NeurIPS 2026 论文列表

Acceleration for deterministic root-finding problems has been extensively studied in recent years; specifically, the anchor-based, or Halpern-type methods achieve optimal convergence rates with respect to the operator norm. However, acceleration via these methods does not directly carry over to stochastic setting due to accumulation of errors, unless one enforces diminishing variance via increasing batch sizes or variance reduction techniques. In this work, we show that another class of acceleration, namely the *dual-anchor* mechanism, extends to the stochastic setting without such error accumulation, in contrast to anchor-based algorithms. Consequently, we cleanly achieve $\mathcal{O}(\epsilon^{-3})$ complexity with iteration-independent batch size, without any variance reduction or double-loop recursive regularization, for stochastic root-finding (*resp.* fixed-point) problems with cocoercivity (*resp.* square-nonexpansivity) in expectation. For strongly monotone operators, the same algorithm attains a sharper $\widetilde{\mathcal{O}}(\epsilon^{-2})$ complexity, nearly matching the lower bound.

Echo State Networks (ESNs) are designed to be \emph{stable}—the echo state property makes the reservoir state a well-defined function of the input history—but it remains unclear how \emph{geometrically rich} the reachable reservoir states are and what controls that richness. We give a partition-free, fractal-geometric theory of contractive reservoirs by viewing a quantized-input ESN as a contractive random dynamical system and, equivalently, an iterated function system (IFS). This identifies the reachable set as the IFS attractor and the stationary reservoir-state law under i.i.d.\ inputs as the unique invariant IFS measure. We prove entropy–contraction (entropy–Lyapunov) bounds on the intrinsic dimension of this measure, and in a conformal/similarity regime with standard separation conditions we obtain sharp closed-form dimension laws of the form “input entropy divided by contraction.” These results yield a quantitative \emph{criticality principle}: weakening contraction drives a transition from low-dimensional to full-dimensional state representations at an explicit threshold set by input entropy and contraction rates, providing practical design guidance for tuning leak/spectral radius and input scaling.

We introduce a novel technique for scalable sampling of spin-system states with continuous symmetries using diffusion models. By applying our approach to the XY model, a fundamental continuous-spin model in condensed matter physics, we show that our technique addresses the shortfalls of the Markov chain Monte Carlo (MCMC) in generalization to varying system sizes. More specifically, we show that training a temperature-conditioned diffusion model on smaller-size XY model lattices enables the generation of accurate samples in larger lattice sizes. By tracking physically important observables of the model, such as spin correlations, our experiments demonstrate that diffusion sampling followed by few MCMC steps reduces the thermalization time by an order of magnitude relative to the standard MCMC with random initialization. Our study provides valuable insight as to how generative models can be used to study continuous-state condensed matter systems at scale.

Diffusion language models generate text through iterative denoising, but current interpretability tools mostly analyze static hidden states and do not explain how concept information evolves across denoising time. We introduce DynaManifold-SAE, a method for discovering sparse autoencoder feature groups whose activations form time-dependent concept manifolds in masked and diffusion language models. The method builds sparse latent codes across mask ratios, constructs candidate feature groups, and evaluates them with held-out coordinate prediction, geodesic consistency, persistence across time, and causal interventions. Across BERT and LLaDA, DynaManifold-SAE reliably identifies sparse sentiment geometry that is stable across seeds and stronger than individual-feature, PCA, random-group, and graph-structured baselines. The discovered groups transfer from controlled templates to natural SST-2 examples, indicating that they capture semantic structure rather than template artifacts. We further show that these groups explain a denoising-specific mechanism: they predict token reveal order and confidence growth during LLaDA unmasking, and targeted interventions alter reveal confidence and token recovery more than matched controls. These results suggest that sparse feature manifolds provide a practical bridge between static representation geometry and the dynamics of diffusion language generation.

