the value of LCSC through two use cases: (a) Reducing training cost. With LCSC, we only need to train DM/CM with fewer number of iterations and/or lower batch sizes to obtain comparable sample quality with the fully trained model. For example, LCSC achieves considerable training speedups for CM (23times on CIFAR-10 and 15times on ImageNet-64). (b) Enhancing pre-trained models. Assuming full training is already done, LCSC can further improve the generation quality or speed of the final converged models. For example, LCSC achieves better performance using 1 number of function evaluation (NFE) than the base model with 2 NFE on consistency distillation, and decreases the NFE of DM from 15 to 9 while maintaining the generation quality on CIFAR-10. Our code is available at https://github.com/imagination-research/LCSC.

Best-of-N decoding methods instruct large language models (LLMs) to generate multiple solutions, score each using a scoring function, and select the highest scored as the final answer to mathematical reasoning problems. However, this repeated independent process often leads to the same mistakes, making the selected solution still incorrect. We propose a novel prompting method named Stepwise Correction (StepCo) that helps LLMs identify and revise incorrect steps in their generated reasoning paths. It iterates verification and revision phases that employ a process-supervised verifier. The verify-then-revise process not only improves answer correctness but also reduces token consumption with fewer paths needed to generate. With StepCo, a series of LLMs demonstrate exceptional performance. Notably, using GPT-4o as the backend LLM, StepCo achieves an average accuracy of 94.1 across eight datasets, significantly outperforming the state-of-the-art Best-of-N method by +2.4, while reducing token consumption by 77.8%.

Recent advancements in latent diffusion models (LDMs) have markedly enhanced text-to-audio generation, yet their iterative sampling processes impose substantial computational demands, limiting practical deployment. While recent methods utilizing consistency-based distillation aim to achieve few-step or single-step inference, their one-step performance is constrained by curved trajectories, preventing them from surpassing traditional diffusion models. In this work, we introduce FlashAudio with rectified flows to learn straight flow for fast simulation. To alleviate the inefficient timesteps allocation and suboptimal distribution of noise, FlashAudio optimizes the time distribution of rectified flow with Bifocal Samplers and proposes immiscible flow to minimize the total distance of data-noise pairs in a batch vias assignment. Furthermore, to address the amplified accumulation error caused by the classifier-free guidance (CFG), we propose Anchored Optimization, which refines the guidance scale by anchoring it to a reference trajectory. Experimental results on text-to-audio generation demonstrate that FlashAudio's one-step generation performance surpasses the diffusion-based models with hundreds of sampling steps on audio quality and enables a sampling speed of 400x faster than real-time on a single NVIDIA 4090Ti GPU.

We study Stochastic Gradient Descent with AdaGrad stepsizes: a popular adaptive (self-tuning) method for first-order stochastic optimization. Despite being well studied, existing analyses of this method suffer from various shortcomings: they either assume some knowledge of the problem parameters, impose strong global Lipschitz conditions, or fail to give bounds that hold with high probability. We provide a comprehensive analysis of this basic method without any of these limitations, in both the convex and non-convex (smooth) cases, that additionally supports a general ``affine variance'' noise model and provides sharp rates of convergence in both the low-noise and high-noise~regimes.

We introduce Multi-view Ancestral Sampling (MAS), a method for generating consistent multi-view 2D samples of a motion sequence, enabling the creation of its 3D counterpart. MAS leverages a diffusion model trained solely on 2D data, opening opportunities to exciting and diverse fields of motion previously under-explored as 3D data is scarce and hard to collect. MAS works by simultaneously denoising multiple 2D motion sequences representing the same motion from different angles. Our consistency block ensures consistency across all views at each diffusion step by combining the individual generations into a unified 3D sequence, and projecting it back to the original views for the next iteration. We demonstrate MAS on 2D pose data acquired from videos depicting professional basketball maneuvers, rhythmic gymnastic performances featuring a ball apparatus, and horse obstacle course races. In each of these domains, 3D motion capture is arduous, and yet, MAS generates diverse and realistic 3D sequences without textual conditioning. As we demonstrate, our ancestral sampling-based approach offers a more natural integration with the diffusion framework compared to popular denoising optimization-based approaches, and avoids common issues such as out-of-domain sampling, lack of details and mode-collapse. https://guytevet.github.io/mas-page/

