ICML 2026 Papers

Discrete Flow Matching (DFM) presents a promising approach for graph generation; however, existing adaptations often introduce substantial complexity by incorporating task-specific heuristics, compromising the continuity equation and significantly expanding the hyperparameter space. Moreover, their sampling efficiency remains limited, as the required number of steps is often comparable to diffusion models, diminishing DFM’s practical advantages. To address these limitations, we propose SimGFM, a simplified graph DFM for graph generation. Leveraging characteristic patterns in graph-generation trajectories, SimGFM relies only on the scheduler and rate matrix, eliminating heavy heuristics and hyperparameter tuning, and achieves large step reductions while preserving SOTA results. SimGFM achieves strong empirical results: on QM9, it matches prior models requiring 500–1000 steps with only 10 steps, and on most datasets, its performance at 50 steps matches or surpasses these baselines, demonstrating both efficiency and competitiveness. Our source code is available at https://github.com/LUOyk1999/SimGFM.

Diffusion Large Language Models (dLLMs) often exhibit severe instability during Group Relative Policy Optimization (GRPO) training, limiting the effectiveness of reinforcement learning for improving reasoning capabilities. In dLLMs, the importance ratios used by GRPO are derived from finite-sample estimates rather than exact likelihoods, making them inherently noisy. In this paper, we show that GRPO is highly sensitive to this noise, which drives training instability. Through theoretical analysis and empirical evidence, we identify a self-reinforcing instability loop in which noisy importance ratios induce gradient spikes and policy drift, further amplifying future importance ratio estimation variance. To address this issue, we propose StableDRL, a novel reinforcement learning framework for dLLMs. StableDRL stabilizes training via (i) unconditional clipping to suppress outlier-induced gradient spikes, and (ii) self-normalization to constrain gradients within the convex hull of per-sample updates. We further extend StableDRL to block-wise diffusion models via a staircase attention mechanism. StableDRL is the first method that enables stable, full-parameter reinforcement learning for dLLMs. It achieves the state-of-the-art performance, outperforming prior best full-attention baselines by 6% on MATH500 and block-diffusion baselines by 25.6% on AIME.

Diffusion models are widely used for high-quality generation, but their performance is sensitive to the accuracy of the estimated score. We first derive a stepwise Wasserstein error bound in a Gaussian-mixture setting, where the score admits a closed-form structure, and the score Hessian can be controlled explicitly, leading to sharp Wasserstein estimates. We then extend the analysis to general data distributions, which yields a more general but typically looser upper bound. This general bound can be sharpened under mild regularity: when the initial distribution has a globally Lipschitz score, the curvature contribution at small times is uniformly bounded, avoiding the worst-case blow-up. The results hold for both variance-preserving (VP) and variance-exploding (VE) diffusions, and apply to both the reverse-time SDE and the associated probability-flow ODE.

Visual Autoregressive Modeling (VAR) based on next-scale prediction achieves strong generation quality, but their explicit deep stacks fix the amount of computation per scale and inflate memory at high resolutions. We introduce Visual Implicit Autoregressive Modeling (VIAR), a next-scale autoregressive generator that embeds an implicit equilibrium layer between shallow pre/post blocks. The implicit layer is trained with Jacobian‑Free Backpropagation, yielding constant training memory, while inference exposes a per‑scale iteration knob that enables compute control. On ImageNet 256 × 256 benchmark, VIAR attains FID 2.16, and sFID 8.07 with only 38.4\% parameters of VAR, matching or surpassing strong AR baselines and remaining competitive with large diffusion models. By controlling the per-scale knob, VIAR can reduce peak memory from 19.24 GB to 8.53 GB and doubles throughput from 15.16 to 32.08 images/s on a single RTX 4090, without retraining. Ablations show that fewer steps are sufficient for fixed-point iterations to converge and that VIAR consistently dominates VAR across quality efficiency operating points. In zero shot in-painting and class‑conditional editing, VIAR produces sharper details and smoother boundaries while preserving global structure, validating the benefits of implicit equilibria and per‑scale compute control for practical, deployable visual generation.

