ICLR 2026 论文列表

Diffusion models (DMs) have recently shown remarkable performance on inverse problems (IPs). Optimization-based methods can fast solve IPs using DMs as powerful regularizers, but it is susceptible to local minima and noise overfitting. Although DMs can provide strong priors for Bayesian approaches, enforcing measurement consistency during the denoising process leads to manifold infeasibility issues. We propose Noise-space Hamiltonian Monte Carlo (N-HMC), a posterior sampling method that treats reverse diffusion as a deterministic mapping from initial noise to clean images. N-HMC enables comprehensive exploration of the solution space, avoiding local optima. By moving inference entirely into the initial-noise space, N-HMC keeps proposals on the learned data manifold. We provide a comprehensive theoretical analysis of our approach and extend the framework to a noise-adaptive variant (NA-NHMC) that effectively handles IPs with unknown noise type and level. Extensive experiments across four linear and three nonlinear inverse problems demonstrate that NA-NHMC achieves superior reconstruction quality with robust performance across different hyperparameters and initializations, significantly outperforming recent state-of-the-art methods. Code will be made available on GitHub upon publication.

Masked diffusion models (MDMs) offer a compelling alternative to autoregres- sive models (ARMs) for discrete text generation because they enable parallel token sampling, rather than sequential, left-to-right generation. This means po- tentially much faster inference. However, effective parallel sampling faces two competing requirements: (i) simultaneously updated tokens must be conditionally independent, and (ii) updates should prioritise high-confidence predictions. These goals conflict because high-confidence predictions often cluster and depend on each other, opportunities for parallel updates. We present PUNT, a model-agnostic sampler that reconciles this trade-off. Our method identifies token dependencies and removes lower-confidence tokens from conflicting groups. This produces sets of indices for unmasking that satisfy both independence and confidence criteria. Our approach ensures improved parallel unmasking through approximate conditional independence testing. Our experiments show that PUNT delivers a superior trade-off between accuracy and compute when compared to other strong training-free baselines, especially for generation of longer sequences. On the IFEval benchmark, it achieves up to 16% higher accuracy over baseline methods, including sequential generation (one-by- one). These gains hold across different values of hyperparameters, mitigating the need for brittle hyperparameter tuning. Moreover, we observe that PUNT induces an emergent hierarchical generation strategy, where the model first establishes high-level paragraph structure before local refinement, suggesting a planning-like generation process that contributes to strong alignment performance.

Frontier reasoning models have exhibited incredible capabilities across a wide array of disciplines, driven by posttraining large language models (LLMs) with reinforcement learning (RL). However, despite the widespread success of this paradigm, much of the literature has been devoted to disentangling truly novel behaviors that emerge during RL but are not present in the base models. In our work, we approach this question from a different angle, instead asking whether comparable reasoning capabilities can be elicited from base models at inference time by pure sampling, without any additional training. Inspired by Markov chain Monte Carlo (MCMC) techniques for sampling from sharpened distributions, we propose a simple iterative sampling algorithm leveraging the base models' own likelihoods. Over different base models, we show that our algorithm offers substantial boosts in reasoning that nearly match and even outperform those from RL on a wide variety of single-shot tasks, including MATH500, HumanEval, and GPQA. Moreover, our sampler avoids the collapse in diversity over multiple samples that is characteristic of RL-posttraining. Crucially, our method does not require training, curated datasets, or a verifier, suggesting broad applicability beyond easily verifiable domains.