This work represents the first effort to scale up continuous-time consistency distillation to general application-level image and video diffusion models. Although continuous-time consistency model (sCM) is theoretically principled and empirically powerful for accelerating academic-scale diffusion, its applicability to large-scale text-to-image and video tasks remains unclear due to infrastructure challenges in Jacobian-vector product (JVP) computation and the limitations of standard evaluation benchmarks. We first develop a parallelism-compatible FlashAttention-2 JVP kernel, enabling sCM training on models with over 10 billion parameters and high-dimensional video tasks. Our investigation reveals fundamental quality limitations of sCM in fine-detail generation, which we attribute to error accumulation and the "mode-covering" nature of its forward-divergence objective. To remedy this, we propose the score-regularized continuous-time consistency model (rCM), which incorporates score distillation as a long-skip regularizer. This integration complements sCM with the "mode-seeking" reverse divergence, effectively improving visual quality while maintaining high generation diversity. Validated on large-scale models (Cosmos-Predict2, Wan2.1) up to 14B parameters and 5-second videos, rCM matches or surpasses the state-of-the-art distillation method DMD2 on quality metrics while offering notable advantages in diversity, all without GAN tuning or extensive hyperparameter searches. The distilled models generate high-fidelity samples in only 1sim4 steps, accelerating diffusion sampling by 15timessim50times. These results position rCM as a practical and theoretically grounded framework for advancing large-scale diffusion distillation.

We study the variance of stochastic policy gradients (SPGs) with many action samples per state. We derive a many-actions optimality condition, which determines when many-actions SPG yields lower variance as compared to a single-action agent with proportionally extended trajectory. We propose Model-Based Many-Actions (MBMA), an approach leveraging dynamics models for many-actions sampling in the context of SPG. MBMA addresses issues associated with existing implementations of many-actions SPG and yields lower bias and comparable variance to SPG estimated from states in model-simulated rollouts. We find that MBMA bias and variance structure matches that predicted by theory. As a result, MBMA achieves improved sample efficiency and higher returns on a range of continuous action environments as compared to model-free, many-actions, and model-based on-policy SPG baselines.

Proper evaluations are crucial for better understanding, troubleshooting, interpreting model behaviors and further improving model performance. While using scalar-based error metrics provides a fast way to overview model performance, they are often too abstract to display certain weak spots and lack information regarding important model properties, such as robustness. This not only hinders machine learning models from being more interpretable and gaining trust, but also can be misleading to both model developers and users. Additionally, conventional evaluation procedures often leave researchers unclear about where and how model fails, which complicates model comparisons and further developments. To address these issues, we propose a novel evaluation workflow, named Non-Equivariance Revealed on Orbits (NERO) Evaluation. The goal of NERO evaluation is to turn focus from traditional scalar-based metrics onto evaluating and visualizing models equivariance, closely capturing model robustness, as well as to allow researchers quickly investigating interesting or unexpected model behaviors. NERO evaluation is consist of a task-agnostic interactive interface and a set of visualizations, called NERO plots, which reveals the equivariance property of the model. Case studies on how NERO evaluation can be applied to multiple research areas, including 2D digit recognition, object detection, particle image velocimetry (PIV), and 3D point cloud classification, demonstrate that NERO evaluation can quickly illustrate different model equivariance, and effectively explain model behaviors through interactive visualizations of the model outputs. In addition, we propose consensus, an alternative to ground truths, to be used in NERO evaluation so that model equivariance can still be evaluated with new, unlabeled datasets.

Self-consistency has emerged as a popular technique for improving large language model accuracy on reasoning tasks. The approach is straightforward: generate multiple reasoning paths and select the most common answer through majority voting. While this reliably boosts accuracy, it remains unclear whether these gains reflect genuine improvements in reasoning quality. We investigate a fundamental question that has not been studied before: does inference scaling improve reasoning faithfulness? We conduct a comprehensive empirical study across four frontier models (GPT-5.2, Claude Opus 4.5, Gemini-3-flash-preview, and DeepSeek-v3.2) on 100 GSM8K mathematical reasoning problems. Our analysis employs bootstrap confidence intervals, McNemar's tests for paired comparisons, and Cohen's d effect sizes to quantify the effects rigorously. The results reveal striking differences across models that challenge common assumptions about self-consistency. GPT-5.2 shows the expected pattern: accuracy improves from 78% to 90% at N=5, with faithfulness remaining relatively stable (0.540 to 0.510). Claude Opus 4.5 tells a completely different story. Its accuracy actually drops from 78% to 74.3% while faithfulness jumps dramatically from 0.270 to 0.891 at N=5. DeepSeek-v3.2, already at 98% accuracy, shows ceiling effects with modest faithfulness gains (0.440 to 0.541). Gemini-3-flash improves from 81% to 86% accuracy with a slight faithfulness decrease (0.260 to 0.212). Problem difficulty analysis reveals that GPT-5.2 solves 82% of hard problems while breaking only 13% of easy ones. Claude, in contrast, breaks 23% of easy problems, explaining its accuracy decrease. These findings matter for practitioners: self-consistency is not universally beneficial, and teams should test their specific models before deployment. We release our code and provide practical recommendations for navigating these tradeoffs.