Sampling from unnormalized densities is analogous to the generative modeling problem, but the target distribution is defined by a known energy function instead of data samples. Because evaluating the energy function is often costly, a primary challenge is to learn an efficient sampler. We introduce Flow Sampling, a framework built on diffusion models and flow matching for the data-free setting. Our training objective is conditioned on a noise sample and regresses onto a denoising diffusion drift constructed from the energy function. In contrast, diffusion models' objective is conditioned on a data sample and regresses onto a noising diffusion drift. We utilize the interpolant process to minimize the number of energy function evaluations during training, resulting in an efficient and scalable method for sampling unnormalized densities. Furthermore, our formulation naturally extends to Riemannian manifolds, enabling diffusion-based sampling in geometries beyond Euclidean space. We derive a closed-form formula for the conditional drift on constant curvature manifolds, including hyperspheres and hyperbolic spaces. We evaluate Flow Sampling on synthetic energy benchmarks, small peptides, large-scale amortized molecular conformer generation, and distributions supported on the sphere, demonstrating strong empirical performance.

Precise camera pose control is critical for video diffusion, yet maintaining geometric consistency remains a challenge. Existing methods that directly inject numerical camera parameters into the diffusion backbone often fail to bridge the gap between abstract coordinates and visual content, leading to structural distortions. To address this issue, we propose CameraNoise, a flow-to-noise warping method that encodes camera motion into a temporally coherent stochastic representation. Unlike conventional conditioning, CameraNoise embeds camera poses directly into the noise space. This decouples motion from scene appearance while faithfully preserving trajectory dynamics. Specifically, we introduce a novel Geometry-guided Reprojection Flow and a noise warping algorithm, which jointly preserve the Gaussian prior of diffusion and ensure consistent noise propagation under camera transformations. By integrating CameraNoise into the diffusion process, our framework delivers stable, high-fidelity videos. Extensive experiments demonstrate that our approach significantly outperforms prior methods in both visual quality and trajectory faithfulness.

Recent progress in large-scale flow and diffusion models raised two fundamental algorithmic challenges: $(i)$ control-based reward adaptation of pre-trained flows, and $(ii)$ integration of multiple models, i.e., flow merging. While current approaches address them separately, we introduce a unifying probability-space framework that subsumes both as limit cases, and enables *reward-guided flow merging*, allowing principled, task-aware combination of multiple pre-trained flows (e.g., merging priors while maximizing drug-discovery utilities). Our formulation renders possible to express a rich family of *operators over generative models densities*, including intersection (e.g., to enforce safety), union (e.g., to compose diverse models), interpolation (e.g., for discovery), their reward-guided counterparts, as well as complex logical expressions via *generative circuits*. Next, we introduce Reward-Guided Flow Merging (RFM), a mirror-descent scheme that reduces reward-guided flow merging to a sequence of standard fine-tuning problems. Then, we provide first-of-their-kind theoretical guarantees for reward-guided and *pure* flow merging via RFM. Ultimately, we showcase the capabilities of the proposed method on illustrative settings providing visually interpretable insights, and apply our method to high-dimensional de-novo molecular design and low-energy conformer generation.

Flow matching models (FMs) have revolutionized text-to-image (T2I) generation, with reinforcement learning (RL) serving as a critical post-training strategy. We show that current RL pipelines for FMs suffer from two underappreciated limitations: sample inefficiency from collapsed generation diversity, and prompt overfitting, where models memorize training phrasings and collapse on semantically equivalent paraphrases. We present **PromptRL** (**P**rompt **M**atters in **RL** for Flow-Based Image Generation), a framework that incorporates language models (LMs) as trainable prompt refinement agents directly within the flow-based RL loop, yielding both a learned prompt rewriter and a synergistic training regime that reshapes optimization dynamics. PromptRL attains state-of-the-art scores of **0.97** on GenEval, **0.98** on OCR accuracy, and **24.05** on PickScore, and on instructional editing it improves FLUX.1-Kontext from **1.19** to **1.43** EditReward with only **0.06M** rollouts, surpassing Gemini 2.5 Flash Image (Nano Banana, **1.37**) and matching ReasonEdit-Think (**1.44**), which relied on fine-grained data annotations and a multi-stage pipeline. Our experiments show that PromptRL achieves higher performance ceilings with approximately **50% fewer rollouts** than naive flow-only RL. Our code is available at [https://github.com/G-U-N/UniRL](https://github.com/G-U-N/UniRL).

