NeurIPS 2026 Papers

Inference-time methods that generate, aggregate, and prune multiple parallel reasoning traces have emerged as a powerful paradigm for steering large language models, yet we lack a principled understanding of their accuracy--cost tradeoffs. We develop such an understanding for multi-particle methods, which maintain multiple partial chains of thought and use a process reward model (PRM) to adaptively score, prune, and replicate them. We focus on Sequential Monte Carlo (SMC), the simplest and most canonical such method. Despite SMC's long history in statistics and recent adoption for steering language and diffusion models, non-asymptotic guarantees have remained elusive. We provide (1) a simple, user-friendly analysis identifying two natural criteria which suffice for non-asymptotic convergence of SMC; (2) a simple modification of SMC achieving stronger, horizon-free guarantees when the PRM is near-perfect; and (3) a fundamental limit faced by all myopic multi-particle methods in the presence of PRM approximation errors. Empirically, we find that our criteria effectively predict the sampling error of SMC though not necessarily its final accuracy, paving the way for future work incorporating theoretical perspectives beyond sampling.

The success of deep learning in medical image analysis is often hindered by the long-tail distribution of disease cases, where rare or early-stage tumors are critically under-represented. While controllable synthesis offers a potential solution, existing methods suffer from a \textit{specification bottleneck}, as low-dimensional signals like text or binary masks fail to capture complex textures and morphological variations. In this paper, we propose an exemplar-driven synthesis framework that utilizes real tumor samples as high-dimensional templates to enable precise, case-specific generation. To the best of our knowledge, this is the first work to introduce reinforcement learning (RL) into the field of 3D medical image generation, called **MedGRPO**. We formulate the unpaired tumor synthesis task as a constrained trajectory optimization problem and leverage Flow-GRPO to find an optimal generation path. By designing a multi-objective reward system encompassing texture, shape, and semantic consistency, our model effectively balances pathological fidelity with anatomical coherence without requiring paired supervision. Rigorous evaluations across four major tumor types and the external AbdomenAtlas 2.0 dataset demonstrate that our method produces high-fidelity synthetic data that significantly enhances the performance of downstream diagnostic models.

Reinforcement learning (RL) has been effective for post-training autoregressive (AR) language models, but extending these methods to diffusion language models (DLMs) is challenging due to intractable sequence-level likelihoods. Existing approaches therefore rely on surrogate likelihoods or heuristic approximations, which can introduce bias and obscure the sequential structure of denoising. We formulate diffusion-based sequence generation as a finite-horizon Markov decision process over the denoising trajectory and derive the policy gradient that decomposes over denoising steps in terms of stepwise advantages, without requiring explicit evaluation of the sequence likelihood. Grounded in this theorem, we develop tractable approximations for large-scale training: (i) denoising steps are selected for policy updates via an entropy-guided approximation bound, and (ii) stepwise advantages are estimated using a one-step denoising completion naturally provided by the diffusion model, avoiding costly multi-step rollouts or auxiliary value networks. Experiments demonstrate state-of-the-art results on nearly all benchmarks spanning coding, logical reasoning, and mathematical reasoning, outperforming existing RL post-training approaches for DLMs.

Diffusion and flow-matching models scale because pretraining simply regresses against a closed-form target built by analytically noising clean data samples. In many settings, only a reward function is available, scoring how desirable a generation is, so training must proceed online from a pretrained model. Existing methods either rely on costly SDE rollouts, sometimes with reward gradients, or adopt heuristic reward-dependent variants of the pretraining objective. Under a stochastic optimal control formulation of KL-regularized reward maximization, the optimal generative process tilts only the clean-endpoint distribution and leaves the conditional noising law unchanged. Combining this path-space characterization with the adjoint-matching optimality condition and a REINFORCE estimator to avoid reward gradients, we derive Reinforce Adjoint Matching (RAM). At each step, we draw a clean endpoint from the current model with any off-the-shelf sampler, evaluate its reward, noise it to several training states, and regress against a closed-form, reward-weighted target. Like the pretraining objective, RAM is simple and scales. On Stable Diffusion 3.5M, RAM achieves the highest reward on composability, text rendering, and human preference. It is much more training efficient, reaching Flow-GRPO's peak GenEval accuracy in~$50\times$ fewer training steps.