Flow-based 3D generation models typically require dozens of sampling steps during inference. Though few-step distillation methods, particularly Consistency Models (CMs), have achieved substantial advancements in accelerating 2D diffusion models, they remain under-explored for more complex 3D generation tasks. In this study, we propose a novel framework, MDT-dist, for few-step 3D flow distillation. Our approach is built upon a primary objective: distilling the pretrained model to learn the Marginal-Data Transport. Directly learning this objective needs to integrate the velocity fields, while this integral is intractable to be implemented. Therefore, we propose two optimizable objectives, Velocity Matching (VM) and Velocity Distillation (VD), to equivalently convert the optimization target from the transport level to the velocity and the distribution level respectively. Velocity Matching (VM) learns to stably match the velocity fields between the student and the teacher, but inevitably provides biased gradient estimates. Velocity Distillation (VD) further enhances the optimization process by leveraging the learned velocity fields to perform probability density distillation. When evaluated on the pioneer 3D generation framework TRELLIS, our method reduces sampling steps of each flow transformer from 25 to 1 or 2, achieving 0.68s (1 step x 2) and 0.94s (2 steps x 2) latency with 9.0x and 6.5x speedup on A800, while preserving high visual and geometric fidelity. Extensive experiments demonstrate that our method significantly outperforms existing CM distillation methods, and enables TRELLIS to achieve superior performance in few-step 3D generation.

Reliable evaluation is fundamental to the progress of Large Language Models (LLMs), yet the evaluation process during pre-training is plagued by significant instability that obscures true learning dynamics. In this work, we systematically diagnose this instability, attributing it to two distinct sources: Parameter Instability from training stochasticity and Evaluation Instability from noisy measurement protocols. To counteract both sources of noise, we introduce MaP, a dual-pronged framework that synergistically integrates checkpoint Merging and the Pass@k metric. Checkpoint merging smooths the parameter space by averaging recent model weights, while Pass@k provides a robust, low-variance statistical estimate of model capability. Extensive experiments show that MaP yields significantly smoother performance curves, reduces inter-run variance, and ensures more consistent model rankings. Ultimately, MaP provides a more reliable and faithful lens for observing LLM training dynamics, laying a crucial empirical foundation for LLM research.

When training neural networks, it has been widely observed that a large step size is essential in stochastic gradient descent (SGD) for obtaining superior models. However, the effect of large step sizes on the success of SGD is not well understood theoretically. Several previous works have attributed this success to the stochastic noise present in SGD. However, we show through a novel set of experiments that the stochastic noise is not sufficient to explain good non-convex training, and that instead the effect of a large learning rate itself is essential for obtaining best performance.We demonstrate the same effects also in the noise-less case, i.e. for full-batch GD. We formally prove that GD with large step size -- on certain non-convex function classes -- follows a different trajectory than GD with a small step size, which can lead to convergence to a global minimum instead of a local one. Our settings provide a framework for future analysis which allows comparing algorithms based on behaviors that can not be observed in the traditional settings.

Image-to-video (I2V) generation aims to use the initial frame (alongside a text prompt) to create a video sequence. A grand challenge in I2V generation is to maintain visual consistency throughout the video: existing methods often struggle to preserve the integrity of the subject, background, and style from the first frame, as well as ensure a fluid and logical progression within the video narrative. To mitigate these issues, we propose ConsistI2V, a diffusion-based method to enhance visual consistency for I2V generation. Specifically, we introduce (1) spatiotemporal attention over the first frame to maintain spatial and motion consistency, (2) noise initialization from the low-frequency band of the first frame to enhance layout consistency. These two approaches enable ConsistI2V to generate highly consistent videos. We also extend the proposed approaches to show their potential to improve consistency in auto-regressive long video generation and camera motion control. To verify the effectiveness of our method, we propose I2V-Bench, a comprehensive evaluation benchmark for I2V generation. Our automatic and human evaluation results demonstrate the superiority of ConsistI2V over existing methods.

