NeurIPS 2026 论文列表

Training-free guidance enables pre-trained diffusion and flow models to optimize application-specific objectives using feedback from external black-box reward functions. However, existing methods are feedback-inefficient because reward feedback is used only transiently to inform a localized gradient approximation or a discrete search decision, and is subsequently discarded. To address this limitation, we propose Flow-Direct, a framework that guides the generation process via a persistent *guidance field*. Theoretically, this guidance field is analytically derived from the log-density ratio between the base and reward-weighted target distributions; it transports the pre-trained distribution to the target distribution. In practice, the field is implemented as a non-parametric estimator constructed from all accumulated reward-evaluated samples. As more samples are collected during optimization, this empirical guidance field becomes increasingly accurate. This persistent formulation yields two major advantages. First, Flow-Direct is highly *feedback-efficient*: because every evaluated sample is used to refine the global guidance field, no reward information is wasted. Second, the framework is naturally *reusable*: once optimization is complete, the collected dataset defines a reusable guidance field for generating novel target samples without additional reward evaluations, and distinct guidance fields can be combined to generate samples that simultaneously satisfy multiple objectives.

Recent work has demonstrated that online reinforcement learning (RL) can substantially improve the quality and alignment of flow matching models for image and video generation. Methods such as Flow-GRPO and CPS cast the denoising process as a Markov Decision Process and apply PPO-style ratio clipping to enforce a trust region. However, we argue that *ratio clipping is structurally ill-suited for flow models*: the probability ratio between new and old policies is a noisy, single-sample estimate of the true policy divergence, leading to over-constraining in some regions of the trajectory and under-constraining in others. We propose **Flow-DPPO** (Flow Divergence Proximal Policy Optimization), which replaces ratio clipping with a divergence proximal constraint. A key observation is that the per-step policy in flow models is Gaussian, enabling *exact* and *cheap* computation of the KL divergence between old and new policies. Flow-DPPO employs an asymmetric divergence mask that blocks gradient updates only when they simultaneously move away from the trusted region and violate the divergence threshold. Experiments show that Flow-DPPO achieves higher rewards with better KL-proximal efficiency, alleviates catastrophic forgetting, promotes balanced multi-objective optimization, and enables stable multi-epoch training where ratio clipping degrades.

Optimizing 3D shapes within the latent spaces of deep generative models is fundamental to computer assisted engineering, yet remains prone to a critical failure mode we term *manifold drift*: the tendency of gradient-based optimization to move latent vectors away from the manifold of valid shapes. This problem is exacerbated in state-of-the-art 3D shape generative models that operate in increasingly high-dimensional latent spaces where valid shapes occupy a vanishingly small fraction of the full space. Existing mitigation strategies, including latent regularization and flow-matching approaches, either sacrifice expressiveness, demand a difficult trade-off between objective guidance and generative fidelity that remains prone to manifold drift, or are computationally infeasible to scale to modern, large-capacity 3D shape models. We introduce a novel optimizer-corrector framework that alternates between gradient steps for objective minimization and guided flow matching to drive the latent state back to the valid shape manifold. By decoupling objective minimization from flow-based correction, optimizing freely and correcting strictly, this alternating design avoids inherent trade-offs, preserving geometric validity without sacrificing expressiveness while remaining computationally feasible on modern 3D shape models. We demonstrate its effectiveness across generative priors of varying complexity, from simple vector latent spaces to large-scale architectures across a variety of downstream optimization tasks, including aerodynamic drag reduction and object compliance optimization.

