ICML 2026 Papers

Sampling from unnormalized densities using diffusion models has emerged as a powerful paradigm. However, while recent approaches that use least-squares `matching' objectives have improved scalability, they often necessitate significant trade-offs, such as restricting prior distributions or relying on unstable optimization schemes. By generalizing these methods as special forms of fixed-point iterations rooted in Nelson's relation, we develop a new method that addresses these limitations. Our approach enables learning a stochastic transport map between arbitrary prior and target distributions with a single, scalable, and stable objective. Furthermore, we introduce a damped variant of this iteration that incorporates a regularization term to mitigate mode collapse. Empirically, we demonstrate that our method enables sampling at unprecedented scales while preserving mode diversity, achieving state-of-the-art results on complex synthetic densities and high-dimensional molecular benchmarks.

Existing insertion-based masked diffusion models that generate sequences by interleaving token insertion with unmasking use fixed schedules that are not dependent on the data. For structured sequences like graphs and molecules, learning data-dependent generation orders can improve generation quality by reducing uncertainty over the action space. We propose LoFlexMDM, an insertion-based masked diffusion model with learnable order dynamics that learns data-dependent insertion and unmasking rates. We generalize the discrete flow matching framework to work with variable-length sequences, propose a tractable schedule parameterization and a training objective for joint training of the generator and the target order dynamics. On De Novo and fragment-constrained molecule generation, LoFlexMDM improves sample quality over FlexMDM by up to 17.5% and 6.7%, respectively. These results show that learning the target generation order can improve insertion-based diffusion models without giving up tractable training. We open source the code at https://github.com/dhruvdcoder/LoFlexMDM.

In generative modeling, we often wish to produce samples that maximize a user-specified reward such as aesthetic quality or alignment with human preferences, a problem known as guidance. Despite their widespread use, existing guidance methods either require expensive multi-particle, many-step schemes or rely on poorly understood approximations. We reformulate guidance as a deterministic optimal control problem, yielding a hierarchy of algorithms that subsumes existing approaches at the coarsest level. We show that the flow map, an object of significant recent interest for its role in fast inference, arises naturally in the optimal solution. Based on this observation, we propose Flow Map Reward Guidance (FMRG): a training-free, single-trajectory framework that uses the flow map to both integrate and guide the flow. At text-to-image scale, FMRG matches or surpasses baselines across inverse problems and reward-guided generation with as few as 3 NFEs, giving at least an order-of-magnitude speedup in comparison to prior state of the art.

Detecting AI-generated images (AIGI) remains challenging because detectors often fail to generalize to unseen generators. Although existing methods are trained on large datasets, their performance still degrades when generation settings change, indicating that data scale alone is insufficient and that limited coverage of generative variations during training is a key factor. Studies on generative model editing show that small changes in internal representations can produce diverse and meaningful image variations, many of which are not explored under standard sampling. Leveraging this insight, we propose PROBE (Probing Robustness via Boundary Exploration), a framework that improves detector generalization by actively exploring challenging regions of the generative process. Instead of treating the generator as a fixed data source, PROBE uses the detector as a critic to steer the generator through manifold-level modifications, producing realistic samples that are difficult to classify. These samples expose failure cases that are uncommon under standard data sampling strategies and are used to refine the detector. Experimental results across multiple benchmarks indicate that PROBE enhances generalization to unseen generators, resulting in more generalizable AIGI detection performance.

Discrete biological sequence optimization often requires goal-directed, parser-valid edits to an existing protein or molecule. Diffusion models support iterative refinement but do not expose a controllable discrete-edit interface, while autoregressive LLMs can be myopic when planning constrained edits over multiple steps. We introduce *STRIDE* (Sequence Trajectory Refinement via Iterative Discrete Editing), a post-training framework that trains an LLM to emit executable INSERT/DELETE/REPLACE trajectories for variable-length refinement. *STRIDE* first learns Levenshtein-aligned shortest-edit demonstrations, then uses supervised fine-tuning and group-based policy optimization to align trajectories with task rewards while preserving coherent editing. On an oracle-based full-action protein stress test, *STRIDE* raises success over Vanilla SFT from 42% to 89% and novelty among unique improvements from 47% to 97%. On instruction-conditioned molecular editing, the GSPO-aligned variant improves strict success, controllability, and SMILES validity over the SFT-only *STRIDE* model (code: https://github.com/daiheng-zhang/STRIDE).