This paper poses two critical issues in evaluating base models (without post-training): (1) Unstable evaluation during training: in the early stages of pre-training, the models lack the capability to answer questions as required, leading to unstable evaluation results. This instability makes it difficult to provide solid conclusions to guide the training, especially for key experiments such as data ablation and scaling law. (2) Inconsistency between base and instruct models: base models generally exhibit poorer evaluation performance compared to corresponding instruct models. This gap poses a challenge for assessing whether a base model with better evaluation can truly lead to a better instruct model. To address these issues, we propose Base model Oriented Systematic Evaluation (BOSE), a method specifically designed to optimize the evaluation of base models. Specifically, BOSE introduces two key innovations: In-Context Light-instruction Prompt (ICLiP) for open-ended tasks and Blank-ppl for multi-choice tasks with candidate options, which transforms the standard perplexity (ppl) metric into a fill-in-the-blank format to mitigate early-stage evaluation fluctuations. Furthermore, we are the first to propose Kendall's rank correlation to quantitatively measure the evaluation stability and consistency. Experimental results demonstrate that BOSE significantly enhances both the stability of evaluations during pre-training and the consistency between base and instruct models, thereby providing more reliable guidance for the LLMs' training.

We present adversarial flow models, a class of generative models that unifies adversarial models and flow models. Our method supports native one-step or multi-step generation and is trained using the adversarial objective. Unlike traditional GANs, where the generator learns an arbitrary transport plan between the noise and the data distributions, our generator learns a deterministic noise-to-data mapping, which is the same optimal transport as in flow-matching models. This significantly stabilizes adversarial training. Also, unlike consistency-based methods, our model directly learns one-step or few-step generation without needing to learn the intermediate timesteps of the probability flow for propagation. This saves model capacity, reduces training iterations, and avoids error accumulation. Under the same 1NFE setting on ImageNet-256px, our B/2 model approaches the performance of consistency-based XL/2 models, while our XL/2 model creates a new best FID of 2.38. We additionally show the possibility of end-to-end training of 56-layer and 112-layer models through depth repetition without any intermediate supervision, and achieve FIDs of 2.08 and 1.94 using a single forward pass, surpassing their 2NFE and 4NFE counterparts.

Benchmarks shape scientific conclusions about model capabilities and steer model development. This creates a feedback loop: stronger benchmarks drive better models, and better models demand more discriminative benchmarks. Ensuring benchmark reliability is therefore essential for trustworthy evaluation and meaningful progress. In this work, we study benchmark reliability from a distributional perspective and introduce benchmark harmony, which measures how uniformly a model's performance is distributed across the subdomains of a benchmark. We posit that high harmony is a desirable benchmark property, indicating that the aggregate metric reflects uniform competence across subdomains. Across 19 multiple-choice benchmarks and five model families, we map each benchmark onto a mean-variance plane of harmony computed across models, where high mean and low variance signal more reliable evaluation. Our analysis shows that less harmonious benchmarks can give misleading results, since overall accuracy may be disproportionately influenced by specific subdomains. For instance, ARC-Easy is overwhelmed by questions on Biological Concepts, overshadowing other critical subdomains such as Geography, Physics, Chemistry, and Environmental Science. By recommending that harmony should be reported alongside accuracy, we reframe evaluation from simple performance averages to a more robust, distributionally reliable measurement of performance.

Flow-based generative models achieve state-of-the-art sample quality, but require the expensive solution of a differential equation at inference time. Flow map models, commonly known as consistency models, encompass many recent efforts to improve inference-time efficiency by learning the solution operator of this differential equation. Yet despite their promise, these models lack a unified description that clearly explains how to learn them efficiently in practice. Here, building on the methodology proposed in Boffi et. al. (2024), we present a systematic algorithmic framework for directly learning the flow map associated with a flow or diffusion model. By exploiting a relationship between the velocity field underlying a continuous-time flow and the instantaneous rate of change of the flow map, we show how to convert any distillation scheme into a direct training algorithm via self-distillation, eliminating the need for pre-trained teachers. We introduce three algorithmic families based on different mathematical characterizations of the flow map: Eulerian, Lagrangian, and Progressive methods, which we show encompass and extend all known distillation and direct training schemes for consistency models. We find that the novel class of Lagrangian methods, which avoid both spatial derivatives and bootstrapping from small steps by design, achieve significantly more stable training and higher performance than more standard Eulerian and Progressive schemes. Our methodology unifies existing training schemes under a single common framework and reveals new design principles for accelerated generative modeling. Associated code is available at https://github.com/nmboffi/flow-maps.