The prevailing inference framework for diffusion models formulates generation fundamentally as a problem of numerical integration. This perspective casts the model as an accurate estimator, neglecting the inherent statistical uncertainty of the denoising process. In this work, we propose Forward-Process Aligned Diffusion prediction (DiFA), a training-free framework that reframes inference-time clean-signal prediction refinement within diffusion sampling as a sequential state estimation problem. Instead of discarding historical predictions, DiFA treats the inference trajectory as a sequence of correlated observations with varying uncertainties. Inspired by Kalman estimation, DiFA builds a logSNR-aware temporal consensus to align historical clean predictions. Crucially, to counteract the over-smoothing typically associated with temporal consensus, we introduce a deviation guidance mechanism that adaptively preserves residual details. Empirically, DiFA yields significant improvements in FID, IS, and FD-DINOv2 scores on CIFAR-10 and ImageNet, demonstrating that aligning inference with the forward statistical structure substantially improves generative fidelity. Our code is publicly available at https://github.com/ShiguiLi/DiFA.

Diffusion models have shown remarkable empirical success in sampling from rich multi-modal distributions. Their inference relies on numerically solving a certain differential equation. This differential equation cannot be solved in closed form, and its resolution via discretization typically requires many small iterations to produce *high-quality* samples. More precisely, prior works have shown that the iteration complexity of discretization methods for diffusion models scales polynomially in the ambient dimension and the inverse accuracy $1/\varepsilon$. In this work, we propose a new solver for diffusion models relying on a subtle interplay between low-degree approximation and the collocation method, and we prove that its iteration complexity scales *polylogarithmically* in $1/\varepsilon$, yielding the first "high-accuracy" guarantee for a diffusion-based sampler that only uses (approximate) access to the scores of the data distribution. In addition, our bound does not depend explicitly on the ambient dimension; more precisely, the dimension affects the complexity of our solver only through the *effective radius* of the support of the target distribution.

While neuroscience experiments have repeatedly demonstrated the involvement of large populations of neurons in even simple behaviors, these studies have just as often reported that the collective dynamics of neural activity are approximately low-dimensional. As a result, methods for identifying low-dimensional latent representations of time series data have become increasingly prominent in neuroscience. However, most existing methods either ignore temporal structure or model time evolution using latent dynamical systems approaches. In the first case, dynamics may be distorted or even scrambled in the latent space, while in the second, many possible latent dynamics may give rise to the same data. Here, we address these challenges using a novel flow-matching approach in which data are generated by a pair of flow fields, one governing time evolution, the other a mapping between data and a low-dimensional latent space. Importantly, the dimension-reducing flow is trained to minimize distortions of the temporal dynamics, learning an identifiable low-dimensional representation that preserves temporal relations in the original data. Additionally, we constrain our latent spaces to have low-dimensional support in a soft, parameterized manner, taking inspiration from ideas on nested dropout. Across both neural and behavioral data, we show that this dual flow approach produces both more interpretable dynamics and higher-quality reconstructions than competing models, including in noise-dominated data sets where conventional approaches fail.

Deep stochastic processes have recently become a central paradigm for image enhancement, with many methods explicitly conditioning the stochastic trajectory on the degraded input. However, the relationship between these conditional processes and standard diffusion models remains unclear. In this work, we introduce a unified perspective on stochastic image enhancement by classifying recent methods into three families of continuous-time processes: unconditional diffusion models, Ornstein–Uhlenbeck (OU) processes, and diffusion bridges. We show that all of these approaches arise from a common stochastic differential equation (SDE) formulation. This framework makes explicit that seemingly disparate methods differ primarily in their drift and diffusion terms, terminal distributions, and boundary conditions, while schedulers and samplers constitute orthogonal design choices. Leveraging this unification, we conduct a controlled empirical study across multiple image enhancement tasks using identical architectures and training protocols. Our results reveal no consistently dominant method; instead, we identify and disentangle the specific design choices that most strongly influence performance. Finally, we release ItoVision, a modular PyTorch library that implements the unified framework and enables rapid prototyping and fair comparison of stochastic image enhancement methods.