Diffusion-based language models (dLLMs) have emerged as a promising alternative to traditional autoregressive LLMs by enabling parallel token generation and significantly reducing inference latency. However, existing sampling strategies for dLLMs, such as confidence-based or semi-autoregressive decoding, often suffer from static behavior, leading to suboptimal efficiency and limited flexibility. In this paper, we propose SlowFast Sampling, a novel dynamic sampling strategy that adaptively alternates between exploratory and accelerated decoding stages. Our method is guided by three golden principles: certainty principle, convergence principle, and positional principle, which govern when and where tokens can be confidently and efficiently decoded. We further integrate our strategy with dLLM-Cache to reduce redundant computation. Extensive experiments across benchmarks and models show that SlowFast Sampling achieves up to 15.63× speedup on LLaDA with minimal accuracy drop, and up to 34.22× when combined with caching. Notably, our approach outperforms strong autoregressive baselines like LLaMA3 8B in throughput, demonstrating that well-designed sampling can unlock the full potential of dLLMs for fast and high-quality generation.

Denoising generative models, such as diffusion and flow-based models, produce high-quality samples but require many denoising steps due to discretization error. Flow maps, which estimate the average velocity between timesteps, mitigate this error and enable faster sampling. However, their training typically demands architectural changes that limit compatibility with pretrained flow models. We introduce Decoupled MeanFlow, a simple decoding strategy that converts flow models into flow map models without architectural modifications. Our method conditions the final blocks of diffusion transformers on the subsequent timestep, allowing pretrained flow models to be directly repurposed as flow maps. Combined with enhanced training techniques, this design enables high-quality generation in as few as 1–4 steps. Notably, we find that training flow models and subsequently converting them is more efficient and effective than training flow maps from scratch. On ImageNet 256$\times$256, our model attains a 1-step FID of 2.16, surpassing prior art by a large margin, and achieves a 4-step FID of 1.51, matching the performance of standard flow models while delivering over 125$\times$ faster inference.

This work introduces a new approximate proximal sampler that operates solely with zeroth-order information of the potential function. Prior theoretical analyses have revealed that proximal sampling corresponds to alternating forward and backward iterations of the heat flow. The backward step was originally implemented by rejection sampling, whereas we directly simulate the dynamics. Unlike diffusion-based sampling methods that estimate scores via learned models or by invoking auxiliary samplers, our method treats the intermediate particle distribution as a Gaussian mixture, thereby yielding a Monte Carlo score estimator from directly samplable distributions. Theoretically, when the score estimation error is sufficiently controlled, our method inherits the exponential convergence of proximal sampling under isoperimetric conditions on the target distribution. In practice, the algorithm avoids rejection sampling, permits flexible step sizes, and runs with a deterministic runtime budget. Numerical experiments demonstrate that our approach converges rapidly to the target distribution, driven by interactions among multiple particles and by exploiting parallel computation.

Guidance provides a simple and effective framework for posterior sampling by steering the generation process towards the desired distribution. When modeling discrete data, existing approaches mostly focus on guidance with the first-order Taylor approximation to improve the sampling efficiency. However, such an approximation is inappropriate in discrete state spaces since the approximation error could be large. A novel guidance framework for discrete data is proposed to address this problem: We derive the exact transition rate for the desired distribution given a learned discrete flow matching model, leading to guidance that only requires a single forward pass in each sampling step, significantly improving efficiency. This unified novel framework is general enough, encompassing existing guidance methods as special cases, and it can also be seamlessly applied to the masked diffusion model. We demonstrate the effectiveness of our proposed guidance on energy-guided simulations and preference alignment on text-to-image generation and multimodal understanding tasks.

Efficient sampling from high-dimensional and multimodal unnormalized probability distributions is a central challenge in many areas of science and machine learning. We focus on Boltzmann generators (BGs) that aim to sample the Boltzmann distribution of physical systems, such as molecules, at a given temperature. Classical variational approaches that minimize the reverse Kullback–Leibler divergence are prone to mode collapse, while annealing-based methods, commonly using geometric schedules, can suffer from mass teleportation and rely heavily on schedule tuning. We introduce *Constrained Mass Transport* (CMT), a variational framework that generates intermediate distributions under constraints on both the KL divergence and the entropy decay between successive steps. These constraints enhance distributional overlap, mitigate mass teleportation, and counteract premature convergence. Across standard BG benchmarks and the here introduced *ELIL tetrapeptide*, the largest system studied to date without access to samples from molecular dynamics, CMT consistently surpasses state-of-the-art variational methods, achieving more than 2.5× higher effective sample size while avoiding mode collapse.

