ICML 2026 Papers

Sampling from unnormalized multimodal distributions with limited density evaluations remains a fundamental challenge in machine learning and natural sciences. Successful approaches construct a bridge between a tractable reference and the target distribution. Parallel Tempering (PT) serves as the gold standard, while recent diffusion-based approaches offer a continuous alternative at the cost of neural training. In this work, we introduce Conditional Diffusion Sampling (CDS), a framework that combines these two paradigms. To this end, we derive Conditional Interpolants, a class of stochastic processes whose transport dynamics are governed by an exact, closed-form stochastic differential equation (SDE), requiring no neural approximation. Although these dynamics require sampling from a non-trivial initialization distribution, we show both theoretically and empirically that the cost of this initialization diminishes for sufficiently short diffusion times. CDS leverages this by a two-stage procedure: (1) PT is used to efficiently sample the initial distribution, and then (2) samples are transported via the transport SDE. This combination couples the robust global exploration of PT with efficient local transport. Experiments suggest that CDS has the potential to achieve a superior trade-off between sample quality and density evaluation cost compared to state-of-the-art samplers.

Existing approaches for analyzing neural network activations, such as PCA and sparse autoencoders, rely on strong structural assumptions. Generative models offer an alternative: they can uncover structure without such assumptions and act as priors that improve intervention fidelity. We explore this direction by training diffusion models on one billion residual stream activations, creating "meta-models" that learn the distribution of a network's internal states. We find that diffusion loss decreases smoothly with compute and reliably predicts downstream utility. In particular, applying the meta-model's learned prior to steering interventions improves fluency, with larger gains as loss decreases. Moreover, the meta-model's neurons increasingly isolate concepts into individual units, with sparse probing scores that scale as loss decreases. These results suggest generative meta-models offer a scalable path toward interpretability without restrictive structural assumptions.

Hyper-relational knowledge graphs (HKGs) effectively represent complex facts. While inferring new knowledge in HKGs is a critical problem, current methods cast it as a simple link prediction, assuming that nearly all entities and relations within a fact are known, leaving only a single blank to be filled. However, this restricted assumption may not hold in real-world scenarios in which multiple, or even all, constituent components of a fact may be missing simultaneously. To bridge this gap, we introduce a task called fact generation: generating a valid hyper-relational fact from an arbitrarily masked query, i.e., completing a partially observed fact or generating a fact from scratch. We propose KREPE, the first generative representation learning method for HKGs that learns to model the probability distributions of missing components conditioned on the local fact components and global structure of HKGs via a masked discrete diffusion. KREPE models both the intra-fact dependencies by contextual message passing and inter-fact correlations by aggregating stochastically sampled contexts. KREPE seamlessly unifies link prediction and fact generation within a single training framework, achieving state-of-the-art performance on standard HKG link prediction benchmarks and outperforming LLM-based baselines in generating novel and correct facts.

Crystal modeling spans a family of conditional and unconditional generation tasks, including crystal structure prediction (CSP) and *de novo* generation (DNG). While recent deep generative models have shown promising performance, they remain largely task-specific, lacking a unified framework that shares crystal representations across tasks. To address this limitation, we propose *Multimodal Crystal Flow (MCFlow)*, a unified multimodal flow model that realizes multiple crystal generation tasks as distinct inference trajectories via independent time variables for atom types and crystal structures. To enable multimodal flow in a standard transformer model, we introduce a composition- and symmetry-aware atom ordering with hierarchical permutation augmentation, injecting compositional and crystallographic priors without explicit structural templates. Experiments on the MP-20 and MPTS-52 benchmarks show that a single MCFlow model is competitive with task-specific baselines across CSP, DNG, and structure-conditioned atom type generation.

We introduce Categorical Flow Maps, a flow-matching method for accelerated few-step generation of categorical data via self-distillation. Building on recent variational formulations of flow matching and the broader trend towards accelerated inference in diffusion and flow-based models, we define a flow map towards the simplex that transports probability mass toward a predicted endpoint, yielding a parametrisation that naturally constrains model predictions. Since our trajectories are continuous rather than discrete, Categorical Flow Maps can be trained with existing distillation techniques, as well as a new objective based on endpoint consistency. This continuous formulation also automatically unlocks test-time inference: we can directly reuse existing guidance and reweighting techniques in the categorical setting to steer sampling toward downstream objectives. Empirically, we achieve state-of-the-art few-step results on images, molecular graphs, and text, with strong performance even in single-step generation.