Masked diffusion language models generate text through iterative masked-token filling, but terminal-only rewards on final completions provide coarse credit assignment for the intermediate filling decisions that shape the generation process. We propose Diffusion-State Policy Optimization (DiSPO), a plug-in credit-assignment layer that directly optimizes intermediate filling decisions. At selected intermediate masked states, DiSPO branches by resampling the currently masked positions from rollout-cached logits, scores the resulting completions, and updates only the newly filled tokens, requiring no additional multi-step diffusion rollouts or optimizer steps. We formalize a fixed-state objective for branched completions and derive a policy-gradient estimator that reuses the same rollouts as terminal-feedback policy optimization. Experiments on LLaDA-8B-Instruct show that DiSPO consistently improves terminal-feedback baselines, including diffu-GRPO and SPG, on math and planning benchmarks under matched rollout compute and optimizer steps, supporting its use as a general plug-in for masked diffusion policy optimization.

Video diffusion alignment has been heavily reliant on scalar rewards. These rewards are typically derived from learned reward models in human preference datasets, requiring additional training and extensive collection. Moreover, scalar rewards provide coarse, global supervision, offering limited prompt-generation mismatch credit assignment and making models prone to reward exploitation and unstable optimization. We propose \textbf{Diffusion-DRF}, a free, rich, and differentiable reward framework for video diffusion fine-tuning. Diffusion-DRF employs a frozen, off-the-shelf Vision-Language Model (VLM) as the critic, eliminating the need for reward model training. Instead of relying on a single scalar reward, it decomposes each user prompt into multi-dimensional questions with freeform dense VQA explanation queries, yielding information-rich feedback. By direct differentiable optimization over this rich feedback, Diffusion-DRF achieves stable reward-based tuning without preference datasets collection. Diffusion-DRF achieves significant gains both quantitatively and qualitatively, outperforming state-of-the-art Flow-GRPO by 4.74 points in overall performance on unseen VBench-2.0.

Distillation and Reinforcement Learning (RL) fine-tuning are the primary pillars of diffusion post-training. While traditionally studied in isolation, the interaction between these phases remains poorly understood, and in particular how fine-tuning impacts the generative quality of distilled models. We introduce Rewarded Moment Matching Distillation (RMMD), a novel framework that simultaneously distills diffusion models and maximizes a reward function. RMMD preserves the high-fidelity "naturalness" characteristic of advanced distillation (e.g., 8-step Moment Matching) by adapting the sampling loop for on-policy training and repurposing the distillation loss as a proxy for integral KL regularization. By evaluating the FID-Reward Pareto fronts on ImageNet, we demonstrate that RMMD achieves superior trade-offs compared to single-step baselines (DI++) and multi-step competitors (DRaFT, HyperNoise). Finally, we apply RMMD to GenCast, a state-of-the-art weather forecasting model, to distill it while optimizing the Continuous Ranked Probability Score (CRPS) metric. The resulting distilled model achieves a 7.5x speedup while outperforming the teacher model on 93% of target weather variables, and being better calibrated. This proves that RMMD scales to complex, high-dimensional scientific domains.

Diffusion-based foundation models for crystal generation have become competent priors over the manifold of plausible materials, but turning that prior into generation of promising candidates requires targeting stability while balancing several conflicting properties at once. Fine-tuning is expensive and produces a new model for every new objective, while differentiable guidance is not applicable to many real-world rewards. We instead adapt these models at \emph{inference time} using Diffusion Tree Search (DTS), a Monte Carlo tree search procedure over the denoising trajectory. We make two technical contributions on top of DTS that are particularly relevant for AI-for-science applications. First, we show how to use existing property-conditional foundation models (e.g., classifier-free guidance variants of MatterGen) as guided proposals inside DTS, with importance-corrected backups and selection that keep the unconditional base model as the target distribution. Second, we extend DTS to multi-objective sampling by maintaining per-objective soft value estimates and selecting expansions through a sampled scalarization, so a single search produces samples spanning a Pareto front while sharing computation across preferences. We instantiate both adaptations on de novo crystal generation: single-objective stability search with different underlying models, conditional generation of crystals belonging to rare space groups, and a multi-objective tasks using a pretrained conditional model. Across these, DTS-based inference-time adaptation improves stability rates and Pareto-front quality without modifying the base models.