Diffusion Transformers (DiTs) have emerged as a powerful backbone for image generation, offering superior scalability over U-Nets. However, their practical deployment is hindered by significant computational costs. While Quantization-Aware Training (QAT) shows promise, its application to DiTs is challenged by the high sensitivity and complex distributions of activations. Identifying activation quantization as the primary bottleneck for low-bit settings, we propose **RobuQ**, a systematic QAT framework. We first establish a strong ternary weight (W1.58A4) baseline. Building on this, we introduce **RobustQuantizer**, which utilizes the Hadamard transform to convert unknown per-token distributions into normal distributions. Furthermore, we propose **AMPN**, the first **A**ctivation-only **M**ixed-**P**recision **N**etwork pipeline, applying ternary weights globally while allocating layer-specific activation precisions to eliminate information bottlenecks. Extensive experiments demonstrate that **RobuQ** achieves state-of-the-art performance on **ImageNet-1K**, representing the first stable image generation with activations quantized to an average of 2 bits. Code is available at https://github.com/racoonykc/RobuQ.

Electrostatic generative models such as PFGM++ have recently emerged as a powerful framework, achieving competitive performance in image synthesis. PFGM++ operates in an extended data space with auxiliary dimensionality $D$, recovering the diffusion model framework as $D\to\infty$, while yielding superior empirical results for finite $D$. Like diffusion models, PFGM++ relies on expensive ODE simulations to generate samples, making it computationally costly. To address this, we propose Inverse Poisson Flow Matching (IPFM), a principled distillation framework that accelerates electrostatic generative models across all values of $D$. Our IPFM reformulates distillation as an inverse problem: learning a generator whose induced electrostatic field matches that of the teacher. We derive a tractable training objective for this problem and show that, as $D\to\infty$, our IPFM closely recovers Score Identity Distillation (SiD), a recent method for distilling diffusion models. Empirically, our IPFM produces distilled generators that achieve near-teacher or even superior sample quality using only a few function evaluations. Moreover, we find that one-step generator distillation converges faster at finite $D$ than in the $D\to\infty$ diffusion limit, aligning with prior evidence that finite-$D$ PFGM++ models offer more favorable optimization and sampling behavior.

Diffusion-based large language models (DLLMs) have shown promise for non-autoregressive text generation, but their deployment is constrained by large model sizes and heavy computational costs. Post-training quantization (PTQ), a widely used method for compressing and accelerating Large Language Models (LLMs), suffers from severe accuracy degradation and reduced generalization performance when directly applied to DLLMs (e.g., AWQ suffers a 16% accuracy drop on LLADA under W4A4). This paper explores how the unique mechanisms of Dynamic Language Models (DLLMs) conflict with quantization, identifying three core issues: 1) During the iterative generation process of DLLMs, dynamic masking ratios are inherently involved, leading to notable differences in token distributions across decoding steps. Unfortunately, these distinct distributions are not sufficiently captured by current PTQ calibration approaches; 2) Quantization errors propogate and accumalte progressively during iterations in DLLMs, leading to a gradual decline in the performance of quantized models as decoding steps advance; 3) The stability of unmasked tokens, combined with the probabilistic nature of masked tokens, gives rise to an overall feature distribution that is uncoordinated and unsuitable for PTQ. To address these issues, we propose DLLMQuant, a PTQ framework tailored for DLLMs, which incorporates three novel techniques: 1) Temporal-Mask Adaptive Sampling (TMAS), a calibration method that accounts for both time and mask factors, with the capacity to capture distributions across timesteps. 2) Interaction-Aware Activation Quantization (IA-AQ), which utilizes bidirectional attention scores to identify important tokens, and prioritizes these tokens when minimizing quantization error. 3) Certainty-Guided Quantization (CGQ) incorporates mask status and token scores as core weighting criteria for error compensation, enabling PTQ to better align with the unique weight distribution of DLLMs. Experiments show that DLLMQuant achieves significant performance gains (e.g., over 10-point accuracy improvement on GSM8K for LLADA under 4-bit quantization) while enhancing efficiency.