A range of recent optimizers have emerged that approximate the same "matrix-whitening" transformation in various ways. In this work, we systematically deconstruct such optimizers, aiming to disentangle the key components that explain performance. Across tuned hyperparameters across the board, all flavors of matrix-whitening methods reliably outperform elementwise counterparts, such as Adam. Matrix-whitening is often related to spectral descent -- however, experiments reveal that performance gains are *not explained solely by accurate spectral normalization* -- particularly, SOAP displays the largest per-step gain, even though Muon more accurately descends along the steepest spectral descent direction. Instead, we argue that matrix-whitening serves two purposes, and the variance adaptation component of matrix-whitening is the overlooked ingredient explaining this performance gap. Experiments show that variance-adapted versions of optimizers consistently outperform their sign-descent counterparts, including an adaptive version of Muon. We further ablate variance adaptation strategies, finding that while lookahead style approximations are not as effective, low-rank variance estimators can effectively reduce memory costs without a performance loss.

Any-to-any generative models aim to enable seamless interpretation and generation across multiple modalities within a unified framework, yet their ability to preserve relationships across modalities remains uncertain. Do unified models truly achieve cross-modal coherence, or is this coherence merely perceived? To explore this, we introduce ACON, a dataset of 1,000 images (500 newly contributed) paired with captions, editing instructions, and Q&A pairs to evaluate cross-modal transfers rigorously. Using three consistency criteria-cyclic consistency, forward equivariance, and conjugated equivariance-our experiments reveal that any-to-any models do not consistently demonstrate greater cross-modal consistency than specialized models in pointwise evaluations such as cyclic consistency. However, equivariance evaluations uncover weak but observable consistency through structured analyses of the intermediate latent space enabled by multiple editing operations. We release our code and data at https://github.com/JiwanChung/ACON.

Consistency models have exhibited remarkable capabilities in facilitating efficient image/video generation, enabling synthesis with minimal sampling steps. It has proven to be advantageous in mitigating the computational burdens associated with diffusion models. Nevertheless, the application of consistency models in music generation remains largely unexplored. To address this gap, we present Music Consistency Models (MusicCM), which leverages the concept of consistency models to efficiently synthesize mel-spectrogram for music clips, maintaining high quality while minimizing the number of sampling steps. Building upon existing text-to-music diffusion models, the MusicCM model incorporates consistency distillation and adversarial discriminator training. Moreover, we find it beneficial to generate extended coherent music by incorporating multiple diffusion processes with shared constraints. Experimental results reveal the effectiveness of our model in terms of computational efficiency, fidelity, and naturalness. Notable, MusicCM achieves seamless music synthesis with a mere four sampling steps, e.g., only one second per minute of the music clip, showcasing the potential for real-time application.

The slow inference process of image diffusion models significantly degrades interactive user experiences. To address this, we introduce Diffusion Preview, a novel paradigm employing rapid, low-step sampling to generate preliminary outputs for user evaluation, deferring full-step refinement until the preview is deemed satisfactory. Existing acceleration methods, including training-free solvers and post-training distillation, struggle to deliver high-quality previews or ensure consistency between previews and final outputs. We propose ConsistencySolver derived from general linear multistep methods, a lightweight, trainable high-order solver optimized via Reinforcement Learning, that enhances preview quality and consistency. Experimental results demonstrate that ConsistencySolver significantly improves generation quality and consistency in low-step scenarios, making it ideal for efficient preview-and-refine workflows. Notably, it achieves FID scores on-par with Multistep DPM-Solver using 47% fewer steps, while outperforming distillation baselines. Furthermore, user studies indicate our approach reduces overall user interaction time by nearly 50% while maintaining generation quality. Code is available at https://github.com/G-U-N/consolver.