Residual connections with PreNorm are the default design in modern transformers due to their strong optimization stability, but recent research has shown that they weaken the functional differentiation of deeper blocks and increase representational redundancy in later layers. This issue also appears in diffusion models using similar architectures, where the deep block is expected to support progressive denoising refinement rather than repeated computation over similar states. Motivated by this, we revisit cross-layer shortcuts in diffusion transformers and argue that their role should go beyond merely transferring shallow information, instead guiding deeper blocks to improve depth utilization. To this end, we propose \textit{\textbf{Res}idual Adaptive Layer \textbf{Norm}alization} (\textbf{ResNorm}), which routes residual cross-layer shortcuts into the existing adaLN modulation. ResNorm preserves the optimization advantages of PreNorm residual connections, while reusing the native adaLN interface to transmit early-layer representations as modulation signals. This design naturally combines cross-layer history with the model's native condition, such as timestep and class embeddings. ResNorm allows the earlier structural representation to adaptively scale, shift, and gate deeper blocks. This not only produces more differentiated deep representations and reduces cross-layer similarity in later blocks, but also accelerates training convergence and improves performance. On ImageNet 256$\times$256, SiT-XL/2 + ResNorm achieves up to $\textbf{2}\times$ and $\textbf{36}\times$ faster training than SiT-XL/2 + REG and SiT-XL/2 + REPA. Moreover, SiT-L/2 + ResNorm trained for only 400K iterations already outperforms SiT-XL/2 + REG.

Long-form spatial reasoning in vision--language models (VLMs) is often bottlenecked by autoregressive chain-of-thought (CoT) decoding, where intermediate reasoning traces and final answers are generated token by token. This sequential decoding path makes high-quality spatial reasoning expensive in latency-sensitive embodied and interactive settings. We propose \emph{Diffusion Thinking}, a post-training framework that converts pretrained autoregressive VLMs into diffusion-style reasoners for fast long-form spatial inference without changing the visual encoder or language backbone. Diffusion Thinking partitions each CoT trace into blocks and refines tokens within the current block in parallel through discrete denoising, while preserving causal dependence across blocks and reusing KV cache for streaming generation. This creates a high-speed operating point, but aggressive parallel refinement can weaken fine-grained reasoning. To address this, we introduce \emph{Diffusion Rethinking}, a cached test-time scaling mechanism that reallocates part of the saved latency budget to self-correction rounds, yielding a controllable speed--accuracy frontier. We construct a 561K-instance Long-CoT Spatial Reasoning dataset with verified final answers and generated CoT traces across six spatial task types. Across Qwen2.5-VL and InternVL3 backbones, Diffusion Thinking with block size $D=32$ achieves 38.18--41.81$\times$ effective wall-clock speedup over autoregressive Long-CoT decoding. With eight rethinking rounds, it retains 4.20--4.60$\times$ speedup and matches or surpasses autoregressive Long-CoT accuracy on the largest backbones. These results show that diffusion-style compute reallocation is a practical path toward fast, accurate long-form spatial reasoning in VLMs.

Offline goal-conditioned reinforcement learning (GCRL) learns goal-directed policies from reward-free data, but in long-horizon tasks, goal-conditioned value functions often provide unstable guidance due to sparse rewards and discounting. Hierarchical methods partially mitigate this issue via subgoal decomposition; however, high-level decision-making still relies on noise-sensitive value estimates, leading to unstable behavior in complex environments. We address this limitation by proposing \textbf{D}iffusion \textbf{S}ubgoal \textbf{P}lanning (\textbf{DSP}), a diffusion-based framework for high-level subgoal generation. DSP casts high-level planning as guided generative inference over goal-conditioned subgoals and learns both conditional and unconditional flows, enabling classifier-free guidance to introduce a goal-directed bias at inference time. By removing explicit value-based guidance from high-level planning, DSP generates reachable and goal-directed subgoals through a generative model while retaining hierarchical execution. Experiments on offline GCRL benchmarks demonstrate that DSP outperforms prior methods on a range of navigation and manipulation tasks, with particularly strong performance in maze environments that require multi-step subgoal planning.