Approximation of a target probability distribution using a finite set of points is a problem of fundamental importance in numerical integration. Several authors have proposed to select points by minimising a maximum mean discrepancy (MMD), but the non-convexity of this objective typically precludes global minimisation. Instead, we consider the concept of \emph{stationary points of the MMD} which, in contrast to points globally minimising the MMD, can be accurately computed. Our main contributions are two-fold and theoretical in nature. We first prove the (perhaps surprising) result that, for integrands in the associated reproducing kernel Hilbert space, the numerical integration error of stationary MMD points vanishes \emph{faster} than the MMD. Motivated by this \emph{super-convergence} property, we consider MMD gradient flows as a practical strategy for computing stationary points of the MMD. We then prove that MMD gradient flow can indeed compute stationary MMD points, based on a refined convergence analysis that establishes a novel non-asymptotic finite-particle error bound.

Can a diffusion model trained on bedrooms recover human faces? Diffusion models are widely used as priors for inverse problems, but standard approaches usually assume a high-fidelity model trained on data that closely match the unknown signal. In practice, one often must use a mismatched or low-fidelity diffusion prior. Surprisingly, these weak priors often perform nearly as well as full-strength, in-domain baselines. We study when and why inverse solvers are robust to weak diffusion priors. Through extensive experiments, we find that weak priors succeed when measurements are highly informative (e.g., many observed pixels), and we identify regimes where they fail. To explain this behavior, we combine Bayesian-consistency theory with local-correlation analysis: the theory gives conditions under which high-dimensional measurements make the posterior concentrate near the true signal, while the correlation analysis shows that weak and stronger natural-image priors can share similar local spatial structure. These results provide a principled justification on when weak diffusion priors can be used reliably. Code is available at https://github.com/jjia131/weak-diffusion-priors-inverse-problem.

Diffusion Large Language Models (dLLMs) have emerged as a promising alternative to purely autoregressive language models because they can decode multiple tokens in parallel. However, state-of-the-art block-wise dLLMs rely on a ``remasking" mechanism that decodes only the most confident tokens and discards the rest, effectively wasting computation. We demonstrate that recycling computation from the discarded tokens is beneficial, as these tokens retain contextual information useful for subsequent decoding iterations. In light of this, we propose Residual Context Diffusion (RCD), a module that converts these discarded token representations into contextual residuals and injects them back for the next denoising step. RCD uses a decoupled two-stage training pipeline to bypass the memory bottlenecks associated with backpropagation. We validate our method on both long CoT reasoning (SDAR) and short CoT instruction following (LLaDA) models. We demonstrate that a standard dLLM can be efficiently converted to the RCD paradigm with merely $\sim$300 million tokens. RCD consistently improves frontier dLLMs by 4--11 percentage points in accuracy with minimal extra computation overhead across a wide range of benchmarks. Notably, on the most challenging AIME tasks, RCD nearly doubles baseline accuracy and attains up to 4--5x fewer denoising steps at baseline's peak accuracy.

Masked Diffusion Language Models (MDLMs) have recently emerged as a promising alternative to Autoregressive Language Models (ARLMs), leveraging a denoising objective that, in principle, should enable more uniform context utilisation. In this work, we examine the context comprehension abilities of MDLMs and uncover two key limitations. First, despite their more global training objective and bidirectional attention mechanism, similarly to ARLMS, **MDLMs exhibit a strong locality bias**: performance is highly sensitive to the position of relevant information within the input, favouring local over distant context. Second, appending a large number of **mask tokens—required for generation—can significantly degrade context comprehension** in models trained from scratch. Through systematic ablations, we find that these masks **act as distractors**, reducing the model's ability to process relevant information. To address and further study this undesirable behaviour, we introduce the mask-agnostic loss function that encourages predictions to remain invariant to the number of appended masks. Fine-tuning with this objective substantially mitigates the distracting effect of masks, improving robustness of MDLMs. Overall, our findings reveal critical limitations of the current MDLM training paradigm, with implications for training, evaluation and deployment.