This article studies the change in the prediction accuracy of a response variable when the number of predictors increases, and all variables follow a multivariate normal distribution. Assuming that the correlations between variables are independently drawn, I show that adding variables leads to globally increasing returns to scale when the mean of the correlation distribution is zero. The speed of learning depends positively on the variance of the correlation distribution. I use simulations to study the more complex case of correlation distributions with a non-zero mean and find a pattern of decreasing returns followed by increasing returns to scale - as long as the variance of correlations is not degenerate, in which case globally decreasing returns emerge. I train a collaborative filtering algorithm using the MovieLens 1M dataset to analyze returns from adding variables in a more realistic setting and find globally increasing returns to scale across 2,000 variables. The results suggest significant scale advantages from additional variables in prediction tasks.

Large language models (LLMs) are increasingly deployed in high-stakes domains, where rare but severe failures can result in irreversible harm. However, prevailing evaluation benchmarks often reduce complex social risk to mean-centered scalar scores, thereby obscuring distributional structure, cross-dimensional interactions, and worst-case behavior. This paper introduces Social Harm Analysis via Risk Profiles (SHARP), a framework for multidimensional, distribution-aware evaluation of social harm. SHARP models harm as a multivariate random variable and integrates explicit decomposition into bias, fairness, ethics, and epistemic reliability with a union-of-failures aggregation reparameterized as additive cumulative log-risk. The framework further employs risk-sensitive distributional statistics, with Conditional Value at Risk (CVaR95) as a primary metric, to characterize worst-case model behavior. Application of SHARP to eleven frontier LLMs, evaluated on a fixed corpus of n=901 socially sensitive prompts, reveals that models with similar average risk can exhibit more than twofold differences in tail exposure and volatility. Across models, dimension-wise marginal tail behavior varies systematically across harm dimensions, with bias exhibiting the strongest tail severities, epistemic and fairness risks occupying intermediate regimes, and ethical misalignment consistently lower; together, these patterns reveal heterogeneous, model-dependent failure structures that scalar benchmarks conflate. These findings indicate that responsible evaluation and governance of LLMs require moving beyond scalar averages toward multidimensional, tail-sensitive risk profiling.

Performing tasks on the web presents fundamental challenges to large language models (LLMs), including combinatorially large open-world tasks and variations across web interfaces. Simply specifying a large prompt to handle all possible behaviors and states is extremely complex, and results in behavior leaks between unrelated behaviors. Decomposition to distinct policies can address this challenge, but requires carefully handing off control between policies. We propose Stacked LLM Policies for Web Actions (SteP), an approach to dynamically compose policies to solve a diverse set of web tasks. SteP defines a Markov Decision Process where the state is a stack of policies representing the control state, i.e., the chain of policy calls. Unlike traditional methods that are restricted to static hierarchies, SteP enables dynamic control that adapts to the complexity of the task. We evaluate SteP against multiple baselines and web environments including WebArena, MiniWoB++, and a CRM. On WebArena, SteP improves (14.9\% to 33.5\%) over SOTA that use GPT-4 policies, while on MiniWob++, SteP is competitive with prior works while using significantly less data. Our code and data are available at https://asappresearch.github.io/webagents-step.

We consider the reinforcement learning (RL) problem with general utilities which consists in maximizing a function of the state-action occupancy measure. Beyond the standard cumulative reward RL setting, this problem includes as particular cases constrained RL, pure exploration and learning from demonstrations among others. For this problem, we propose a simpler single-loop parameter-free normalized policy gradient algorithm. Implementing a recursive momentum variance reduction mechanism, our algorithm achieves mathcal{O}(epsilon^{-3}) and mathcal{O}(epsilon^{-2}) sample complexities for epsilon-first-order stationarity and epsilon-global optimality respectively, under adequate assumptions. We further address the setting of large finite state action spaces via linear function approximation of the occupancy measure and show a mathcal{O}(epsilon^{-4}) sample complexity for a simple policy gradient method with a linear regression subroutine.

We propose a new score-based model with one-step sampling. Previously, score-based models were burdened with heavy computations due to iterative sampling. For substituting the iterative process, we train a standalone generator to compress all the time steps with the gradient backpropagated from the score network. In order to produce meaningful gradients for the generator, the score network is trained to simultaneously match the real data distribution and mismatch the fake data distribution. This model has the following advantages: 1) For sampling, it generates a fake image with only one step forward. 2) For training, it only needs 10 diffusion steps.3) Compared with consistency model, it is free of the ill-posed problem caused by consistency loss. On the popular CIFAR-10 dataset, our model outperforms Consistency Model and Denoising Score Matching, which demonstrates the potential of the framework. We further provide more examples on the MINIST and LSUN datasets. The code is available on GitHub.