Recent advances in generative modeling have enabled the efficient computation of Schrödinger bridges (SB) in high-dimensional settings by leveraging partially simulation-free training methods inspired by flow matching. However, these have not covered SBs with reflecting dynamics, a useful model choice with built-in guarantees that generated samples stay in the data domain. Existing alternatives for reflected SBs instead rely on more complex training based on forward--backward SDE theory, requiring expensive higher-order derivatives and sampling entire paths during training. In this article, we introduce a partially simulation-free framework that allows reflected SBs to be trained similarly to flow matching, using a new sampling method and regression target. We demonstrate our results by coupling pairs of well-known high-dimensional image datasets. Using reflected dynamics incurs negligible additional wall-clock time during both training and inference while maintaining or slightly improving generative performance.

Compositional diffusion planning generates long-horizon trajectories by stitching together overlapping short-horizon segments through score composition. However, when local plan distributions are multimodal, existing compositional methods suffer from mode-averaging, where averaging incompatible local modes leads to plans that are neither locally feasible nor globally coherent. We propose *Refining Compositional Diffusion* (RCD), a training-free guidance method that steers compositional sampling toward high-density, globally coherent plans. RCD leverages the *self-reconstruction error* of a pretrained diffusion model as a proxy for the log-density of composed plans, combined with an *overlap consistency* term that enforces consistency at segment boundaries. We show that the combined guidance concentrates sampling on high-density plans that mitigate mode-averaging. Experiments on challenging long-horizon tasks from OGBench, including locomotion, object manipulation, and pixel-based observations, demonstrate that RCD consistently outperforms existing methods. Project website at [https://refining-compositional-diffusion.github.io/](https://refining-compositional-diffusion.github.io/).

Image-to-video generation powers a vast array of downstream applications. However, while the de facto standard, ie, latent diffusion models, typically employ heavily conditioned denoising networks, their decoders often remain unconditional. We observe that this architectural asymmetry leads to significant loss of detail and inconsistency relative to the input image. To address this, we argue that the decoder requires equal conditioning to preserve structural integrity. We focus specifically on image-based generation tasks, where maintaining the structural and textural integrity of the source image is paramount. We introduce RefDecoder, a reference-conditioned video VAE decoder by injecting the reference image directly into the decoding process via reference attention. Specifically, a lightweight image encoder maps the reference frame into the detail-rich high-dimensional tokens, which are co-processed with the denoised video latent tokens at each decoder up-sampling stage. We demonstrate consistent improvements across several distinct decoder backbones (eg, Wan 2.1 and VideoVAE+) achieving consistent improvement on three reconstruction benchmarks. Notably, RefDecoder can be directly swapped into existing video generation systems without additional fine-tuning, and we report across-the-board improvements in subject consistency, background consistency, and overall quality scores on the VBench I2V benchmark. Furthermore, RefDecoder generalizes well to other visual generation tasks such as style transfer.

Recursive training of generative models on their own outputs can lead to model collapse, a compounding drift away from the true data distribution. Existing theoretical works bound finite-round error accumulation in the context of diffusion models, but two questions remain open:~what distribution does the recursion converge to, and how fast? We answer both, isolating a mechanism distinct from imperfect learning: even with perfect score estimation and exact sampling, the early stopping of the reverse diffusion (required for numerical stability) drives a progressive drift away from the data distribution. We prove that this recursion converges geometrically to a unique limiting distribution, which admits a closed-form characterization as an infinite mixture of increasingly Gaussian-smoothed versions of the data distribution. A Hermite spectral decomposition of this limit reveals that recursive training acts as a low-pass filter: higher-order modes, which encode fine non-Gaussian structure, are attenuated much more strongly than coarse modes. This spectral picture motivates annealed truncation schedules that progressively shrink truncation times across retraining rounds; we prove that any schedule converging to $0$ asymptotically eliminates recursive compounding. Finally, we show our idealized characterization is robust: in the presence of discretization and score estimation errors, the learned distribution remains in a Wasserstein-2 ball around the ideal limit, with mode-dependent contraction rates that contract high-order errors faster than low-order ones. We validate the theory on synthetic Gaussian mixtures and CIFAR-10.