Diffusion models have shown impressive capabilities in text-to-image synthesis. However, multi-concept personalized generation remains challenging, particularly in aligning multiple reference concepts while preserving fidelity. To address this, we propose a novel Sketch-to-Rendering framework that leverages $\textit{Dual Optimal Transport (OT)}$ for structure alignment and texture injection. Our approach consists of two key components: $\textit{Structure Sketching via Barycentric Soft-Transport}$, which ensures shape alignment by using mass-preserving OT for spatial consistency, and $\textit{Texture Rendering via Geometry-Guided Transport}$, which leverages low-frequency structure alignment to inject high-frequency texture details via OT-based residual transfer, thereby preserving texture fidelity without distorting structure. Extensive experiments demonstrate that our method significantly enhances both conceptual fidelity and visual quality. Ablation studies further validate the effectiveness of our optimal transport guidance and the decoupling of structure and texture during the generation process. Our code is available at https://github.com/fuhao7i/OTComp.

Flow matching Vision-Language-Action (VLA) models promise precise continuous control, but their iterative denoising nature introduces fundamental incompatibilities with real-time robotics: global timestep injection invalidates KV-caching, forcing a choice between slow $O(N^2)$ re-computation or mathematically incorrect cache reuse. We present **Reflex**, a framework that enables *real-time streaming inference* for flow matching policies by exploiting the *Timestep-Invariance Property*---that perception encoders are functionally independent of the denoising loop. Reflex partitions the attention context into static, sliding, and dynamic regions, enabling $O(1)$ incremental cache updates while preserving full-batch-equivalent attention outputs for fixed inputs. To ensure stability under continuous high-frequency inference, we introduce *AdaRMSNorm*, an adaptive normalization layer that prevents BFloat16 numerical collapse by gating on flow phase. We further maximize throughput through an *async pipeline* that decouples visual encoding from action generation, combined with *operator fusion* that reduces kernel overhead. On LIBERO and Kinetix benchmarks, Reflex achieves a 2.58$\times$ inference speedup and 50Hz stable streaming, reducing reaction latency by up to 54\% and enabling efficient deployment without performance degradation.

Diffusion models (DMs) are a powerful framework for image generation and restoration. However, existing DMs are primarily trained in a supervised manner by using a large corpus of clean images. This poses fundamental challenges in many real-world scenarios, where acquiring noise-free data is hard or infeasible. While some methods are capable of training DMs using noisy data, they are effective only when the amount of noise is very mild or when additional noise-free data is available. In addition, existing methods for training DMs from incomplete measurements require access to multiple complementary acquisition processes, a significant practical limitation. Here we introduce the first approach for learning DMs for image restoration using only noisy measurement data from a single operator. First, we show that DMs, and more broadly minimum mean squared error denoisers, exhibit a weak form of scale equivariance linking rescaling in signal amplitude to changes in noise intensity. We then leverage this theoretical insight to develop a denoising score-matching strategy that generalizes robustly to noise levels below the training data, thereby enabling the learning of DMs from noisy measurements. For problems involving measurements both noisy and incomplete, we integrate our method with equivariant imaging, a complementary self-supervised learning framework that exploits the inherent invariants of imaging problems. This allows training DMs for image restoration from single-operator noisy measurements. We validate the effectiveness of our approach through extensive experiments on image denoising, demosaicing, inpainting, and MRI reconstruction along with comparisons with the state of the art.