Many existing multivariate time series anomaly detection methods formulate anomaly detection as a reconstruction problem, where detections are derived from reconstruction errors in the time domain. While effective for large deviations, reconstruction-based scoring struggles with subtle anomalies where only a small subset of features deviates slightly. In such cases, most features are well reconstructed, causing the overall reconstruction error to remain low and indistinguishable from normal data. To address these challenges, we propose Flow+Diff, a novel framework that detects anomalies via discrepancies in a latent space, where two complementary representations, induced by distinct modeling paradigms, diverge under anomalous inputs. One representation is obtained via a normalizing flow, which provides an invertible mapping that preserves temporal dependencies and captures inter-feature dependencies. The other is produced by a diffusion model that learns the distribution of normal samples in the latent space via a stochastic denoising process. When given anomalous inputs, the normalizing flow maps the inputs to latent representations that lie in low-probability regions of the learned latent distribution, while the diffusion model generates representations aligned with normal data distributions, resulting in a pronounced discrepancy between the two. We compute the anomaly score based on this latent-space discrepancy, thereby shifting anomaly detection from the time domain to the latent space. Finally, the invertibility of the normalizing flow enables reconstruction in the time domain, facilitating interpretation of anomalous features. Extensive experiments across six benchmark datasets show that Flow+Diff achieves state-of-the-art performance on four datasets against competitive baselines.

We propose Flow Mismatching, an unsupervised anomaly detection method that deliberately avoids reconstruction-based paradigms. Instead, we treat flow matching as geometric dynamics and leverage a key insight: anomalies occur at places where the learned normal flow disagrees with the geometric path toward a test image. Given a flow matching model trained only on normal images, we probe its learned velocity field along affine paths from Gaussian noise to a target image. Along each path, we compare the model-predicted velocity, which follows normal generative dynamics, with the geometric velocity toward the target, which includes any anomalous content. Anomalies induce strong local disagreement between these velocities. Aggregating the mismatch over different time steps and multiple paths yields pixel-wise heatmaps and image-level scores without test-time optimization, feature memories, or additional calibration. Our analysis shows that the population mismatch decomposes into an irreducible denoising term and a Fisher-divergence term between the test-path and normal-path score functions, which identifies the score-gap component that drives anomaly separation and explains the effectiveness of robust path aggregation. Extensive experiments on MVTec-AD and VisA demonstrate superior performance compared with SOTA reconstruction-based and recent flow matching-based approaches.

Conditional flow matching produces realistic out-of-distribution samples across modalities from images to proteins, yet the conditioning signals that enable extrapolation remain poorly understood for biological time series. While considerable work has focused on areas of biology such as proteins and molecules, generative models of neural time series have been largely restricted to categorical conditioning, which precludes compositional and zero-shot generalization. In this work, we propose a per-timestep conditioned diffusion transformer for generating realistic fMRI brain dynamics during unseen cognitive tasks, by injecting both compositional language and optional spatial priors in-context. Such zero-shot generation would support in-silico task design and counterfactual evaluation of novel cognitive experiments before costly scanner acquisition. Leveraging this model, we evaluate across hundreds of held-out task conditions and characterize predictive performance in relation to the training manifold. From language alone, the model recovers region-specific recruitment across tasks and held-out spatial activation patterns. Spatial priors, when available, complement the text pathway by anchoring generation in regions of task space where language alone degrades, while retaining the compositional structure needed for counterfactual task specification. To our knowledge this is the first generative model of whole-cortex fMRI dynamics for unseen cognitive tasks, enabling counterfactual neuroscience and data-driven experimental design.

We reformulate Optimal Transport Conditional Flow Matching (OT-CFM), showing that it admits an exact proximal form via an extended Brenier potential, without assuming that the target distribution has a density. In particular, the mapping to recover the target point is expressed by a proximal operator, which yields an explicit proximal expression of the vector field. We also discuss the convergence of minibatch OT-CFM to the population OT formulation as the sample and batch sizes increase. Using second epi-derivatives of convex potentials, we prove that, for manifold-supported targets, the manifold structure is stable by perturbation to the dynamics: after time rescaling, the dynamics contracts exponentially in directions normal to the manifold while remaining neutral along tangential directions.

Generative policies based on diffusion models and flow matching have shown strong promise for offline reinforcement learning (RL), but their applicability remains largely confined to continuous action spaces. To address a broader range of offline RL settings, we extend flow matching to a general framework that supports discrete action spaces with multiple objectives. Specifically, we replace continuous flows with continuous-time Markov chains, trained using a Q-weighted flow matching objective. We then extend our design to multi-agent settings, mitigating the exponential growth of joint action spaces via a factorized conditional path. We theoretically show that, under idealized conditions, optimizing this objective recovers the optimal policy. Extensive experiments further demonstrate that our method performs robustly across diverse settings and benchmarks, including high-dimensional control, multi-agent games, and dynamically changing preferences over multiple objectives, while outperforming traditional offline RL methods in practical multi-modal decision-making scenarios. Our discrete framework can also be applied to continuous-control problems through action quantization, providing a flexible trade-off between representational complexity and performance.

