ICML 2026 Papers

Standard diffusion models for graph generation typically rely on uniform time-stepping, an approach that overlooks the non-homogeneous dynamics of distributional evolution on complex manifolds. In this paper, we present an information-geometric framework that reinterprets the diffusion sampling trajectory as a parametric curve on a Riemannian manifold. Our key observation is that the Fisher-Rao metric provides a principled measure of the intrinsic distance. By analyzing this metric, we derive the Drift Variation Score (DVS), a geometry-aware indicator that quantifies the instantaneous rate of distributional change. Unlike prior heuristic-based adaptive samplers, our DVS solver enforces a constant informational speed on the statistical manifold, automatically maintaining a uniform rate of distributional change along the sampling trajectory. This equal arc-length strategy ensures that each discretization step contributes equally to the information speed. Theoretical analysis verifies that DVS characterizes the local stiffness of the sampling dynamics in the Fisher-Rao sense. Experimental results on molecule and social network generation show that DVS significantly improves structural fidelity and sampling efficiency.

Flow maps enable high-quality image generation in a single forward pass. However, unlike iterative diffusion models, their lack of an explicit sampling trajectory impedes incorporating external constraints for conditional generation and solving inverse problems. We put forth _Variational Flow Maps_, a framework for conditional sampling that shifts the perspective of conditioning from "guiding a sampling path", to that of "learning the proper initial noise". Specifically, given an observation, we seek to learn a _noise adapter model_ that outputs a noise distribution, so that after mapping to the data space via flow map, the samples respect the observation and data prior. To this end, we develop a principled variational objective that jointly trains the noise adapter and the flow map, improving noise-data alignment, such that sampling from complex data posterior is achieved with a simple adapter. Experiments on various inverse problems show that VFMs produce well-calibrated conditional samples in a single (or few) steps. For ImageNet, VFM attains competitive fidelity while accelerating the sampling by orders of magnitude compared to alternative iterative diffusion/flow models.

Diffusion Large Language Models (dLLMs) support arbitrary-order generation, yet their inference performance critically depends on the unmasking order. Existing strategies rely on heuristics that greedily optimize local confidence, offering limited guidance for identifying unmasking paths that are globally consistent and accurate. To bridge this gap, we introduce path log-likelihood (Path LL), a trajectory-conditioned objective that strongly correlates with downstream accuracy and enables principled selection of unmasking paths. To optimize Path LL at inference time, we propose POKE, an efficient value estimator that predicts the expected future Path LL of a partial decoding trajectory. We then integrate this lookahead signal into POKE-SMC, a Sequential Monte Carlo-based search framework for dynamically identifying optimal unmasking paths. Extensive experiments across 6 reasoning tasks show that POKE-SMC consistently improves accuracy, achieving 2\%--3\% average gains over strong decoding-time scaling baselines at comparable inference overhead on LLaDA models and advancing the accuracy--compute Pareto frontier.

Diffusion models learn a time-indexed score field $\mathbf{s}_\theta(\mathbf{x}_t,t)$ that often inherits approximate equivariances (flips, rotations, circular shifts) from in-distribution (ID) data and convolutional backbones. Most diffusion-based out-of-distribution (OOD) detectors exploit score magnitude or local geometry (energies, curvature, covariance spectra) and largely ignore equivariances. We introduce Group-Equivariant Posterior Consistency (GEPC), a training-free probe that measures how consistently the learned score transforms under a finite group $G$, detecting equivariance breaking even when score magnitude remains unchanged. At the population level, we propose the ideal GEPC residual which averages an equivariance-residual functional over $G$, and we derive ID upper bounds and OOD lower bounds under mild assumptions. GEPC requires only score evaluations and produces interpretable equivariance-breaking maps. On OOD image benchmark datasets, we show that GEPC achieves competitive or improved AUROC compared to recent diffusion-based baselines while remaining computationally lightweight. On high-resolution synthetic aperture radar imagery where OOD corresponds to targets or anomalies in clutter, GEPC yields strong target-background separation and visually interpretable equivariance-breaking maps. The official implementation is available at https://github.com/RouzAY/gepc-diffusion/.