World model-based policy evaluation is a practical proxy for testing real-world robot control by rolling out candidate actions in action-conditioned video diffusion models. As these models increasingly adopt latent diffusion modeling (LDM), choosing the *right latent space* becomes critical. While the status quo uses autoencoding latent spaces like VAEs that are primarily trained for pixel *reconstruction*, recent work suggests benefits from pretrained encoders with representation-aligned *semantic* latent spaces. We systematically evaluate these latent spaces for action-conditioned LDM by comparing six reconstruction and semantic encoders to train world model variants under a fixed protocol on BridgeV2 dataset, and show effective world model training in high-dimensional representation spaces with and without dimension compression. We then propose three axes to assess robotic world model performance: visual fidelity, planning and downstream policy performance, and latent representation quality. Our results show visual fidelity alone is insufficient for world model selection. While reconstruction encoders like VAE and Cosmos achieve strong pixel-level scores, semantic encoders such as V-JEPA 2.1 (strongest overall on policy), Web-DINO, and SigLIP 2 generally excel across the other two axes at all model scales. Our study advocates semantic latent space as stronger foundation for policy-relevant robotics diffusion world models.

Masked diffusion language models (MDLMs) generate text by unmasking tokens in parallel and have recently emerged as alternatives to autoregressive language models. They can be viewed as parallel decoders trained with a position-wise cross-entropy (CE) loss, the same setup as non-autoregressive translation (NAT). In NAT, CE-trained parallel decoders have been argued to be sensitive to small positional shifts, since CE penalizes them harshly. We ask whether CE-trained MDLMs are similarly sensitive to such shifts under iterative decoding. To probe this, we apply a controlled intervention that introduces them during decoding. On LLaDA-8B-Instruct with Arena-Hard, displacing as little as 1\% of generated tokens by one position substantially reduces win rates against the unintervened model, showing that MDLMs are sensitive to such small shifts under iterative parallel decoding. Motivated by this, we adapt connectionist temporal classification (CTC), an alignment-flexible objective known to mitigate it there, to MDLM supervised fine-tuning. By relaxing the strict position-wise match that CE imposes, CTC gives the loss room to absorb small positional shifts; concretely, we modified CTC objective to use a special \ token that absorbs positional uncertainty between target tokens and output positions, and a updated collapse map that preserves target surface forms. Across four open-ended generation benchmarks, the resulting model consistently improves over both the original model and a matched cross-entropy-trained baseline, with statistically significant gains on all four. These results identify training-side alignment flexibility as a useful design dimension for MDLM SFT, complementary to the inference-time approaches explored in prior work.

Discrete diffusion models have recently become competitive with autoregressive models for language modeling, even outperforming them on reasoning tasks requiring planning and global coherence, but diffusion requires more computation at inference time. We trace this trade-off to a key mechanism: diffusion models are trained to jointly predict all unknown tokens simultaneously, including those that will not actually be decoded in the current step. Ablating this joint prediction yields faster inference but degrades performance, revealing that accurate prediction at the decoded position relies on joint reasoning about the undecoded tokens. We interpret these undecoded positions as latent tokens and introduce a method for modulating their number, achieving a smooth tradeoff between inference speed and sample quality. Furthermore, we demonstrate that latent tokens can be introduced into autoregressive models through an auxiliary multi-token prediction objective, yielding substantial improvements on the same reasoning tasks where they have traditionally struggled. Our results suggest that latent tokens--arising from jointly predicting multiple unknown positions--represent a general mechanism for improving performance on tasks requiring global coherence or lookahead.