We develop a unified framework for flow-based reinforcement learning (RL) grounded in diffusion–flow duality and establish its theoretical foundations. The frameworks enables RL for deterministic flow matching inference by introducing diffusion stochastic inference dynamics that supports exploration while admitting deterministic deployment. We show that our frameworks subsumes several existing flow-based RL methods as special cases and inspire effective now methods. Then we provide theoretical foundations for the frameworks by establishing the correctness and performance transfer guarantee. Specifically, we prove that the policies optimized under stochastic dynamics close to deterministic dynamics at deployment when the pretrained model is well-trained. Moreover, we show that the policy improvement achieved under training-time SDE inference transfers to deployment-time ODE inference. Finally, we conduct experiments to validate our theoretical results.

Balancing policy expressiveness with the exploration-exploitation trade-off is a core challenge in online Reinforcement Learning (RL). While Stochastic Differential Equation (SDE)-based diffusion policies can represent complex, multimodal action distributions, they suffer from two critical limitations: their stochastic reverse processes render entropy intractable (necessitating heuristic exploration), and computing policy gradients through long denoising chains is expensive and unstable. In this work, we show that ODE-based flow matching inherently resolves these issues by enabling both simulation-free policy optimization and tractable entropy computation. Building on this, we introduce Flow Matching Policy Optimization with Mirror Descent and Entropy Constraints (FMER). Our framework exploits this insight in three ways. First, we theoretically establish that minimizing an advantage-weighted conditional flow matching loss acts as a simulation-free surrogate for policy mirror descent. This steers the velocity field toward high-value regions while entirely avoiding backpropagation through the ODE solver. Second, we derive an analytic entropy objective that corrects for the density distortion caused by the $\tanh$ transformation (mapping an unbounded latent space to bounded actions), thereby facilitating principled maximum-entropy optimization. Finally, we dynamically tune the mirror descent temperature based on the effective sample size to enforce a robust trust region during training. Empirical evaluations demonstrate that FMER achieves superior performance on the challenging sparse-reward FrankaKitchen environment, while maintaining competitive results across standard dense-reward MuJoCo benchmarks. Code is available at \url{https://anonymous.4open.science/r/submission-25E2/}.

Image restoration faces a fundamental tradeoff: methods that minimize error produce blurry reconstructions, while those that maximize perceptual quality yield sharp but less faithful images. Existing approaches either commit to a single operating point on this distortion–perception (DP) frontier or require retraining, auxiliary models, or changes in discretization to access different points. We show that flow map models, a recent extension of flow matching for few-step sampling that learns an average field, implicitly define a one-parameter family of denoisers that continuously spans the DP frontier. The parameter, the lookahead $t$, acts as a knob: varying it traces a smooth path from the MMSE estimator to a perceptually aligned one. For Gaussian targets, we prove that this path recovers the optimal DP frontier exactly; for natural images, we demonstrate empirically that it closely follows the same behavior. Embedded within a Plug-and-Play solver, a single trained flow map matches or exceeds specialized baselines at both ends of the DP spectrum and uniquely traces a continuous curve in between without retraining, paired data, or auxiliary networks. Extensive experiments on CelebA ($128\times 128$) and AFHQ ($256\times 256$) across several linear and nonlinear inverse tasks validate our findings.