Diffusion Transformers (DiTs) achieve strong video generation quality but suffer from high inference cost due to dense 3D attention, leading to the development of sparse attention technologies to improve efficiency. However, existing training-free sparse attention methods in video generation still face two unresolved limitations: *ignoring layer heterogeneity in attention pruning* and *ignoring query-key coupling in block partitioning*, which hinder a better quality-speedup trade-off. In this work, we uncover a critical insight that **the attention sparsity of each layer is its intrinsic property, with minor effects across different inputs**. Motivated by this, we propose **SVOO**, a training-free **S**parse attention framework for fast **V**ideo generation via **O**ffline layer-wise sparsity profiling and **O**nline bidirectional co-clustering. Specifically, SVOO adopts a two-stage paradigm: (i) offline layer-wise sensitivity profiling to derive intrinsic per-layer pruning levels, and (ii) online block-wise sparse attention via a novel bidirectional co-clustering algorithm. Extensive experiments on seven widely used video generation models demonstrate that SVOO achieves a superior quality-speedup trade-off over state-of-the-art methods, delivering up to 1.93× speedup while maintaining a PSNR of up to 29 dB on Wan2.1.

Advances in generative modeling have recently been adapted to tabular data containing discrete and continuous features. However, generating mixed-type features that combine discrete states with an otherwise continuous distribution in a single feature remains challenging. We advance the state-of-the-art in diffusion models for tabular data with a cascaded approach. We first generate a low-resolution version of a tabular data row, that is, the collection of the purely categorical features and a coarse categorical representation of numerical features. Next, this information is leveraged in the high-resolution flow matching model via a novel guided conditional probability path and data-dependent coupling. The low-resolution representation of numerical features explicitly accounts for discrete outcomes, such as missing or inflated values, and therewith enables a more faithful generation of mixed-type features. We formally prove that this cascade tightens the transport cost bound. The results indicate that our model generates significantly more realistic samples and captures distributional details more accurately, for example, the detection score improves by 51.9%. Code is available at https://github.com/muellermarkus/tabcascade.

Diffusion-based large language models (dLLMs) have emerged as a promising alternative to autoregressive models, leveraging simultaneous denoising to enable global planning and iterative refinement. These properties make dLLMs attractive for long-context generation. However, deploying dLLMs faces a prohibitive memory barrier, as existing inference systems are inefficient for the diffusion paradigm. We observe that current inference systems are misaligned with dLLMs. Unlike autoregressive models, whose memory footprint is dominated by the KV-Cache, dLLMs are bottlenecked by transient activations rematerialized per step. Moreover, generic memory reuse mechanisms lack the global visibility to handle dynamic memory peaks of dLLMs, which alternate between logits and feed-forward networks. To address these challenges, we present Mosaic, a memory-efficient inference system that shifts dLLM execution from local, static management to a global, dynamic paradigm. Mosaic integrates (i) a mask-only logits kernel eliminating redundant activation materialization, (ii) a lazy chunking optimizer using online heuristics to tame dynamic memory peaks, and (iii) a global memory manager leveraging virtual addressing to mitigate memory fragmentation. Evaluations show that Mosaic reduces the memory peak-to-average ratio by 2.71$\times$ on average and increases the maximum inference sequence length on identical hardware by 15.30--32.34$\times$. Crucially, Mosaic is training-free and preserves exact model outputs, while reducing end-to-end latency by 2.5\%--55.4\%. Our code is publicly available at https://github.com/flashserve/Mosaic.

Instruction-based image editing (IIE) has advanced rapidly with the success of diffusion models. However, existing efforts primarily focus on simple and explicit instructions to execute editing operations such as adding, deleting, moving, or swapping objects. They struggle to handle more complex implicit hypothetical instructions that require deeper reasoning to infer plausible visual changes and user intent. Additionally, current datasets provide limited support for training and evaluating reasoning-aware editing capabilities. Architecturally, these methods also lack mechanisms for fine-grained detail extraction that support such reasoning. To address these limitations, we propose Reason50K, a large-scale dataset specifically curated for training and evaluating hypothetical instruction–reasoning image editing, along with ReasonBrain, a novel framework designed to reason over and execute implicit hypothetical instructions across diverse scenarios. Reason50K includes over 50K samples spanning four key reasoning scenarios: Physical, Temporal, Causal, and Story reasoning. ReasonBrain leverages Multimodal Large Language Models (MLLMs) for editing guidance generation and a diffusion model for image synthesis, incorporating a Fine-grained Reasoning Cue Extraction (FRCE) module to capture detailed visual and textual semantics essential for supporting instruction reasoning. To mitigate the semantic loss, we further introduce a Cross-Modal Enhancer (CME) that enables rich interactions between the fine-grained cues and MLLM-derived features. Extensive experiments demonstrate that ReasonBrain consistently outperforms state-of-the-art baselines on reasoning scenarios while exhibiting strong zero-shot generalization to conventional IIE tasks. Our dataset and code will be released publicly.