We identify and analyze a surprising phenomenon of $\textit{Latent}$ Diffusion Models (LDMs) where the final steps of the diffusion can $\textit{degrade}$ sample quality. In contrast to conventional arguments that justify early stopping for numerical stability, this phenomenon is intrinsic to the dimensionality reduction in LDMs. We provide a principled explanation by analyzing the interaction between latent dimension and stopping time. Under a Gaussian framework with linear autoencoders, we characterize the conditions under which early stopping is needed to minimize the distance between generated and target distributions. More precisely, we show that lower-dimensional representations benefit from earlier termination, whereas higher-dimensional latent spaces require later stopping time. We further establish that the latent dimension interplays with other hyperparameters of the problem such as constraints in the parameters of score matching. Crucially, this framework suggests that the reconstruction quality of the autoencoder alone can serve as a proxy to estimate the potential performance of the full LDM. Experiments on synthetic and real datasets illustrate these properties, underlining that early stopping can improve generative quality. Together, our results offer a theoretical foundation for understanding how the latent dimension influences the sample quality, and highlight stopping time as a key hyperparameter in LDMs.

Flow-matching has emerged as a leading framework for high-fidelity text-to-image generation. However, its alignment with human preferences through RL is often hindered by substantial computational overhead. In this paper, we introduce Flow-TTRL, the first test-time reinforcement learning framework that achieves alignment on the fly. Our approach reinterprets intermediate latent representations as an implicit policy and utilizes SDE-based rollouts to explore high-reward trajectories within the learned vector field. Specifically, we propose a two-stage optimization strategy: Proximal Reward Difference Prediction (PRDP) ensures structural stability in high-noise regimes through pairwise reward regression, while Group Relative Policy Optimization (GRPO) refines fine-grained aesthetic details by maximizing relative advantages within sampled candidate groups. Experimental results show that Flow-TTRL significantly boosts aesthetic quality, text-image alignment, and human preference across diverse backbones. On the GenEval benchmark, Flow-TTRL elevates the accuracy of SD 3.5-Medium from 63\% to 87\% and Flux.1 Dev from 66\% to 83\%. Furthermore, our framework achieves an average gain of 15\% to 20\% across T2I-CompBench metrics, delivering performance comparable to state-of-the-art RL-based fine-tuning methods without the need for additional fine-tuning. Our code is available at ~\url{https://github.com/TheShy-Dream/Flow-TTRL}.

Diffusion inversion, which maps images back to the Gaussian latent space of a diffusion model, is a critical task for image reconstruction and editing. While DDIM enables fast deterministic inversion, it inherently introduces deviations that accumulate into noticeable inversion errors. Existing methods often address this by solving a fixed-point problem but largely overlook how the selection of the diffusion timestep in the noise scheduler influences inversion fidelity. In this work, we reveal that the deviation scale in diffusion inversion is strongly dependent on the timestep size, and exhibits a parabolic trend, with larger errors concentrated at both small and large timesteps. Based on this finding, we propose a simple yet effective nonuniform timestep scheduler that integrates a global rescaling with a local dynamic programming based rescheduling, enabling a strategic allocation of computational effort that minimizes the overall inversion error and preserves higher inversion accuracy. Our method serves as an off-the-shelf enhancement for existing inversion techniques and requires no extra parameters or computational overhead. Through extensive experiments, we verify that integrating our scheduler consistently boosts the performance of existing inversion methods, achieving superior results in image reconstruction and editing.