Designing functional biological sequences requires navigating vast discrete spaces under strict evolutionary and biophysical constraints. Discrete Flow Matching (DFM) offers a generative framework over such spaces, but existing approaches rely on biologically uninformative couplings and offer limited flexibility for variable-length sequence generation and fine-grained control. We propose a structured coupling that encodes domain-specific preferences among sequence elements, biasing the source distribution toward plausible regions without modifying the flow objective or training procedure. Building on this, we introduce a latent edit-based rate parameterization that models variable-length generation via edit operations conditioned on a shared global latent, akin to a latent variable model, while remaining tractable. We further introduce a latent classifier-free guidance mechanism that steers generation coherently in continuous latent space, along with Dirichlet-prior temperature scaling for test-time control over edit operations. Our method achieves state-of-the-art performance across diverse biological sequence tasks, including density estimation, unconditional and conditional DNA sequence generation, and peptide sequence generation.

Diffusion and flow matching have emerged as expressive generative planners for autonomous driving planning, owing to their ability to model high-fidelity and multi-modal trajectory distributions. Nevertheless, existing generative planners are predominantly optimized through imitation learning, which induces a fundamental mismatch between supervised trajectory fitting and closed-loop planning metrics, while their iterative sampling procedures often impose substantial computational overhead. In this paper, we propose FlashPlanner, a goal-conditioned flow-matching planner with online RL finetuning for closed-loop AD planning. FlashPlanner introduces a continuous future goal point as a compact navigation interface for the generative planning policy. This goal is produced by a continuous goal predictor, which is first pretrained and subsequently optimized with RL using closed-loop feedback from multiple candidate goals at each decision step. To support efficient online reinforcement fine-tuning and real-time deployment, FlashPlanner adopts a data-prediction flow-matching objective and removes redundant architectural components in existing diffusion-based planners. Experiments on the closed-loop nuPlan and interPlan benchmarks demonstrate that \textit{FlashPlanner} achieves state-of-the-art planning performance while delivering 6× faster inference (166 FPS) than the previous SOTA baseline (28 FPS). We will open-source our project.

Diffusion models have become a leading approach in visual generative modeling, particularly effective in text-to-image and controllable generation. Their main drawback is slow inference as it requires many sampling steps. While recent distillation methods enable one-step text-to-image generation, extending these techniques to controllable generation is still challenging. Existing controllable models, such as ControlNet, rely on dual-branch design that make distillation difficult. In this work, we adopt a simpler strategy. Instead of adding extra conditional branches, we finetune a selected subset of layers in the original text-to-image diffusion model to directly enable controllable generation. This results in DeltaControl, a single-flow, multi-step diffusion model capable of supporting spatial-condition generation while matching the performance of dual-branch approaches. Building on this teacher model, we further apply step-distillation to obtain FlashControl, a one-step model capable of spatial controllable generation with a single forward pass.

Masked Generative Models (MGMs) enable parallel decoding and achieve strong performance across modalities, but require full-sequence bidirectional transformers at every step, making training costly and degrading quality under low sampling budgets. Existing work improves efficiency via better samplers or fixed-depth backbones, but does not vary the depth of the denoiser across sampling steps. We introduce Fixed-Point Masked Generative Models (FP-MGMs), which replace part of the denoiser with a fixed-point solver over shared attention layers to enable adaptive depth with fewer parameters. To make it more effective for masked generation, we first introduce a cross-step consistency loss, which aligns hidden representations at neighboring denoising steps and, second, three-state reuse (3SR) which warm-starts the solver using the previous solution by treating unchanged, still-masked, and newly revealed tokens differently. Together, these components define our complete training-to-inference framework for fixed-point masked generation, \emph{CoFRe}. We also show that pre-trained MGMs can be converted into FP-MGMs with short fine-tuning, avoiding full retraining. Across modalities, CoFRe improves the quality and cost trade-off. On OpenWebText, CoFRe reduces parameters by 38.8\%, training time by 11.5\%, and VRAM by 16.9\%, while improving generative perplexity from 830.8 to 101.8 at a budget of $96$ transformer-block forward passes, compared to MDLM. In ImageNette, CoFRe reduces training time by 48.6\% and VRAM by 50.7\%, while improving FID in all sample budgets tested. Overall, CoFRe offers a practical framework for cheaper training and stronger low-budget masked generation.

