NeurIPS 2026 论文列表

Dataset distillation seeks to synthesize a highly compact surrogate dataset that achieves performance comparable to the original dataset on downstream tasks. For the scenario where pre-trained self-supervised models serve as priors, traditional $\textit{Linear Gradient Matching}$ optimizes synthetic images by encouraging them to mimic the gradient updates induced by real images on the linear probe or classifier. However, this batch-level formulation requires loading thousands of real images and applying multiple differentiable augmentations to synthetic images at each distillation step, leading to substantial computational and memory overheads. In this paper, we revisit the linear gradient and theoretically derive that it is essentially a $\textit{local}$ relative distribution directed from target class centers toward non-target class centers, which we term ``flow”. This property causes instability and suboptimality, often necessitating expensive multiple augmentations to compensate. To address this, we introduce $\textit{Statistical Flow Matching}$, a stable and efficient supervised learning framework that optimizes synthetic images by aligning $\textit{global}$ statistical flows in the original data. Our approach loads raw statistics only once and performs a single augmentation pass on the synthetic data, achieving performance comparable to or better than the state-of-the-art method with 10× less GPU memory usage and 4× faster distillation time. Moreover, increasing the number of augmentations for our method yields further performance gains while incurring lower additional cost.

Text-guided image editing has advanced rapidly with diffusion models and unified multimodal foundation models. However, most existing methods remain confined to single-turn settings, overlooking the more realistic scenario of multi-turn in-context editing, where users iteratively refine an image through a sequence of instructions. In this setting, a model must follow each new instruction while preserving accumulated session-level constraints, challenged by two coupled failure modes: long-context dilution, where sparse textual constraints become difficult to recover from growing interleaved image-text histories, and state contamination, where earlier editing mistakes degrade subsequent generations. We introduce Edit-R2, a novel reinforcement learning post-training framework for unified multimodal models. Edit-R2 reconstructs the operative session intent, which effectively consolidates scattered historical constraints into an explicit reasoning trace before each editing turn. It further enables multi-turn RL over both reasoning and generation through a unified objective that jointly optimizes intent reconstruction generation in discrete text space and flow-matching image generation in continuous latent space, while a trajectory filtering mechanism suppresses corrupted rollouts to stabilize training under state contamination. To support systematic evaluation, we introduce MICE-Bench, a large-scale benchmark for multi-turn in-context editing with automated metrics for instruction following (IF), content consistency (CC), and global awareness (GA) over accumulated session constraints. Experiments show that Edit-R2 substantially improves multi-turn in-context editing and achieves competitive performance compared against strong baselines.

Guiding pretrained flow-based generative models for conditional generation or to produce samples with desired target properties enables solving diverse tasks without retraining on paired data. We present ESS-Flow, a gradient-free method that leverages the Gaussian prior of the source distribution in flow-based models to perform Bayesian inference directly in the source space using Elliptical Slice Sampling. ESS-Flow only requires forward passes through the generative model and observation process, making it applicable even when gradients are unavailable, such as with non-differentiable simulation-based observations or quantization in the generation process. We demonstrate its effectiveness on scientific applications including designing materials with desired target properties and predicting protein structures from sparse inter-residue distance measurements.

Generative models have made rapid progress in ordered crystal structure prediction, yet many functional materials are intrinsically disordered, with substitutional mixing, vacancies, or interstitial species controlling their properties. Existing crystal generators either assume deterministic site occupations or require site-level disorder annotations, which are often unavailable when the chemical formula is the primary input. We formulate disordered crystal structure prediction through an Occupancy Distribution Matrix (ODM), a continuous site-by-species representation that unifies ordered crystals, solid solutions, vacancy disorder, and interstitial occupancy. A valid ODM must satisfy coupled site-wise occupancy, mass-conservation, and non-negativity constraints, placing each sample on a formula-dependent transportation polytope. We propose Entropic Polytope Flow (EP-Flow), a marginal-constrained flow matching framework that canonicalizes heterogeneous polytopes into a shared double-centered space, learns a marginal-preserving flow, and recovers feasible occupancies through a Sinkhorn inverse map. By jointly generating occupancies, fractional coordinates, and lattice parameters, EP-Flow achieves state-of-the-art performance on formula-conditioned disordered CSP benchmarks derived from COD and MPDS, substantially outperforming adapted ordered-crystal generators. Analyses further show that EP-Flow recovers sparse and chemically meaningful local disorder patterns rather than merely matching global composition statistics.