The increasingly realistic and diverse generative data has led some deepfake detection methods to shift towards learning robust real content, e.g., via reconstruction-based tasks. However, most existing approaches rely primarily on prevalent continuous modeling (e.g., GMMs, VAEs, Diffusion Models) to construct a continuous latent manifold of real data, with the aim of improving the generalization capability, while overlooking a critical issue, i.e., such continuity may facilitate the interpolation of forgery artifacts, consequently causing ambiguity in detection. To alleviate this problem, we integrate discrete modeling into the feature space of the CLIP vision encoder, striking a balance between continuous manifold modeling and discrete representation. By incorporating a learnable vector quantized codebook, the real latent manifold is discretized, imposing a more stringent information bottleneck that reduces the likelihood of embedding generative artifacts. In order to further enhance the generalization of discrete modeling, we propose an adaptive tangent space projection mechanism that yields a continuous relaxation of the discrete real distribution within a controllable range. With these components, our method constructs a real distribution that is both tightly constrained and broadly generalizable, enhancing robustness to unseen forgeries. Extensive experiments on diverse datasets demonstrate the effectiveness of our method.

Adapting large-scale pre-trained video generators for Video Super-Resolution (VSR) in novel domains remains computationally prohibitive. Methods that reformulate generation as direct Low-Quality to High-Quality mappings deviate from the original generative formulation, demanding extensive fine-tuning. ControlNet-style adapters lose their efficiency under modern Diffusion Transformers since the absence of encoder-decoder hierarchy forces duplication of the entire backbone. We observe that flow matching offers a principled alternative for cross-domain VSR adaptation. By predicting a constant velocity field across all timesteps, the adaptation task reduces to learning a fixed injection pattern rather than time-varying transformations. Building on this insight, we propose LiteVSR, a minimalist framework that performs VSR using a completely frozen Diffusion Transformer with a lightweight State-Aware Adapter. The adapter employs a dual-stream architecture that extracts static structural cues from the LQ input and dynamic cues from intermediate denoising states, aligning them through time-dependent cross-attention to enable adaptive transition from structural alignment to texture refinement as denoising proceeds. LiteVSR achieves competitive restoration quality with only 11.25% trainable parameters and 12 GPU-hours of training on a single A100, while maintaining fast sampling (down to a single step) compatibility.

Incomplete multi-view clustering is challenging due to view missingness and the entanglement of shared semantics with view-specific factors in latent representations. Existing methods often rely on heuristic fusion or direct completion strategies, which suffer from error propagation and unreliable generation under missing views. In this paper, we propose an **I**nformation-guided **D**isentangled latent modeling framework with **C**onditional **D**iffusion for incomplete multi-view clustering (IDCD). Specifically, we first encode each view into a latent representation that is variationally decomposed into a view-wise semantic latent and a view-specific factor. Information-theoretic objectives are introduced to guide the disentanglement of view-wise latents, preserving essential multi-view information while reducing the dependency between semantic and view-specific factors and encouraging cross-view semantic consistency. Besides, we aggregate the semantic latents via a mixture of Wasserstein distributions to obtain a unified global representation, where we impose a Gaussian mixture prior to explicitly couple representation learning with clustering. Based on the learned disentangled latent space, a conditional diffusion model guided by both the global semantic latent and view-specific factors is employed to generate missing views in a consistent manner. Extensive experiments on benchmark datasets demonstrate superior clustering performance and robust missing-view generation compared to state-of-the-art methods.

Simulating trajectories of dynamical systems is a fundamental problem in a wide range of fields such as molecular dynamics, biochemistry, and pedestrian dynamics. Machine learning has become an invaluable tool for scaling physics-based simulators and developing models directly from experimental data. In particular, recent advances in deep generative modeling and geometric deep learning enable probabilistic simulation by learning complex trajectory distributions while respecting intrinsic permutation and time-shift symmetries. However, trajectories of N-body systems are commonly characterized by high sensitivity to perturbations leading to bifurcations, as well as multi-scale temporal and spatial correlations. To address these challenges, we introduce STFlow (Spatio-Temporal Flow), a generative model based on graph neural networks and hierarchical convolutions. By incorporating data-dependent couplings within the Flow Matching framework, STFlow denoises starting from conditioned random-walks instead of Gaussian noise. This novel informed prior simplifies the learning task by reducing transport cost, increasing training and inference efficiency. We validate our approach on N-body systems, molecular dynamics, and human trajectory forecasting. Across these benchmarks, STFlow achieves the lowest prediction errors with fewer simulation steps and improved scalability.