Understanding how transformers encode position and context is central to interpreting their behavior, because it determines how information flows across tokens and shapes the model's predictions. Common tools, such as linear probes and attribution methods, operate on single-position activations and are not designed to capture cross-position dependencies. We introduce Score-Block Token Geometry (SBTG), a score-based diagnostic that recovers cross-position dependency structure from activations and reveals distinct signatures of positional encoding mechanisms that these methods do not expose. SBTG trains a denoising score model on windows of activations and constructs lag-indexed operators that quantify coupling between positions within a layer. Applied to transformers with different positional encodings, it recovers distinct coupling signatures consistent with their architectures: ALiBi exhibits near rank-one coupling in early layers, RoPE distributes coupling across directions in patterns consistent with its rotation frequencies, and absolute embeddings show the strongest position-specific variation. We show that these signatures are stable across seeds and model sizes, and the activation-space directions identified by SBTG are causally relevant: ablating them causes larger performance drops on tasks that require reasoning over relative positions than on tasks that depend on absolute position signals. These results show that joint activation structure provides a lens on how positional encoding mechanisms are realized, revealing differences in how models use cross-position dependencies that are not apparent from the architecture alone.

In this paper, we propose **SpectraReward**, a training-free reward function that turns pretrained MLLMs into off-the-shelf reward models for image-generation reinforcement learning. Instead of asking the MLLM to judge a generated image or answer decomposed verification questions, SpectraReward measures how well the original prompt can be recovered from the generated image through a single image-conditioned, teacher-forced forward pass. We use the average image-conditioned prompt log-likelihood as the reward, directly reusing the MLLM's pretrained image-text alignment ability without preference labels, reward-model fine-tuning. We further introduce **Self-SpectraReward,** a special case for unified multimodal models where the policy's own understanding branch serves as the reward model for its generation branch, forming a closed-loop self-improving framework without external reward models or external knowledge. Extensive experiments validate SpectraReward through a broad image-generation RL study covering two diffusion models, three RL algorithms, nine reward MLLM backbones from four MLLM families spanning 4B to 235B parameters, and five out-of-distribution text-to-image benchmarks. Results show that both SpectraReward and Self-SpectraReward significantly and consistently improve generation performance and outperform prior MLLM-derived reward training methods. Further analysis reveals that larger reward MLLMs are not always better, while Self-SpectraReward can match or surpass much larger external reward models, suggesting that reward-policy alignment is a key factor for effective image-generation RL.

Recent pixel-space generative models avoid the reconstruction bottleneck of latent diffusion, but direct denoising over high-dimensional pixel tokens remains computationally demanding. This paper studies a recursive alternative for efficient pixel-space diffusion. We propose RePiD, a hierarchical patch-level diffusion framework that recursively partitions an image and performs the core denoising computation on lower-dimensional pixel groups instead of repeatedly operating on full-resolution images. To preserve spatial coherence across patch-wise processing, RePiD introduces a neighborhood embedding module that conditions each patch on its surrounding regions. Experiments on class-to-image generation and unpaired image-to-image translation show that RePiD provides a favorable quality--efficiency trade-off for direct pixel-space generation. These results suggest that recursive patch-level denoising is a practical design direction for efficient pixel-space generative modeling. Our code is publicly available at \textcolor[HTML]{387FB9}{https://anonymous.4open.science/r/Recursive-Pixel-based-Diffusion-Model-1735}.

In recent years there has been a flurry of activity around using pretrained diffusion models as informed data priors for solving inverse problems, and more generally around steering these models towards certain reward models. Training-free methods like gradient guidance have offered simple, flexible approaches for these tasks, but when the reward is not informative enough, e.g., in inverse problems with highly compressive measurements, these techniques can veer off the data manifold, failing to produce realistic data samples. To address this challenge, we devise a simple algorithm, *ReGuidance*, that leverages prior methods' solutions as strong initializations and substantially enhancing their realism. Given a candidate solution $x$ produced by a given method, we propose inverting the solution by running the unconditional probability flow ODE in reverse starting from $x$, and then using the resulting latent as an initialization for a deterministic steering process. Empirically, we evaluate our algorithm on difficult image restoration tasks including large box inpainting, heavily downscaled superresolution, and high noise deblurring with both linear and nonlinear blurring operations. We find that, using a wide range of baseline methods as initializations, applying our method results in much stronger samples with better realism and measurement consistency. We complement these results with rigorous proofs in commonly studied theoretical settings showing our technique boosts the reward and brings $x$ closer to the data manifold.