Conditional diffusion models appear capable of compositional generalization, i.e., generating convincing samples for out-of-distribution combinations of conditioners, but the mechanisms underlying this ability remain unclear. To make this concrete, we study length generalization, the ability to generate images with more objects than seen during training. In a controlled CLEVR setting (Johnson et al., 2017), we find that length generalization is achievable in some cases but not others, suggesting that models only sometimes learn the underlying compositional structure. We then investigate locality as a structural mechanism for compositional generalization. Prior works proposed score locality as a mechanism for creativity in unconditional diffusion models (Kamb & Ganguli, 2024; Niedoba et al., 2024), but did not address flexible conditioning or compositional generalization. In this paper, we prove an exact equivalence between a specific compositional structure (*conditional projective composition*) (Bradley et al., 2025) and scores with sparse dependencies on both pixels and conditioners (*local conditional scores*). This theory also extends to compositions of concepts (such as style+content) in feature-space. We validate our theory empirically: CLEVR models that succeed at length generalization exhibit local conditional scores, while those that fail do not. Furthermore, we show that a causal intervention explicitly enforcing local conditional scores enables length generalization in a previously failing model. Finally, we investigate feature-space compositionality in color-conditioned CLEVR, and find preliminary evidence of compositional structure and corresponding local mechanisms in SDXL.

Reconstructing 3D scenes using 3D Gaussian Splatting (3DGS) from sparse views is an ill-posed problem due to insufficient information, often resulting in noticeable artifacts. While recent approaches have sought to leverage generative priors to complete information for under-constrained regions, they struggle to generate content that remains consistent with input observations. To address this challenge, we propose GSFixer, a novel framework designed to improve the quality of 3DGS representations reconstructed from sparse inputs. The core of our approach is the reference-guided video restoration model, built upon a DiT-based video diffusion model trained on paired artifact 3DGS renders and clean frames with additional reference-based conditions. Considering the input sparse views as references, our model integrates both 2D semantic and 3D geometric features of reference views extracted from the visual geometry foundation model, enhancing the semantic coherence and 3D consistency when fixing artifact novel views. Furthermore, we introduce a reference-guided trajectory sampling strategy that ensures both angular coverage and view quality, further enhancing reconstruction fidelity. Considering the lack of suitable benchmarks for 3DGS artifact restoration evaluation, we present DL3DV-Res which contains artifact frames rendered using low-quality 3DGS. Extensive experiments demonstrate our GSFixer outperforms current state-of-the-art methods in 3DGS artifact restoration and sparse-view 3D reconstruction. Project page: https://github.com/GVCLab/GSFixer.

Learning-based methods for sampling from the Gibbs distribution in finite-dimensional spaces have progressed quickly, yet theory and algorithmic design for infinite-dimensional function spaces remain limited. This gap persists despite their strong potential for sampling the paths of conditional diffusion processes, enabling efficient simulation of trajectories of diffusion processes that respect rare events or boundary constraints. In this work, we present the adjoint sampler for infinite-dimensional function spaces, a stochastic optimal control-based diffusion sampler that operates in function space and targets Gibbs-type distributions on infinite-dimensional Hilbert spaces. Our Functional Adjoint Sampler (FAS) generalizes Adjoint Sampling (Havens et al., 2025) to Hilbert spaces based on a SOC theory called stochastic maximum principle, yielding a simple and scalable matching-type objective for a functional representation. We show that FAS achieves superior transition path sampling performance across synthetic potential and real molecular systems, including Alanine Dipeptide and Chignolin.

Agent planning faces dynamic heterogeneity—nonstationary observations, dynamics, and objectives with sparse, delayed rewards—which dominant methods largely ignore, leading to poor generalization under environment shifts. We propose Flow-Matching for Agent Planning (FlowMAP), which formulates planning as a continuous-time flow-matching problem by learning a planning-time velocity field that transports an initial meta-state distribution toward a task-conditioned target. FlowMAP introduces Value-Transport Flow Matching to provide a distribution-level planning objective that steers transport toward high-value regions in the meta-state distribution, mitigating error accumulation under environmental shifts. To enforce alignment between meta-state distribution transport and action--environment interaction, FlowMAP further proposes Flow--Policy Co-Training, which jointly optimizes the planning flow and policy so that the flow transport directly regularizes the policy-induced meta-distribution dynamics. Across diverse agent planning benchmarks, FlowMAP consistently outperforms strong baselines, yielding improvements in planning generalization.