Discovering heterogeneous catalysts tailored for specific reaction intermediates remains a fundamental bottleneck in materials science. While traditional trial-and-error methods and recent generative models have shown promise, they struggle to capture the intrinsic coupling between surface geometry and adsorbate interactions. To address this limitation, we propose CatFlow, a flow matching-based framework for de novo design and structure prediction of heterogeneous catalysts. Our model operates on a primitive cell-based factorized representation of the slab-adsorbate complex, reducing the number of learnable variables by an average of 9.2x while explicitly encoding the surface orientation of the slab-adsorbate interface. Experiments on the Open Catalyst 2020 dataset demonstrate that CatFlow significantly improves the structural fidelity of generated catalysts compared to autoregressive and sequential baselines. Further experiments show that the generated structures accurately capture the adsorption energy distributions of physically plausible interfaces and lie closer to thermodynamic local minima.

Offline Reinforcement Learning (RL) relies on static datasets and often enforces conservative constraints to mitigate out-of-distribution errors, but this inevitably gives rise to learning dataset biases and limited behavioral generalization. Recent Data Augmentation (DA) methods leverage generative models to enrich offline data, yet they mainly operate within a single rollout paradigm and tend to preserve the original trajectory-level connectivity of the dataset. As a result, such methods often introduce local variations and fail to recover connections between distinct behavior patterns. In this paper, we propose Bidirectional Trajectory Diffusion (BiTrajDiff), a novel DA framework that explicitly addresses this limitation. BiTrajDiff decomposes trajectory synthesis into two independent diffusion processes that generate forward-future and backward-history segments conditioned on shared intermediate anchor states. By stitching the generated segments at these anchors, BiTrajDiff can synthesize trajectories that bridge disconnected behavior patterns and recover global trajectory-level connectivity absent from the original data. Extensive experiments demonstrate that BiTrajDiff consistently outperforms advanced DA methods across a range of offline RL backbones. Our code is available at [https://github.com/Plankson/BiTrajDiff](https://github.com/Plankson/BiTrajDiff).

We present a mechanism to steer the sampling diversity of denoising diffusion and flow matching models, allowing users to sample from a sharper or broader distribution than the training distribution. We build on the observation that these models leverage (learned) score functions of noisy data distributions for sampling and show that rescaling these allows one to effectively control a 'local' sampling temperature. Notably, this approach does not require any finetuning or alterations to training strategy, and can be applied to any off-the-shelf model and is compatible with both deterministic and stochastic samplers. We first validate our framework on toy 2D data, and then demonstrate its application for diffusion models trained across five disparate tasks -- image generation, pose estimation, depth prediction, robot manipulation, and protein design. We find that across these tasks, our approach allows sampling from sharper (or flatter) distributions, yielding performance gains e.g., depth prediction models benefit from sampling more likely depth estimates, whereas image generation models perform better when sampling a slightly flatter distribution.

Large language models (LLMs) have demonstrated that large-scale pretraining enables systems to adapt rapidly to new problems with little supervision in the language domain. This success, however, has not translated as effectively to the visual domain, where models, including LLMs, continue to struggle with compositional understanding, sample efficiency, and general-purpose problem-solving. We investigate Video Diffusion Models (VDMs) as a promising direction for bridging this gap. Pretraining on spatiotemporal data endows these models with strong inductive biases for structure and dynamics, which we hypothesize can support broad task adaptability. To test this, we design a controlled evaluation in which both a pretrained LLM and a pretrained VDM are equipped with lightweight adapters and presented with tasks in their natural modalities. Across benchmarks including ARC-AGI, ConceptARC, visual games, route planning, and cellular automata, VDMs demonstrate higher data efficiency than their language counterparts. Taken together, our results indicate that video pretraining offers inductive biases that support progress toward visual foundation models.