The design of the forward diffusion process is a foundational yet under-theorized aspect of diffusion modeling. Although it determines how data are corrupted and how quickly the forward dynamics approach a reference distribution, forward-process design remains largely governed by canonical defaults rather than a unified analytical framework. We propose Eigenvalue-Guided Control and Analysis (EGCA) for diffusion models, a spectral framework that uses the principal eigenvalue of the infinitesimal generator to analyze and guide forward-process design. Under suitable ergodicity conditions, this eigenvalue governs the exponential convergence rate to stationarity, providing a compact and interpretable summary of forward dynamics. We establish sufficient uniqueness and ergodicity conditions, derive eigenvalue-based convergence bounds, and adapt a practical numerical estimator for the principal eigenvalue. Empirically, we show that the eigenvalue strongly tracks forward convergence speed and serves as an organizing coordinate for the efficiency--quality trade-off across tractable forward-generator families. Experiments across multiple image datasets and diverse diffusion settings, including training formulations, architectures, and samplers, demonstrate that eigenvalue-guided design maintains or improves generation quality while reducing training cost. Beyond a single generator choice, our framework offers a spectral perspective for understanding and comparing forward-process choices in diffusion models.

Euclidean combinatorial optimization problems (ECOPs), such as the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP), possess inherent symmetries under the two-dimensional Euclidean group E(2), including rotations, reflections, and translations. Existing learning-based methods, including recent diffusion-based methods, rely on data augmentation or regularization to approximate E(2)-equivariance. This paper presents EDISCO, the first discrete diffusion model for ECOPs with exact E(2)-invariant generative distributions over node-index solutions. EDISCO introduces an E(2)-equivariant edge-score network coupled with a categorical continuous-time Markov chain over discrete edge variables, and exact posterior sampling provides efficient multi-step inference. This design gives EDISCO a local geometric inductive bias: edge neighborhoods with the same relative geometry and combinatorial context are represented consistently regardless of absolute position or orientation, making learning more efficient and inference more robust than non-equivariant methods. EDISCO outperforms previous learning-based state-of-the-art solvers on synthetic TSP from 100 to 10000 nodes and CVRP from 50 to 2000 customers, while using only 33--50\% of the training instances. Trained only on uniform synthetic data, EDISCO also outperforms competing learning-based baselines under spatial distribution shift and CVRP constraint-tightness shift. Code is available at https://anonymous.4open.science/r/EDISCO-7F54.

Diffusion language models (DLMs) have recently emerged as a promising alternative to autoregressive models, primarily due to their ability to enable parallel decoding. Despite this advantage, most existing DLMs rely on a fixed generation length specified prior to decoding, which restricts their flexibility in real-world applications. While a few recent works attempt to support flexible-length generation, they typically suffer from notable limitations: some require costly retraining to accommodate variable-length outputs, while others depend solely on local confidence signals during decoding. Such local criteria fail to capture the evolving structure of the sequence, often resulting in suboptimal generation quality. In this paper, we propose a training-free, Bayesian structured decoding framework that formulates flexible-length generation as a dynamic structural inference problem. Our approach learns the posterior inference over the dynamic block length, block formations and growth, and block decoding order within a unified Bayesian inference framework to jointly reason about how much to grow, where to grow, and how to organize content structurally. At each window expansion step, the method integrates local uncertainty with structural signals to (i) dynamically expand the sequence via adaptive length growth, (ii) infer block boundaries through Chinese Restaurant Process (CRP)-style partitioning, and (iii) allocate different number of decoding steps for different blocks and determine block decoding order via context-aware scheduling. This yields a unified mechanism that supports dynamic structured generation, including both flexible block expansion and block organization, while maintaining coherence. Extensive experiments across multiple benchmarks demonstrate that our approach significantly improves generation quality and flexibility over existing fixed-length and flexible-length baselines. These results highlight the advantage of Bayesian structured decoding for diffusion language model, providing a principled and efficient solution for structured text generation.