Diffusion probabilistic models have shown significant progress in video generation; however, their computational efficiency is limited by the large number of sampling steps required. Reducing sampling steps often compromises video quality or generation diversity. In this work, we introduce a distillation method that combines variational score distillation and consistency distillation to achieve few-step video generation, maintaining both high quality and diversity. We also propose a latent reward model fine-tuning approach to further enhance video generation performance according to any specified reward metric. This approach reduces memory usage and does not require the reward to be differentiable. Our method demonstrates state-of-the-art performance in few-step generation for 10-second videos (128 frames at 12 FPS). The distilled student model achieves a score of 82.57 on VBench, surpassing the teacher model as well as baseline models Gen-3, T2V-Turbo, and Kling. One-step distillation accelerates the teacher model's diffusion sampling by up to 278.6 times, enabling near real-time generation. Human evaluations further validate the superior performance of our 4-step student models compared to teacher model using 50-step DDIM sampling.

Weight-space merging aims to combine multiple fine-tuned LLMs into a single model without retraining, yet most existing approaches remain fundamentally parameter-space heuristics. This creates three practical limitations. First, linear averaging, task vectors, and related rules operate on Euclidean coordinates, even though the desired goal is to merge functionality, i.e., predictive behaviors across tasks. Second, when the source checkpoints are farther apart or more heterogeneous, Euclidean blends often trigger representation collapse, manifested as activation variance shrinkage and effective-rank degradation, which sharply degrades accuracy. Third, many geometry-inspired methods are most natural for two-model interpolation and do not extend cleanly to merging N>2 experts with a principled objective. We address these issues by formulating model merging as computing a weighted Karcher mean on the Fisher--Rao manifold, which is locally equivalent to minimizing a KL-based function distance between predictive distributions. We derive a practical fixed-point algorithm using a lightweight spherical proxy that preserves norms and generalizes directly to multi-expert merging. Across various benchmarks and collapse diagnostics, our method remains stable as the number and heterogeneity of merged models increase, consistently outperforming prior baselines.

Modern ML systems ingest data aggregated from diverse sources, such as synthetic, human-annotated, and live customer traffic. Understanding which examples are important to the performance of a learning algorithm is crucial for efficient model training. Recently, a growing body of literature has given rise to various "influence scores," which use training artifacts such as model confidence or checkpointed gradients to identify important subsets of data. However, these methods have primarily been developed in computer vision settings, and it remains unclear how well they generalize to language-based tasks using pretrained models. In this paper, we explore the applicability of influence scores in language classification tasks. We evaluate a diverse subset of these scores on the SNLI dataset by quantifying accuracy changes in response to pruning training data through random and influence-score-based sampling. We then stress-test one of the scores -- "variance of gradients" (VoG) from Agarwal et al. (2022) -- in an NLU model stack that was exposed to dynamic user speech patterns in a voice assistant type of setting. Our experiments demonstrate that in many cases, encoder-based language models can be finetuned on roughly 50% of the original data without degradation in performance metrics. Along the way, we summarize lessons learned from applying out-of-the-box implementations of influence scores, quantify the effects of noisy and class-imbalanced data, and offer recommendations on score-based sampling for better accuracy and training efficiency.

Large language models perform near-Bayesian inference yet violate permutation invariance on exchangeable data. We resolve this by showing transformers minimize expected conditional description length (cross-entropy) over orderings, E_pi[ell(Y mid Gamma_pi(X))], which admits a Kolmogorov-complexity interpretation up to additive constants, rather than the permutation-invariant description length ell(Y mid X). This makes them Bayesian in expectation, not in realization. We derive (i) a Quantified Martingale Violation bound showing order-induced deviations scale as O(log n) with constants; (ii) the Expectation-level Decompression Law linking information budgets to reliability for Bernoulli predicates; and (iii) deployable planners (B2T/RoH/ISR) for answer/abstain decisions. Empirically, permutation dispersion follows a+bln n (Qwen2-7B b approx 0.377, Llama-3.1-8B b approx 0.147); permutation mixtures improve ground-truth likelihood/accuracy; and randomized dose-response shows hallucinations drop by sim 0.13 per additional nat. A pre-specified audit with a fixed ISR=1.0 achieves near-0\% hallucinations via calibrated refusal at 24\% abstention. The framework turns hallucinations into predictable compression failures and enables principled information budgeting.