The performance of pre-trained masked diffusion models is often constrained by their sampling procedure, which makes decisions irreversible and struggles in low-step generation regimes. We introduce a novel sampling algorithm that works with pre-trained models and, after a lightweight fine-tuning of a single layer, significantly improves sample quality and efficiency. Our method reformulates the generation process using a star-shaped paradigm, which inherently allows for error correction. To make this process effective, we augment it with a learnable remasking module that intelligently identifies and revises likely errors. This approach yields a substantial quality boost, particularly when using a small number of sampling steps. We extensively ablate key components of our approach and show its usability in different scenarios. In experiments on text, and code generation, our sampling algorithm outperforms or matches existing methods. Code is available at https://github.com/EgorShibaev/G-Star.

Data Assimilation (DA) aims to integrate observations with model forecasts to estimate the state of dynamical systems. Despite the widespread application of diffusion-based assimilation methods, they remain constrained by the high dimensionality of atmospheric states and the reliance on imperfect state-observation mappings. This leaves regions lacking observations spatially unconstrained, leading to severe error accumulation and physical inconsistency.. In this paper, we propose LoPhyDA, a diffusion assimilation algorithm dual-guided by low-rank tensor and physical gradients. By leveraging the low-rank property of meteorological field, we employ tensor completion to exploit spatial continuity and dynamic correlations, reconstructing a globally informative dense field from sparse observations to serve as a global prior. This approach mitigates the information deficit inherent in sparse settings. The framework further incorporates physical constraints into the iterative denoising process, utilizing Partial Differential Equation (PDE) residual gradients to rectify the generative trajectory in real-time. Experimental results demonstrate that LoPhyDA outperforms state-of-the-art generative assimilation models in global weather prediction. It achieves robust and physically consistent assimilation, significantly reducing error accumulation in regions lacking observations.

Denoising diffusion sampling (DDS) is an emerging approach for generating new samples that have the same distribution as some training samples. However, it is vulnerable to adversarial attacks by even a Gaussian perturbation. In this work, we propose a complete set of adversarial attack and defense methodology for DDS. In the attack side, we propose to inject a perturbation to the sampling stage, which significantly worsen the performance of sample generation. In the defense side, we propose a local variation based regularization model for the potential function minimization, which effectively tolerates the adversarial perturbations. Moreover, we develop a conjugate gradient algorithm to solve the defense model, which integrates with a recently-developed zeroth order rejection sampling method that saves computational cost. Experimental results show that the proposed attack significantly worsen the existing state-of-the-art methods, but can be defended by the proposed local variation regularization.

Editing the content of an image with a pretrained text-to-image model remains challenging. Existing methods often distort fine details or introduce unintended artifacts. We propose using coupled stochastic differential equations (coupled SDEs) to guide the sampling process of any pre-trained generative model that can be sampled by solving an SDE, including diffusion and rectified flow models. By driving both the source image and the edited image with the same correlated noise, our approach steers new samples toward the desired semantics while preserving visual similarity to the source. The method works out-of-the-box—without retraining or auxiliary networks—and achieves high prompt fidelity along with near-pixel-level consistency. These results position coupled SDEs as a simple yet powerful tool for controlled generative AI.

Scaling video generation from seconds to minutes faces a critical bottleneck: while short-video data is abundant and high-fidelity, coherent long-form data is scarce and limited to narrow domains. While multi-resolution image training works because higher resolution is largely an interpolation of the same underlying patch distribution, training across video lengths is fundamentally different: a longer video is an extrapolation that must invent new events and causal structure beyond the short-clip horizon. To address this, we propose a training paradigm where Mode Seeking meets Mean Seeking, decoupling local fidelity from long-term coherence from a unified representation via a Decoupled Diffusion Transformer. Our approach utilizes a global Flow Matching head trained via supervised learning on long videos to capture narrative structure, while simultaneously employing a local Distribution Matching head that aligns sliding windows to a frozen short-video teacher via a mode-seeking reverse-KL divergence. This strategy enables the synthesis of minute-scale videos that learns long-range coherence and motions from limited long videos via supervised flow matching, while inheriting local realism by aligning every sliding-window segment of the student to a frozen short-video teacher.