Recent advances in video diffusion models have demonstrated remarkable generative capability, yet adapting these large pretrained text-to-video (T2V) models to video super‑resolution (VSR) typically encounters challenges, such as artifacts introduced by complex degradations in real-world scenarios and compromised fidelity due to the strong generative capacity of the powerful T2V models. We present WEVSR, a novel approach that adapts a pretrained flow-matching video diffusion transformer to VSR. First, we design a task-oriented adaptation strategy that leverages timestep sampling and noise augmentation to enhance detail restoration while preserving structural stability. Second, we propose a lightweight multi-level discrete wavelet transform (DWT) front-end for the VAE encoder, injecting explicit frequency priors into the latent space without modifying the pretrained decoder. Extensive experiments across multiple VSR benchmarks demonstrate that WEVSR achieves state-of-the-art performance against existing approaches. Code and models will be released here.

Modern diffusion/flow-based models for image generation typically exhibit two core characteristics: (i) using multi-step sampling, and (ii) operating in a latent space. Recent advances have made encouraging progress on each aspect individually, paving the way toward one-step diffusion/flow without latents. In this work, we take a further step towards this goal and propose "pixel MeanFlow" (pMF). Our core guideline is to formulate the network output space and the loss space separately. The network target is designed to be on a presumed low-dimensional image manifold (i.e., x-prediction), while the loss is defined via MeanFlow in the velocity space. We introduce a simple transformation between the image manifold and the average velocity field. In experiments, pMF achieves strong results for one-step latent-free generation on ImageNet at 256$\times$256 resolution (2.22 FID) and 512$\times$512 resolution (2.48 FID), filling a key missing piece in this regime. We hope that our study will further advance the boundaries of diffusion/flow-based generative models.

Pre-trained diffusion models have emerged as powerful generative priors for both unconditional and conditional sample generation, yet their outputs often deviate from the characteristics of user-specific target data. Such mismatches are especially problematic in domain adaptation tasks, where only a few reference examples are available and retraining the diffusion model is infeasible. Existing inference-time guidance methods can adjust sampling trajectories, but they typically optimize surrogate objectives such as classifier likelihoods rather than directly aligning with the target distribution. We propose *MMD Guidance*, a training-free mechanism that augments the reverse diffusion process with gradients of the *Maximum Mean Discrepancy (MMD)* between generated samples and a reference dataset. MMD provides reliable distributional estimates from limited data, exhibits low variance in practice, and is efficiently differentiable, which makes it particularly well-suited for the guidance task. Our framework naturally extends to prompt-aware adaptation in conditional generation models via product kernels. Also, it can be applied with computational efficiency in latent diffusion models (LDMs), since guidance is applied in the latent space of the LDM. Experiments on synthetic and real-world benchmarks demonstrate that MMD Guidance can achieve distributional alignment while preserving sample fidelity. The project code is available at [https://github.com/matinamehdizadeh/MMD-Guidance](https://github.com/matinamehdizadeh/MMD-Guidance).

Uniform Discrete Diffusion Model (UDM) has recently emerged as a promising paradigm for discrete generative modeling; however, its integration with reinforcement learning remains largely unexplored. We observe that naively applying GRPO to UDM leads to training instability and marginal performance gains. To address this, we propose **UDM-GRPO**, the first framework to integrate UDM with RL. Our method is guided by two key insights: (i) treating the final clean sample as the action provides more accurate and stable optimization signals; and (ii) reconstructing trajectories via the diffusion forward process better aligns probability paths with the pretraining distribution. Additionally, we introduce two strategies, Reduced-Step and CFG-Free, to further improve training efficiency. **UDM-GRPO** significantly improves base model performance across multiple T2I tasks. Notably, GenEval accuracy improves from $69\\%$ to $96\\%$ and PickScore increases from $20.46$ to $23.81$, achieving state-of-the-art performance in both continuous and discrete settings. On the OCR benchmark, accuracy rises from $8\\%$ to $57\\%$, further validating the generalization ability of our method. Code is available at https://github.com/Yovecent/UDM-GRPO.