Test-time algorithms that combine the *generative* power of language models with *process verifiers* that assess the quality of partial generations offer a promising lever for eliciting new reasoning capabilities, but the algorithmic design space and computational scaling properties of such approaches are still opaque, and their benefits are far from apparent when one accounts for the cost of learning a high-quality verifier. Our starting point is the observation that seemingly benign errors in a learned verifier can lead to catastrophic failures for standard decoding techniques due to *error amplification* during the course of generation. We then ask: can this be improved with more sophisticated decoding strategies? We introduce a new process-guided test-time sampling algorithm, VGB, which uses theoretically grounded *backtracking* to achieve *provably* better robustness to verifier errors. VGB interprets autoregressive generation as a random walk on a tree of partial completions, with transition probabilities guided by the process verifier and base model; crucially, backtracking occurs probabilistically. This process generalizes the seminal *Sinclair-Jerrum random walk* (Sinclair & Jerrum, 1989) from the literature on approximate counting and sampling in theoretical computer science, and a conceptual contribution of our work is to highlight parallels with this literature. Empirically, we demonstrate on both synthetic and real language modeling tasks that VGB outperforms baselines on a variety of metrics.

Sampling from trained predictors is fundamental for interpretability and as a compute-light alternative to diffusion models, but local samplers struggle on the rugged, high-frequency functions such models learn. We observe that standard neural‑network training implicitly produces a coarse‑to‑fine sequence of models. Early checkpoints suppress high‑degree/ high‑frequency components (Boolean monomials; spherical harmonics under NTK), while later checkpoints restore detail. We exploit this by running a simple annealed sampler across the training trajectory, using early checkpoints for high‑mobility proposals and later ones for refinement. In the Boolean domain, this can turn the exponential bottleneck arising from rugged landscapes or needle gadgets into a near-linear one. In the continuous domain, under the NTK regime, this corresponds to smoothing under the NTK kernel. Requiring no additional compute, our method shows strong empirical gains across a variety of synthetic and real-world tasks, including constrained sampling tasks that diffusion models are unable to natively handle.

Obtaining high-quality outputs from Large Language Models (LLMs) often depends upon the choice of a sampling-based decoding strategy to probabilistically choose the next token at each generation step. While a variety of such sampling methods have been proposed, their performance can be sensitive to the selection of hyperparameters which may require different settings depending upon the generation task and temperature configuration. In this work, we introduce $p\textrm{-less}$ sampling: an information-theoretic approach to sampling which dynamically sets a truncation threshold at each decoding step based on the entire token probability distribution. Unlike existing methods, $p\textrm{-less}$ sampling has no hyperparameters and consistently produces high-quality outputs as temperature increases. We provide theoretical perspectives on $p$-less sampling to ground our proposed method and conduct experiments to empirically validate its effectiveness across a range of math, logical reasoning, and creative writing tasks. Our results demonstrate how $p\textrm{-less}$ sampling consistently outperforms existing sampling approaches while exhibiting much less degradation in text quality at higher temperature values. We further show how $p$-less achieves greater inference-time efficiency than alternative methods through lower average token sampling times and shorter generation lengths, without sacrificing accuracy. Finally, we provide analyses to highlight the benefits of $p\textrm{-less}$ through qualitative examples, case studies, and diversity assessments.