We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a simple base distribution and the target, popularised by diffusion models. We tackle the score estimation problem by developing an efficient sequential Monte Carlo sampler that evolves auxiliary variables from conditional distributions along the path, providing principled score and density estimates for time-varying distributions. To control the variance of score estimates, we further propose practical control variate schedules that incur minimal overhead. We adapt this general framework to paths induced by the Ornstein–Uhlenbeck (OU) time-reversal process, stochastic interpolants, and diffusion annealed Langevin dynamics, outlining their trade-offs. Finally, we provide theoretical guarantees and empirically demonstrate the effectiveness of our method on several synthetic and real-world datasets.

Classifier-free Guidance (CFG) is central to modern diffusion models, but operates as an inference-time correction where the training objective learns the unbiased conditional score, while guided sampling targets a posterior-tilted score that never explicitly learned. Rather than another inference-time patch or distillation, Model-guidance (MG) directly integrates the posterior tilt into the training objective and eliminates CFG during inference. MG serves as a plug-and-play module compatible with existing methods, yet accelerates convergence by online self-bootstrapping and doubles inference speed. Unlike distillation surrogates, a reparameterisation property reveals that MG implicitly learns the vanilla score without mode collapse. Extensive experiments demonstrate that MG matches and even surpasses CFG baselines, and achieves a state-of-the-art FID of $1.34$ on ImageNet $256$ benchmark.

Score-based diffusion models are typically trained by minimizing the $L^2$ score matching error, and standard theoretical analyses rely on this quantity to bound the sampling discrepancy between the learned and target distributions. We show the $L^2$ score error is not the right intrinsic measure of marginal distributional quality: a learned diffusion model can incur arbitrarily large $L^2$ score error while perfectly matching the target distribution. By decomposing score errors into a gradient and a solenoidal component (a Helmholtz-Hodge decomposition), we identify the geometric reason behind this: only the gradient component enters the marginal Fokker-Planck dynamics, while the solenoidal component is structurally invisible. We make this precise in three results. First, building on the corrected geometry, we prove an impossibility result: no monotone function of the $L^2$ score error can uniformly lower bound any divergence between the learned and target distributions. Second, we derive an upper bound on the Kullback-Leibler divergence that depends only on the observable gradient component of the error, tightening the standard Girsanov bound and identifying its looseness as the cost of operating on path-space rather than marginal-space dynamics. Third, we give a tractable estimator of the gradient component via a dual Sobolev identity, which is shown to empirically correlate substantially better with sample quality than the full $L^2$ error.

We study a data-dependent notion of diffusion-model generalization: when a model does not memorize the training set, where do its generated samples go relative to the geometry induced by the data? To answer this, we introduce a time-dependent family of log-density ridge manifolds constructed from the smoothed empirical distribution, and use it to characterize reverse-time inference. Our main result shows that generated samples evolve by a **reach-align-slide** mechanism: they first enter a neighborhood of the ridge, then their distance to the ridge is controlled by the normal component of training error, and finally their motion along the ridge is controlled by the tangential component. We further connect this geometric picture to training dynamics through directional decompositions of the learned error, and make this link explicit for random feature models, where architectural bias and optimization error can be separated quantitatively. Experiments on synthetic multimodal data and MNIST latent diffusion support the predicted geometric behavior in both low and high dimensions.

Prompt learning is a popular parameter-efficient method for adapting foundation models, but learned prompts are typically task-specific and fail to generalize to new classes, domains, or compositions of tasks. In this paper, we introduce a $\textbf{Diffusion Meta-Prompt (DMP)}$ model , a framework that models the distribution of learned prompts using diffusion models. DMP is trained only on a repository of previously learned prompts to synthesize new prompts conditioned on natural language task descriptions, without access to the task data. To improve the sampling stability, we introduce a test-time steering strategy for DMP, which uses the best training-selected prompt in the repository as a latent anchor during diffusion sampling, without retraining the DMP or accessing test classes. DMP improves generalization across classification, retrieval and text-to-image generation tasks, supports concept composition and negative prompting without explicit training. It reduces storage and inference costs by over 90% compared to prompt retrieval methods. For composite classification, DMP achieves upto $\textbf{2.0}$% average gain over prior meta-learning methods across 55 pairs of datasets with gains as high as $\textbf{8.5}$% on specific pairs such as Eurosat and Flowers. DMP also enhances cross-task generalization with $\sim$$\textbf{2-9}$% improvement for hierarchical classification task. We further provide a theoretical guarantee bounding the expected task loss of prompts sampled from a DMP.