With the rapid advancement of agent-based methods in recent years, Agentic RAG has undoubtedly become an important research direction. Multi-hop reasoning, which requires models to engage in deliberate thinking and multi-step interaction, serves as a critical testbed for assessing such capabilities. However, existing benchmarks typically provide only final questions and answers, while lacking the intermediate hop-level questions that gradually connect atomic questions to the final multi-hop query. This limitation prevents researchers from analyzing at which step an agent fails and restricts more fine-grained evaluation of model capabilities. Moreover, most current benchmarks are manually constructed, which is both time-consuming and labor-intensive, while also limiting scalability and generalization. To address these challenges, we introduce AgenticRAGTracer, the first Agentic RAG benchmark that is primarily constructed automatically by large language models and designed to support step-by-step validation. Our benchmark spans multiple domains, contains 1,305 data points, and has no overlap with existing mainstream benchmarks. Extensive experiments demonstrate that even the best large language models perform poorly on our dataset. For instance, GPT-5 attains merely 22.6\% EM accuracy on the hardest portion of our dataset. Hop-aware diagnosis reveals that failures are primarily driven by distorted reasoning chains -- either collapsing prematurely or wandering into over-extension. This highlights a critical inability to allocate steps consistent with the task's logical structure, providing a diagnostic dimension missing in traditional evaluations. We believe our work will facilitate research in Agentic RAG and inspire further meaningful progress in this area. Our code and data are available at https://github.com/YqjMartin/AgenticRAGTracer.

Latent Diffusion models (LDMs) have achieved remarkable results in synthesizing high-resolution images. However, the iterative sampling process is computationally intensive and leads to slow generation. Inspired by Consistency Models (song et al.), we propose Latent Consistency Models (LCMs), enabling swift inference with minimal steps on any pre-trained LDMs, including Stable Diffusion (rombach et al). Viewing the guided reverse diffusion process as solving an augmented probability flow ODE (PF-ODE), LCMs are designed to directly predict the solution of such ODE in latent space, mitigating the need for numerous iterations and allowing rapid, high-fidelity sampling. Efficiently distilled from pre-trained classifier-free guided diffusion models, a high-quality 768 x 768 2~4-step LCM takes only 32 A100 GPU hours for training. Furthermore, we introduce Latent Consistency Fine-tuning (LCF), a novel method that is tailored for fine-tuning LCMs on customized image datasets. Evaluation on the LAION-5B-Aesthetics dataset demonstrates that LCMs achieve state-of-the-art text-to-image generation performance with few-step inference. Project Page: https://latent-consistency-models.github.io/

Uniform-state discrete diffusion models hold the promise of fast text generation due to their inherent ability to self-correct. However, they are typically outperformed by autoregressive models and masked diffusion models. In this work, we narrow this performance gap by leveraging a key insight: Uniform-state diffusion processes naturally emerge from an underlying Gaussian diffusion. Our method, Duo, transfers powerful techniques from Gaussian diffusion to improve both training and sampling. First, we introduce a curriculum learning strategy guided by the Gaussian process, doubling training speed by reducing variance. Models trained with curriculum learning surpass autoregressive models in zero-shot perplexity on 3 of 7 benchmarks. Second, we present Discrete Consistency Distillation, which adapts consistency distillation from the continuous to the discrete setting. This algorithm unlocks few-step generation in diffusion language models by accelerating sampling by two orders of magnitude. We provide the code and model checkpoints on the project page: http://s-sahoo.github.io/duo

As general purpose vision models get increasingly effective at a wide set of tasks, it is imperative that they be consistent across the tasks they support. Inconsistent AI models are considered brittle and untrustworthy by human users and are more challenging to incorporate into larger systems that take dependencies on their outputs. Measuring consistency between very heterogeneous tasks that might include outputs in different modalities is challenging since it is difficult to determine if the predictions are consistent with one another. As a solution, we introduce a benchmark dataset, COCOCON, where we use contrast sets created by modifying test instances for multiple tasks in small but semantically meaningful ways to change the gold label, and outline metrics for measuring if a model is consistent by ranking the original and perturbed instances across tasks. We find that state-of-the-art systems suffer from a surprisingly high degree of inconsistent behavior across tasks, especially for more heterogeneous tasks. Finally, we propose using a rank correlation-based auxiliary objective computed over large automatically created cross-task contrast sets to improve the multi-task consistency of large unified models, while retaining their original accuracy on downstream tasks. Project website available at https://adymaharana.github.io/cococon/