Flow Matching models have demonstrated strong performance across a wide range of generative tasks. However, their reliance on ODE-based iterative sampling incurs substantial computational overhead, which limits their applicability in real-time scenes. While distillation is a promising solution, existing approaches largely borrow from diffusion-based score matching, often failing to exploit the intrinsic geometric structure of flows and suffering from training instability, high variance, and degraded generation quality. In this paper, we propose Mean Flow Distillation (MFD), a novel distillation framework tailored for flow matching models. We theoretically demonstrate that MFD acts as a temporal low-pass filter, effectively suppressing the high-frequency optimization noise inherent in variational score distillation (VSD) while ensuring global trajectory consistency. We further prove the Mean Flow Matching Theorem, establishing that matching expected average velocities is sufficient for strict distribution alignment. Empirically, on challenging high-dimensional manifolds including 4D occupancy forecasting and text-to-image generation, MFD achieves state-of-the-art performance, enabling high-fidelity single-step generation.

Step-level caching accelerates diffusion models by exploiting temporal redundancy across denoising steps. Existing methods make per-step cache decisions using threshold-based heuristics, without directly optimizing for final output quality. As a result, their inference latency varies across inputs and is difficult to control at deployment. In this work, we propose BudCache, which inverts this formulation: rather than letting per-step error thresholds dictate the runtime cost, we fix the compute budget in advance and search for the cache policy that best preserves the final output. To tackle the combinatorial complexity of step selection, we combine Simulated Annealing with deterministic Hill Climbing. This offline search identifies high-quality cache policies within minutes and introduces no online search or thresholding overhead during inference. When the compute budget is very tight, we further introduce cache-aware schedule alignment, which adapts the time discretization to the selected cache policy to reduce cache-induced trajectory mismatch. Experiments on FLUX.1-dev and Wan2.1 show that BudCache achieves better generation quality than heuristic caching baselines under the same inference budgets.

Although peptides are well suited for flexible and shallow binding interfaces, their intrinsic flexibility induces a strongly coupled sequence–structure relationship that current fixed-geometry latent models cannot simultaneously model with conformational diversity and physical feasibility, ultimately limiting design quality. To overcome this bottleneck, PepFGLD is proposed as a receptor-conditioned, flexibility-aware framework for full-atom peptide design. The framework is motivated by a systematic analysis of existing limitations: geometry shifts driven by interfacial flexibility are not well captured by standard equivariant encoders; the static combination of sequence information and 3D geometry cannot represent their dynamic interactions; and diffusion models without timely geometric feedback tend to drift away from physically reasonable energy landscapes. In PepFGLD, FlexEGNN is used to improve the sensitivity of geometric representations to local flexibility, a coherent and adaptable latent conformational manifold is formed through bidirectional sequence–structure interaction and nonlinear latent mapping, and a time-dependent energy-guided diffusion mechanism is incorporated to balance exploration and convergence during diffusion so that sampling trajectories are continuously guided toward physically feasible full-atom structures. PepFGLD yields improved binding affinity and design success across multiple peptide design tasks.

Diffusion models are typically trained with objectives that focus on local denoising targets at individual time steps (or adjacent pairs), which do not enforce consistency between predictions along the denoising trajectory. This lack of cross-time consistency can degrade performance, especially for few-step samplers. We introduce a temporal difference (TD) objective that penalizes inconsistency of the model’s \emph{multi-step} progress along the denoising path. By reformulating the diffusion process as a Markov reward process and casting denoising as a policy evaluation problem in reinforcement learning, we derive a unified TD approach that applies to both discrete- and continuous-time diffusion formulations. We further propose a principled sample-based reweighting method that stabilizes training. Empirically, we show that using our TD training can significantly improve sample quality measured by FID, with stronger advantages when the number of sampling steps is small, highlighting its practical utility under low-computation-budget scenarios. We provide ablation studies to justify our design choices, including pairwise loss reweighting, regularization weight, and one-step stride. Overall, our TD approach can be a general drop-in that enforces cross-time consistency and improves generation quality across different diffusion generative models.

Video Diffusion Transformers (VDiTs) represent the state of the art in video generation but remain constrained by the quadratic complexity of dense self-attention. To address this attention bottleneck, we analyze the pre-softmax matrix ($QK^\top$) and reveal two key properties: (1) video attention exhibits an effective low-dimensional structure with rapid singular-value decay, and (2) real motion induces hybrid spatio-temporal patterns rather than rigid ``spatial vs. temporal'' layouts. Guided by these observations, we propose Video-SVD, a training-free and plug-and-play acceleration method that does not modify the original network parameters. Video-SVD learns checkpoint-adaptive orthogonal bases offline and, at inference time, replaces expensive dense attention computation with lightweight online subspace projection and basis composition. To preserve high fidelity, Video-SVD further employs layer-shared dual-stream residual modules to recover fine-grained content details and positional information. Across HunyuanVideo and Wan2.1 backbones, Video-SVD achieves significant end-to-end speedups while maintaining high visual quality, reaching 1.92$\times$ on HunyuanVideo, 1.75$\times$ on Wan2.1-1.3B, and 1.79$\times$ on Wan2.1-14B.