Diffusion models have achieved impressive performance in video generation, but their iterative denoising process remains computationally expensive due to the large number of tokens processed at each timestep. Recently, progressive resolution sampling has emerged as a promising acceleration approach by reducing latent resolution in early stages. However, scaling this idea to video generation remains challenging, as the additional temporal dimension introduces diverse spatio-temporal demands across different videos, and compressing only a single dimension often leads to limited acceleration or degraded quality. Therefore, we propose \textbf{DVG}, a \textbf{D}ynamic \textbf{V}ideo \textbf{G}eneration framework that jointly allocates computation across time and space, automatically selecting content-aware acceleration strategies without manual tuning or retraining. \textbf{DVG} achieves near-lossless acceleration across models and tasks, reaching up to \textbf{7$\times$} speedup on HunyuanVideo and HunyuanVideo-1.5, and \textbf{18$\times$} when combined with distillation, demonstrating its potential as a key component in today’s large-scale efficient video generation systems. \emph{Our code is in supplementary material and will be released on Github.}

Federated Domain Generalization (FDG) aims to learn a global model robust to heterogeneous domain shifts without sharing raw data, a critical challenge in multi-center medical imaging. Most existing methods implicitly assume static inter-domain discrepancies, overlooking the fact that client representations evolve continuously during local optimization. We identify this phenomenon as representation dynamics, which refers to the temporal evolution of latent features induced by training updates rather than shifts in underlying data distributions. Such dynamics often lead to unstable aggregation, particularly in heterogeneous medical imaging scenarios. To address this issue, we propose Dynamic Knowledge Tracked FDG (DKT-FDG), a framework that explicitly tracks these dynamics by leveraging flow matching to model continuous representation trajectories. By aligning representation evolution instead of static snapshots, DKT-FDG improves robustness to domain shifts. Comprehensive experiments on multiple multi-center medical benchmarks demonstrate consistent improvements over state-of-the-art FDG methods, highlighting the importance of modeling representation dynamics in federated learning.

Drifting Models have recently achieved state-of-the-art performance in one-step image generation by training generators to follow corrective vector fields. However, their standard reverse-style drift improves samples from the model side, which can severely underutilize training samples and bottleneck early convergence. To address this, we introduce DualDrift, a unified framework that augments the original reverse drift with a novel forward drift. The forward drift lets each data sample assign correction to generated rollouts, providing denser data-side signals and accelerating early training. At the same time, this dense data-side signal can overemphasize dominant regions when used alone. DualDrift therefore uses a parameter-free scheduler driven by empirical batch statistics to balance the fast early correction of forward drift with the stable refinement of reverse drift. Evaluated on ImageNet $256\times256$, DualDrift achieves faster convergence and significantly improves over the baseline Drifting Models in both FID and Inception Score.

Diffusion models achieve state-of-the-art generative performance but suffer from high computational costs during inference due to the repeated evaluation of a heavy neural network. In this work, we propose Dual-Rate Diffusion, a method to accelerate sampling by interleaving the execution of a heavy high-capacity context encoder and a light efficient denoising model. The context encoder is evaluated sparsely to extract high-dimensional features, which are effectively reused by the light denoising model at every step to refine the sample efficiently. This approach significantly accelerates inference without compromising sample quality. On ImageNet benchmarks, Dual-Rate Diffusion matches the performance of standard baselines while reducing computational cost by a factor of $2$--$4$. Furthermore, we demonstrate that our method is compatible with distillation techniques, such as Moment Matching Distillation, enabling further efficiency gains in few-step generation.

Pretrained foundation models have become an important basis for end-to-end autonomous driving. In contrast to vision-language models pretrained primarily on static image-text pairs, video generative models capture temporal dynamics and motion priors that are naturally suited for driving. We present DriveWAM, a driving world-action model that adapts a pretrained video diffusion transformer into an autoregressive video-action policy. DriveWAM organizes video and action streams into a unified temporal token sequence and trains them under a joint flow-matching objective, preserving the pretrained video-generation architecture while adapting its large-scale video priors to action generation. To incorporate high-level scene understanding, we introduce scene-evolving driving guidance, where a frozen VLM produces chunk-specific semantic intent to guide video-action generation. To keep long-horizon rollout bounded, we further introduce selective KV memory, which maintains bounded modality-aware video and action memory pools through relevance-redundancy cache selection at inference time. Experiments on NAVSIM and the PhysicalAI-Autonomous-Vehicles benchmark show that DriveWAM achieves strong planning performance, and a data-scaling study from 4k to 100k driving clips further confirms the scaling potential of world-action modeling for end-to-end autonomous driving.