Variational autoencoders (VAEs) compress high resolution CT volumes into compact latents while preserving clinically relevant structure. However, training CT-specific VAEs from scratch or heavily fine-tuning them incurs substantial computational and engineering cost, and often degrades under heterogeneous scanners, protocols, and diseases. This paper makes a progressive stride toward training-free medical VAEs by leveraging a critical observation: a single Foundation VAE, pretrained at scale on natural images and videos, can serve as a unified interface for CT Reconstruction, Augmentation, and Generation. With both encoder and decoder frozen, the Foundation VAE reconstructs CT volumes with preserved anatomy while suppressing acquisition noise; training segmentation models on these reconstructions improves surface accuracy by 3.9\% NSD on average for pancreatic tumor and lung tumor. Within the same Foundation VAE latent space, a conditional latent diffusion model achieves 3.9\% lower average FVD with 36.2\% higher CT CLIP score, and improves multi-disease generation faithfulness across 18 types by 2.76\% AUC. These results demonstrate Foundation VAEs as a practical interface for scalable CT representation reuse and faithful CT generation. Our code and demo are available at https://github.com/qic999/Foundation-VAE.

Simulation-Based Inference (SBI) is critical for scientific discovery, with generative models offering a promising path toward efficient inference. However, existing methods struggle with effective multimodal modeling. They often rely on brute-force fusion strategies that ignore the structural disparities between parameters and observations, thus limiting estimation fidelity. In this work, we introduce FUSE (Feynman-Kac steered mUlti-modal flow matching for efficient Simulation-based posterior Estimation). Unlike prior work, FUSE employs a dual-track architecture that preserves the distinct features of multimodal inputs while facilitating dynamic interaction. Additionally, we propose an FK-steered sampling strategy that leverages intermediate observation likelihoods to guide the generative trajectories, effectively improving the sample quality during inference. Our approach outperforms state-of-the-art baselines on standard SBI benchmarks, producing posteriors that closely match ground-truth MCMC. Furthermore, in a real-world exoplanet orbital estimation task, FUSE successfully resolves complex parameter degeneracies that challenge existing methods, highlighting its potential to accelerate complex scientific discoveries in astrophysics and beyond.

Diffusion language models theoretically allow for efficient parallel generation but are practically hindered by the "factorization barrier": the assumption that simultaneously predicted tokens are independent. This limitation forces a trade-off: models must either sacrifice speed by resolving dependencies sequentially or suffer from incoherence due to factorization. We argue that this barrier arises not from limited backbone expressivity, but from a structural misspecification: models are restricted to fully factorized outputs because explicitly parameterizing a joint distribution would require the Transformer to output a prohibitively large number of parameters. We propose **Co**upled **D**iscrete **D**iffusion (**CoDD**), a hybrid framework that breaks this barrier by replacing the fully-factorized output distribution with a lightweight, tractable probabilistic inference layer. This formulation yields a distribution family that is significantly more expressive than standard factorized priors, enabling the modeling of complex joint dependencies, yet remains compact enough to avoid the prohibitive parameter explosion associated with full joint modeling. Empirically, CoDD seamlessly enhances diverse diffusion language model architectures with negligible overhead, matching the reasoning performance of computationally intensive Reinforcement Learning baselines at a fraction of the training cost. Furthermore, it prevents performance collapse in few-step generation, enabling high-quality outputs at significantly reduced latencies. Code available at: https://github.com/liuanji/CoDD