Diffusion large language models (DLLMs) have emerged as powerful generative models with the promise of fast text generation through parallel decoding. However, realizing this potential in practice remains challenging: reducing the number of decoding steps, typically causes a substantial degradation in output quality due to token factorization error. To alleviate this, we propose a self-distillation framework that trains a few-step student to match the \emph{generative trajectory} of a full-step teacher. We theoretically and empirically show that trajectory-level supervision mitigates this factorization error, thereby enabling effective few-step decoding. We further incorporate Direct Discriminative Optimization (DDO), a reverse-KL objective that encourages mode-seeking toward the teacher’s modes, yielding stronger performance on challenging reasoning tasks. Across reasoning and code-generation benchmarks, our method substantially narrows the gap between few-step and full-step decoding.

All-atom generative modeling of $3\mathrm{D}$ biomolecular complexes has emerged as the dominant paradigm for predicting the structure of proteins and protein-ligand systems. Generating structures at the atomic level of fidelity, however, typically requires expensive iterative diffusion rollouts, making both conventional deployment and inference-time search techniques computationally costly. In this paper, we introduce the $\textbf{De}$noiser $\textbf{C}$ofolding $\textbf{A}$ll-atom $\textbf{F}$lowmap (DeCAF) framework for distilling state-of-the-art all-atom cofolding models into all-atom flow maps that produce high-quality samples in only a few inference steps. We build DeCAF on a denoiser-based formulation of flow maps with endpoint losses that naturally support $\mathrm{SE(3)}$ rigid alignment, which we show is critical for training accurate models. We further derive a simple change of variables that lets DeCAF operate in the $\sigma$-space noise schedule of EDM-style architectures, enabling direct distillation from pretrained cofolding diffusion models. Equipped with DeCAF's flowmap lookahead, we introduce a purpose-built inference-time framework that improves sampling through reward-guided search. Empirically, DeCAF statistically improves over Boltz-1(x) in both accuracy (RMSD) and physical validity scores of protein-ligand poses at strict NFE budgets on the challenging Runs N’ Poses, while also showing a more optimal Pareto frontier across all inference compute budgets on PoseBusters.

Diffusion models generate data through a continuum of denoising problems, and are widely observed to reveal coarse structure before fine detail. Yet, this intuition is mostly empirical and qualitative. We introduce \emph{feature information dynamics}, an information-theoretic framework for localizing when a feature is generated during diffusion. Using the I-MMSE identity, we connect the rate of feature mutual information change to a gap between optimal unconditional and feature-conditional denoising losses, yielding practical estimators for feature information density. We further develop a chained decomposition that separates shared from incremental information in a feature hierarchy. We use this framework first to quantitatively confirm spectral autoregression in pixel diffusion, and then to extend the analysis beyond frequency: under a class$\to$mask$\to$Canny conditioning chain, the per-feature information densities differ across pixel, SDVAE, VAVAE, and RAE, exposing fundamental differences between these representations.

Diffusion large language models promise parallel token generation, yet inference remains bottlenecked by deciding which masked tokens can be safely committed together. Fast-dLLM addressed this with KV caching and confidence-guided parallel decoding, but its decoding theory uses a homogeneous high-confidence assumption that effectively reduces each candidate set to its weakest selected token. We argue that this leaves speed on the table because real decoding steps exhibit heterogeneous confidence profiles. We propose **Fast-dLLM++**, a training-free extension that introduces *Fr\'{e}chet profile decoding*: selecting parallel commit sets from the full sorted confidence profile rather than a single worst-case confidence. The resulting rule is a heterogeneous-confidence generalization of Fast-dLLM's factor selector and it recovers the previous rule exactly in the equal-confidence case and adds a provable *heterogeneity bonus* when the selected tokens have uneven confidences. Fast-dLLM++ leaves the model, diffusion process, and cache implementation entirely unchanged, making it a drop-in replacement for existing Fast-dLLM decoding. Experiments on GSM8K, MATH, HumanEval, and MBPP with the LLaDA-8B model show that the theoretical improvement translates directly into empirical gains: profile-aware selection improves the accuracy-throughput frontier by exploiting safe parallelism that weakest-token rules miss, achieving up to 37\% higher throughput at comparable accuracy. Our anonymous code release is at https://anonymous.4open.science/r/fast-dllm-plus-plus/.