Masked diffusion models (MDMs) are a promising alternative to autoregressive models (ARMs), but they suffer from **inherently** much higher training variance. High variance leads to noisier gradient estimates and unstable optimization, so even equally strong pretrained MDMs and ARMs that are competitive at initialization often diverge after task-specific training, with MDMs falling far behind. Currently, there has been no theoretical explanation or systematic solution. In this paper, we derive **the first decomposition** of MDM training variance into three sources: {A} masking pattern noise, {B} masking rate noise, and {C} data noise -- while ARMs are only affected by {C}. This cleanly explains the fundamental training gap. Building on this foundation, we design six variance-reduction methods, including two core methods: (1) P-POTS, a **Pareto-optimal** $t$-sampler that minimizes training variance by sampling harder $t$ values more often with appropriately smaller update steps, and (2) MIRROR, which uses negatively correlated samples to reduce {A}. Experiments show that, compared to standard MDM training, our methods improve accuracy by **7–8\%** on complex reasoning tasks, while simultaneously reducing run-to-run variability to **near ARM levels**, substantially narrowing the gap with strong ARM baselines; in most settings, even the best baseline method runs remain below the worst run of our method.

Preference-based reinforcement learning (PbRL) enables agent training without explicit reward design by leveraging human feedback. Although various query sampling strategies have been proposed to improve feedback efficiency, many fail to enhance performance because they select queries from outdated experiences with low likelihood under the current policy. Such queries may no longer represent the agent's evolving behavior patterns, reducing the informativeness of human feedback. To address this issue, we propose a policy likelihood-based query sampling and critic-exploited reset (PoLiCER). Our approach uses policy likelihood-based query sampling to ensure that queries remain aligned with the agent’s evolving behavior. However, relying solely on policy-aligned sampling can result in overly localized guidance, leading to overestimation bias, as the model tends to overfit to early feedback experiences. To mitigate this, PoLiCER incorporates a dynamic resetting mechanism that selectively resets the reward estimator and its associated Q-function based on critic outputs. Experimental evaluation across diverse locomotion and robotic manipulation tasks demonstrates that PoLiCER consistently outperforms existing PbRL methods. Our code is available at https://github.com/JongKook-Heo/PoLiCER.

Watermarking is a principled approach for tracing the provenance of large language model (LLM) outputs, but its deployment in practice is hindered by inference inefficiency. Speculative sampling accelerates inference, with efficiency improving as the acceptance rate between draft and target models increases. Yet recent work reveals a fundamental trade-off: higher watermark strength reduces acceptance, preventing their simultaneous achievement. We revisit this trade-off and show it is not absolute. We introduce a quantitative measure of watermark strength that governs statistical detectability and is maximized when tokens are deterministic functions of pseudorandom numbers. Using this measure, we fully characterize the trade-off as a constrained optimization problem and derive explicit Pareto curves for two existing watermarking schemes. Finally, we introduce a principled mechanism that injects pseudorandomness into draft-token acceptance, ensuring maximal watermark strength while maintaining speculative sampling efficiency. Experiments further show that this approach improves detectability without sacrificing efficiency. Our findings uncover a principle that unites speculative sampling and watermarking, paving the way for their efficient and practical deployment.

KV caches, typically used only to speed up autoregressive decoding, encode contextual information that can be reused for downstream tasks at no extra cost. We propose treating the KV cache as a lightweight representation, eliminating the need to recompute or store full hidden states. Despite being weaker than dedicated embeddings, KV-derived representations are shown to be sufficient for two key applications: (i) Chain-of-Embedding, where they achieve competitive or superior performance on Llama-3.1-8B-Instruct and Qwen2-7B-Instruct; and (ii) Fast/Slow Thinking Switching, where they enable adaptive reasoning on Qwen3-8B and DeepSeek-R1-Distil-Qwen-14B, reducing token generation by up to $5.7\times$ with minimal accuracy loss. Our findings establish KV caches as a free, effective substrate for sampling and reasoning, opening new directions for representation reuse in LLM inference.