Drifting models have recently gained attention for generating high-quality samples in a single forward pass. During training, they learn a push-forward map by following a vector-valued field, the *drift field*. We ask whether this procedure is equivalent to optimizing a scalar loss and find that, in general, it is not: drift fields are *not conservative* and cannot be written as the gradient of any scalar potential. We identify the position-dependent normalization as the source of non-conservatism, with the Gaussian kernel as the unique radial exception. Guided by this, we introduce the *sharp kernel* $k^\\#$ and a sharp-normalized drift field that is conservative for general radial kernels. The resulting vector field is the gradient of a scalar potential that can be optimized directly using stochastic gradient descent. Moreover, the field has the form of a score difference of kernel density estimates, and gives exact equilibrium identifiability. Thus, sharp normalization closes the gap to related literature, such as Wasserstein gradient-flows and denoising score matching, also for non-Gaussian kernels. Empirically, sharp normalization preserves the performance of the original drifting objective, suggesting that the non-conservative flexibility is not required for high-quality generation.

We propose Drifting Field Policy (DFP), a non-ODE one-step generative policy built on the drifting model paradigm. Under online RL finetuning, we frame the policy update as a reverse-KL Wasserstein-2 gradient flow toward a soft target policy, realized by DFP as a steepest-descent step on probability space. By construction, this gradient step is decomposed into an ascent toward higher action-value regions and a score matching with the anchor policy as a trust region. We further derive a simple, tractable surrogate of the otherwise intractable update loss, akin to behavior cloning on top-K critic-selected actions. We find empirically that this mechanism uniquely benefits the drifting backbone owing to its non-ODE parameterization. With one-step inference, DFP achieves state-of-the-art performance on several manipulation tasks across Robomimic and OGBench, outperforming ODE-based policies.

Mapping reaction pathways and transition states (TS) is fundamental to chemistry but computationally expensive at scale. The minimum energy pathway (MEP) dictates reaction rates and mechanisms, yet recovering it via electronic-structure methods requires thousands of costly force evaluations. Recent generative models accelerate TS identification but require slow iterative inference and only predict isolated saddle-point snapshots, missing the continuous reaction trajectory. We introduce Drift-React, an $\mathrm{SE}(3)$-equivariant generative framework that predicts complete reaction pathways in a single forward pass from only reactant and product geometries. By shifting distribution evolution to training via a Sinkhorn-weighted drifting field, Drift-React eliminates both the iterative force evaluations of NEB-style methods and the sequential ODE/SDE integration of diffusion and flow matching models. Evaluated on the Transition1x and Halo8 datasets, our one-step model generates physically consistent MEPs that accurately capture energetic bottlenecks and enable arbitrary-resolution sampling along the reaction coordinate. For isolated TS prediction, Drift-React matches the sub-Ångström accuracy of state-of-the-art iterative models while delivering orders-of-magnitude acceleration, clearing a major computational bottleneck for large-scale reaction network exploration.

Real-world machine learning systems often operate on imperfect measurements: sensors are noisy, annotations are produced by non-experts, and scientific observations are often indirect. In these settings, classic distribution comparison tools such as maximum mean discrepancy (MMD) can be systematically biased, matching artifacts of the measurement process rather than the underlying mechanisms of interest. We study a practical regime in which noisy observations are abundant, but only a small audited subset contains ground-truth measurements. We propose measurement-error-corrected MMD (MEC-MMD), an audit-based estimator that debiases kernel evaluations without requiring a noise model. MEC-MMD is exactly unbiased for the oracle MMD under simple random auditing, admits an explicit variance decomposition, and is consistent for the population MMD, achieving the standard $O_p(N^{-1/2})$ rate when the audit size scales with the dataset. We demonstrate the utility of distributional matching with MEC-MMD loss for both parameter estimation and unsupervised applications, showing that MEC-MMD consistently outperforms MMD and alternative methods. These results provide a principled foundation for robust distribution comparison, simulation-based inference, and learning in noisy real-world machine learning pipelines.