Dynamic point cloud pretraining is still dominated by masked reconstruction objectives. However, these objectives inherit two key limitations. Existing methods inject ground-truth tube centers as decoder positional embeddings, causing spatio-temporal positional leakage. Moreover, they supervise inter-frame motion with deterministic proxy targets that systematically discard distributional structure by collapsing multimodal trajectory uncertainty into conditional means. To address these limitations, we propose Diffusion Masked Pretraining (DiMP), a unified self-supervised framework for dynamic point clouds. DiMP introduces diffusion modeling into both positional inference and motion learning. It first applies forward diffusion noise only to masked tube centers, then predicts clean centers from visible spatio-temporal context. This removes positional leakage while preserving visible coordinates as clean temporal anchors. DiMP also reformulates point-wise inter-frame displacement supervision as a DDPM noise-prediction objective conditioned on decoded representations. This design drives the encoder to target the full conditional distribution of plausible motions under a variational surrogate, rather than collapsing to a single deterministic estimate. Extensive experiments demonstrate that DiMP consistently improves downstream accuracy over the backbone alone, with absolute gains of 11.21% on offline action segmentation and 13.65% under causally constrained online inference.

Diffusion language models (DLMs) provide a bidirectional generation framework naturally suited for infilling, yet their performance is constrained by the pre-specified infilling length. In this paper, we reveal that DLMs possess an inherent ability to discover the correct infilling length. We identify two key statistical phenomena in the first-step denoising confidence: a local Oracle Peak that emerges near the ground-truth length and a systematic Length Bias that often obscures this signal. By leveraging this signal and calibrating the bias, our training-free method CAL (Calibrated Adaptive Length) enables DLMs to approximate the optimal length through an efficient search before formal decoding. Empirical evaluations demonstrate that CAL improves Pass@1 by up to 47.7% over fixed-length baselines and 40.5% over chat-based adaptive methods in code infilling, while boosting BLEU-2 and ROUGE-L by up to 8.5% and 9.9% in text infilling. These results demonstrate that CAL paves the way for robust DLM infilling without requiring any specialized training.

While Large Vision-Language Models (LVLMs) excel at bounding-box grounding, they struggle with precise spatial tasks such as polygon grounding. We attribute this bottleneck to two properties of the vertex-level autoregressive (AR) paradigm used by current LVLMs: (1) errors in early-emitted vertices propagate uncorrected through the rest of the sequence, and (2) the model commits to local vertex placement before observing the full contour, leading to suboptimal allocation of a fixed vertex budget. We propose Diffusion Fine-Tuning (DFT), which removes the vertex-level sequential dependency by placing all 2N coordinate tokens under a single discrete-diffusion denoiser, while introducing a much shorter digit-level factorisation: each coordinate is decomposed into hundreds, tens, and units digits, and the reverse process is trained to predict them coarse-to-fine. We train this with a Hierarchical Curriculum Learning strategy that progressively refines loss supervision from macro-contour to per-pixel detail. Under matched fine-tuning protocols, DFT matches strong AR LVLMs on 2D bounding-box grounding and improves over them on 16-point polygon grounding; the same network and training recipe extend to 9-DoF monocular 3D bounding-box grounding under a 9-parameter coordinate parameterisation. A block-wise top-k decoder closes most of the latency gap to AR and recovers most of the quality lost when scaling beyond 16 vertices. We do not claim to eliminate sequential dependence in general: vertex-level O(N) AR decoding is replaced by K joint denoising steps (K=12 in this work), with the three-stage digit hierarchy entering as a training-time loss factorisation rather than an inference-time chain.