Reflections reveal scene content beyond the camera's direct field of view, but faithfully recovering this hidden information is challenging as reflective observations are heterogeneous, incomplete, and physically modulated. Existing methods either rely on explicit reflection modeling with privileged geometric priors or defer to generative synthesis that may hallucinate plausible but unfaithful content. To address these challenges, we propose \textbf{ReFlex}, an observation-constrained framework that casts faithful panorama reconstruction as a controlled inverse problem. We first develop an \emph{Observation-Consistent Estimator} with hierarchical token prediction and signed routing to integrate heterogeneous reflection cues while stabilizing global structure. Subsequently, we propose a \emph{Reliability-Guided Refiner}, which estimates spatial reliability from token predictions and guides a frozen diffusion model to refine uncertain regions without overwriting observation-supported structures. To validate the effectiveness of ReFlex, we further build ReFlex-Bench, a paired benchmark with 110,760 reflective RGB inputs and aligned target panoramas across diverse scenes, reflective geometries, and observation regimes. Experiments show that ReFlex delivers superior reconstruction fidelity without normals, field-of-view annotations, masks, or other privileged information, and obtains the best performance on eight of nine downstream full-view perception protocols.

We present Reflow-regularized Flow Matching Policy Gradients (ReFPO), a simple online RL method that adds explicit Reflow regularization to FPO for efficient flow-based control. We uncover a key structural property: the gradient updates in Flow Matching Policy Gradients (FPO) can be interpreted as an implicit advantage-weighted Reflow process, providing a new geometric perspective on flow-based policy gradients. Building on this insight, ReFPO introduces an explicit geometric regularizer that can be implemented with a single line of code change without incurring additional computational overhead or auxiliary distillation stages. By synergizing advantage-guided updates with path rectification, our method reduces CFM proxy-ratio spikes, stabilizes PPO-style training, and enables high-fidelity one-step inference that often matches or exceeds multi-step performance. We experimentally demonstrate that ReFPO improves average performance and discretization robustness across GridWorld, MuJoCo Playground, and high-dimensional Humanoid Control tasks, providing a scalable and stable approach for generative policies in complex physical simulations.

Masked diffusion language models (dLLMs) have recently emerged as a competitive alternative to autoregressive language models, with the promise of faster inference via parallel token generation. A notable limitation of the masked formulation, however, is that once a token has been unmasked it can no longer be revised, leaving dLLMs vulnerable to early sampling mistakes. To address this, a growing body of work has sought to extend masked dLLMs with self-correcting (remasking) capabilities. One appealing subset of these methods does so in a training-free, post-hoc manner based on token confidence, with encouraging early reported results. In this work, we revisit the empirical evaluation of a representative post-hoc remasking method, WINO, and find that under standard decoding settings (shorter block lengths) it brings little-to-no benefit over confidence-based unmasking alone. Extending the evaluation to non-greedy decoding, we find that while confidence-based remasking can mitigate errors introduced by increased stochasticity to some extent, it also exacerbates the diversity collapse previously reported for confidence-based unmasking. Overall, our results show that the benefits of post-hoc confidence-based remasking are highly setting-dependent, underscoring the need for a more comprehensive evaluation framework.

Radar-based human pose estimation is a promising alternative to camera-based perception, but remains challenging due to sparse observations, noisy measurements, and severe pose ambiguity. Existing methods infer both global skeletal structure and flexible peripheral joints from sparse radar observations, often compromising structural plausibility and fine-grained local accuracy. Motivated by the coarse-to-fine nature of human visual perception, we propose RadarFlowPose, a framework that decomposes radar-based human pose estimation into coarse pose prior generation and flow-based refinement. The coarse model first produces a structurally plausible and temporally coherent pose prior from sparse radar observations, providing a global initialization for subsequent refinement. Instead of estimating the full pose from scratch, the refinement stage focuses on correcting the remaining local ambiguities and motion-induced errors. By incorporating localised Doppler motion cues into the flow-matching process, the model performs motion-aware residual refinement around the coarse prior, leading to more accurate and anatomically consistent pose estimates. Experiments on three benchmark radar pose datasets show consistent effectiveness, especially in motion-sensitive and fine-grained joint-level evaluation.