Diffusion Transformers (DiTs) have achieved remarkable success in image generation, yet their deployment is hindered by high computational costs. We identify two sources of redundancy. First, $\textbf{temporal redundancy}$: Classifier-Free Guidance (CFG) applies costly dual forward passes at every timestep, yet guidance matters only at specific steps, and variable scales at critical steps can compensate for skipping others. Second, $\textbf{spatial redundancy}$: under variable guidance, different transformer blocks exhibit heterogeneous sensitivity, yet uniform calibration across all blocks wastes computation while failing to address their varying requirements. We present RSTR, the first framework to jointly reduce spatiotemporal redundancy in diffusion transformers. Stage-1 addresses temporal redundancy through evolutionary search, discovering sparse guidance schedules with variable scales. Stage-2 addresses spatial redundancy through adaptive rank allocation, assigning calibration capacities to transformer regions based on their sensitivity. Experiments on DiT-XL/2, PixArt-$\alpha$, FLUX, and state-of-the-art Qwen-Image demonstrate 50\%-70\% compute savings while maintaining or improving quality. On DiT-XL/2, RSTR achieves 57\% savings with 15\% FID improvement; on Qwen-Image, 3.43$\times$ speedup with preserved quality.

Estimating the difference of two Stein's score functions is a fundamental problem in generative modeling. In particular, score differences arise naturally in transfer learning, where the score difference provides the mechanism for adapting a pre-trained model to a new target distribution, and in diffusion model-based post-training methods such as discriminator guidance. Existing estimators for score differences in these settings either lack of statistical consistency or are difficult to scale up in high-dimensions. We propose a statistically consistent and scalable estimator for score differences based on Sobolev regularization, which plays a crucial role in ensuring consistency and stablizing the training in the small-sample regime. Mathematically, we establish a convergence rate of $\tilde{\mathcal{O}}(n^{-\frac{s-1}{d+2s-2}})$ where $d$ is the dimension and $s$ denotes the smoothness of the underlying densities, and provide a minimax lower bound of $\tilde{\Omega}(n^{-\frac{2(s-1)}{d+2s}})$ (in mean-squared error). Empirically, our estimator exhibits significantly improved stability in small-sample regimes compared to existing methods. We demonstrate its effectiveness on real-world tasks, including transfer learning for ECG signal generation, where it substantially outperforms non-regularized score difference estimators in downstream classification performance.

Autonomous vehicles operating in open-world environments must continually adapt to rare long-tail scenarios while preserving previously acquired driving skills. However, existing trajectory planning approaches struggle with this stability--plasticity trade-off, as they rely on static models or rigid rule-based controllers that cannot robustly handle evolving and complex traffic dynamics. Against this background, we propose **NOMAD**, a lifelong trajectory planning framework that integrates non-parametric Bayesian memory with diffusion-based trajectory generation, enabling continuous adaptation to long-tail scenarios without catastrophic forgetting. Our method maps growing scene contexts to a dynamically growing set of discrete memory clusters, which guide a conditional diffusion model to function as a mixture of experts specialized for diverse driving behaviors. To retain past knowledge during incremental learning, we introduce a generative replay mechanism that synthesizes pseudo-experiences from previously learned memory clusters. Extensive closed-loop evaluations on the nuPlan benchmark demonstrate that our approach achieves state-of-the-art performance on long-tail scenarios, improving the interPlan score by **9.4%** over the strongest baseline, while maintaining competitive performance on regular driving benchmarks. Moreover, our method exhibits robust continual learning capability, achieving the highest average closed-loop score with positive backward transfer when adapting to sequentially introduced long-tail scenarios.

Inference-time steering adapts pretrained diffusion and flow models to new tasks without retraining, often utilizing ratio-of-densities constructions that reweight time-indexed marginals with fixed exponents. We identify Marginal Path Collapse, a failure mode in which the intermediate density defined by such compositions becomes non-normalizable despite valid endpoints. This collapse can arise when composing heterogeneous experts trained with mismatched noise schedules (and/or negative exponents / partial supports). To address this, we provide (i) a sharp sufficient Path Existence Criterion that characterizes when the composed intermediate densities are mathematically well-defined, and (ii) Adaptive Path Correction with Exponents (ACE), which generalizes Feynman–Kac steering to support time-varying exponents. Our analysis reveals that ACE controls the quantile radius of the intermediate distributions, providing a theoretical mechanism for path stabilization observed in experiments. On flexible-pose scaffold decoration, a drug design task composed of de-novo, conformer, and protein-conditioned experts, ACE prevents collapse and significantly outperforms constant-exponent baselines. Furthermore, ACE improves attribute success rates in compositional image generation, establishing it as a general framework for compositional sampling.