Diffusion models (DMs) and flow-matching models have demonstrated remarkable performance in image and video generation. However, such models require a significant number of function evaluations (NFEs) during sampling, leading to costly inference. Consequently, quality-preserving fast sampling methods that require fewer NFEs have been an active area of research. However, prior training-free sampling methods fail to simultaneously address two key challenges: the stiffness of the ODE (i.e., the non-straightness of the velocity field) and dependence on the semi-linear structure of the DM ODE (which limits their direct applicability to flow-matching models). In this work, we introduce the Stabilized Taylor Orthogonal Runge–Kutta (STORK) method, addressing both design concerns. We demonstrate that STORK consistently improves the quality of diffusion and flow-matching sampling for image and video generation.

Diffusion and flow-based models benefit from simple regression losses, but inference (i.e, producing samples) incurs significant computational overhead because it requires integration. Consistency models address this overhead by directly learning the flow maps along the ODE trajectory, revealing a design space for the learning problem between one-step and many-step approaches. However, existing consistency training methods feature computational challenges such as requiring model inverses or backpropagation through iterated model calls, and do not always prove that the desired ODE flow map is a solution to the loss. We introduce CurlFlow, an approach for learning flow maps that bypasses explicit invertibility constraints and expensive differentiation through model iteration. CurlFlow trains a model to compute both the ODE solutions and the implied velocity from scratch by following non-conservative dynamics (i.e., those with curl) with stationary point at the desired flow map. On the CIFAR image benchmark, CurlFlow attains a favorable relationship of FID to step count, relative to flow matching, MeanFlow, and several other flow map learning methods.

Diffusion and flow-based models have enabled significant progress in generation tasks across various modalities and have recently found applications in predictive learning. However, unlike typical generation tasks that encourage sample diversity, predictive learning entails different sources of stochasticity and requires sampling consistency aligned with the ground-truth trajectory, which is a limitation we empirically observe in diffusion models. We argue that a key bottleneck in learning sampling-consistent predictive diffusion models lies in suboptimal predictive ability, which we attribute to the entanglement of condition understanding and target denoising within shared architectures and co-training schemes. To address this, we propose **Foresight Diffusion (ForeDiff)**, a framework for predictive diffusion models that improves sampling consistency by decoupling condition understanding from target denoising. ForeDiff incorporates a separate deterministic predictive stream to process conditioning inputs independently of the denoising stream, and further leverages a pretrained predictor to extract informative representations that guide generation. Extensive experiments on robot video prediction and scientific spatiotemporal forecasting show that ForeDiff improves both predictive accuracy and sampling consistency over strong baselines, offering a promising direction for predictive diffusion models.

Given an unnormalized probability density $\pi\propto\mathrm{e}^{-V}$, estimating its normalizing constant $Z=\int_{\mathbb{R}^d}\mathrm{e}^{-V(x)}\mathrm{d}x$ or free energy $F=-\log Z$ is a crucial problem in Bayesian statistics, statistical mechanics, and machine learning. It is challenging especially in high dimensions or when $\pi$ is multimodal. To mitigate the high variance of conventional importance sampling estimators, annealing-based methods such as Jarzynski equality and annealed importance sampling are commonly adopted, yet their quantitative complexity guarantees remain largely unexplored. We take a first step toward a non-asymptotic analysis of annealed importance sampling. In particular, we derive an oracle complexity of $\widetilde{O}\left(\frac{d\beta^2{\mathcal{A}}^2}{\varepsilon^4}\right)$ for estimating $Z$ within $\varepsilon$ relative error with high probability, where $\beta$ is the smoothness of $V$ and $\mathcal{A}$ denotes the action of a curve of probability measures interpolating $\pi$ and a tractable reference distribution. Our analysis, leveraging Girsanov theorem and optimal transport, does not explicitly require isoperimetric assumptions on the target distribution. Finally, to tackle the large action of the widely used geometric interpolation, we propose a new algorithm based on reverse diffusion samplers, establish a framework for analyzing its complexity, and empirically demonstrate its efficiency in tackling multimodality.