Diffusion-based visual generative models are powerful, but understanding their generalization behavior remains challenging. Current evaluations rely on human preference scores for text-to-image models and distribution-level metrics such as Frechet Inception Distance (FID) and Inception Score (IS) for class-conditional models, but these do not test whether models learn basic visual skills or largely match training patterns. To overcome this gap, we introduce the Visual Generative Lab (VGL), a controlled experimental framework for understanding how diffusion models learn and generalize basic visual skills, including size, position, rotation, count, color, shape, and their composition. By generating synthetic training data for each skill from explicit rules, VGL enables precise measurement of generalization using task-specific, rule-based metrics. Training models from scratch on these data reveals three consistent patterns. (1) Models extrapolate rotation better than size, skill, or count on far-out-of-range queries; healthy rotation seeds match most extrapolation angles within a few degrees, although a non-trivial fraction of seeds collapse near the wraparound, while skill and position saturate at small distances outside training regardless of seed. (2) For compositional generalization, coverage of basic visual skill combinations matters more than dataset size. (3) Basic visual skills are learned jointly, so an out-of-distribution request in one skill can degrade the others even when they remain in range.

Personalized image generation aims to synthesize text-driven images conditioned on reference images, while mainly casting the generation as image customization for foreground and style transfer for background. Previous arts of diffusion models suffers from the text misalignment with background for image customization and foreground for style transfer during the denoising process. Such facts, as we observed, rooted from the entanglement among hybrid frequency bands during the denoising process. In particular, the low-frequency band primarily captures color information, mid-frequency band encodes global structure, while high-frequency band corresponds to local texture. Besides, the early (high-noise) denoising stage mainly focuses on the low-and-mid frequency bands, while the late (low-noise) denoising stage progressively exhibits the high-frequency band, resulting in the dominance of low-and-mid over high frequency bands, especially when entangled within a single image reference, tends to reinforce each other at the early stage, hence the pitfall of overwhelming suppression of text prompt guidance. To address such salient limitation, in this paper, we study personalized generation based on dual references - customization and color and style reference - and propose a paradigm to disentangle these **Dual** image references within **F**requency-aware **D**iffusion **M**odels, dubbed **Dual-FDM**, to simultaneously tackle two crucial personalized image generation tasks: customization style transfer and color style transfer, by disentangling different frequency bands via mask strategy within frequency domain. For customization style transfer, we replace the mid-frequency band of the background in the style reference with that from the foreground of the customized reference. For color style transfer, we substitute the low-frequency band of the background in the style reference with that from both the foreground and background of the color reference. Both the substituted frequency bands are used as the key and value to reconstruct the query foreground and background of the denoised personalized image. We further compute the ratio of information entropy of the substituted frequency bands to adaptively modulate the denoising timesteps between the early and late stages. Extensive experiments validate the superiority of **Dual-FDM** over the state-of-the-art diffusion models for personalized image generation. Our code can be accessed from the supplementary material package.

Causal representation learning for time series has developed strong identifiability results in discrete-time latent causal models, but identifiability in continuous-time latent stochastic differential equation (SDE) models remains largely open. We address this gap using environment-induced shifts in diffusion covariance. We study additive-noise latent SDEs observed through an unknown nonlinear diffeomorphism, with shared drift but environment-specific diffusion covariance. We show that two diagonal diffusion regimes with pairwise distinct coordinate-wise variance ratios identify the latent coordinates up to permutation and scaling, without any sparsity assumption on the drift. We first prove this result for linear Ornstein--Uhlenbeck systems and then extend it to general additive-noise latent SDEs. Under mild smoothness, the instantaneous drift-Jacobian causal graph is identifiable up to the same permutation. We propose a two-stage estimator for latent disentanglement and optional graph recovery; experiments on synthetic systems confirm the predicted identifiability boundary, and an application to Hardanger Bridge monitoring data illustrates the approach on real sensor trajectories.