ICML 2026 Papers

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.

Score-based and flow-based generative models exhibit remarkable expressive capacity in capturing complex distributions, and have been extensively deployed in tasks ranging from image generation to reinforcement learning. Nevertheless, these models suffer from prolonged inference latency, which imposes a significant computational bottleneck in RL with iterative sampling. To overcome this limitation, we propose a new framework named *Moment Matching Q-Learning* (MoMa QL), which utilizes a technique from statistical hypothesis testing known as maximum mean discrepancy (MMD) that intend to match all orders of statistics between the original and target distribution. By enforcing strong regularization on all moment statistics, this algorithm guarantees distribution-level convergence for conditional score function and remains stable under various hyperparameters. Empirically, we show that our method MoMa QL is more computationally efficient with a comparable if not competitive performance in various D4RL tasks. Remarkably, by accelerating the action sampling process for flow-based policies, MoMa QL demonstrates superior performance in offline-to-online RL tasks because of faster and stronger adaptability for online interactive finetuning.

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.

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.

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.

Large language models (LLMs) are increasingly deployed in privacy-sensitive domains, where users must balance the risk of data exposure through external APIs against the high computational cost of local deployment. Split learning has therefore emerged as a promising paradigm for LLM fine-tuning and inference under limited local resources. However, it introduces new privacy risks. Prior work primarily studies leakage of private input prompts, typically via inversion attacks on intermediate representations, while the potential for sensitive information leakage through generative response outputs remains largely unexplored. In this work, we unveil novel vulnerabilities of Split-LLM by presenting **P**atched Model **I**nversion with **D**ual-Sided **I**nitialization(**PIDI**), a two-stage attack that simultaneously targets both private input prompts and output responses in Split-LLM settings. It combines dual-sided initialization with a patched inversion strategy to tackle long sequences, substantially outperforming prior inversion methods. To counter threats from both sides, we further propose the **A**dapter-based **D**ualGuard with **M**utual **I**nformation Defense(**ADMI**), which integrates an adapter-based local warmup strategy and mutual information regularization to provide a strong empirical privacy protection with minimal impact on task performance. Extensive experiments across diverse tasks and models demonstrate that ADMI effectively defends against PIDI and other state-of-the-art inversion attacks. Our code is publicly available at \url{https://github.com/FLAIR-THU/VFLAIR-LLM}.

The In-context generation paradigm has demonstrated strong power in instructional image editing for better synthesis quality. Nevertheless, shaping such in-context learning for instructional video editing is not trivial. Without specifying editing regions, the results can suffer from the issue of inaccurate editing regions and the token interference between different areas. To address these, we present ReCo, a new instructional video editing paradigm that novelly delves into **Re**gional **Co**nstraint modeling between editing and non-editing areas. Technically, ReCo width-wise concatenates source and target video for joint denoising. In model training, ReCo formulates regional constraints with two regularization terms, i.e., latent and attention regularization, on one-step backward denoised latents and attention maps, respectively. The former increases the latent discrepancy of the editing region between source and target videos while reducing that of non-editing areas, emphasizing editing area modification and alleviating unexpected content generation. The latter suppresses the attention of tokens in the editing region to the tokens in counterpart of the source video, thereby mitigating their interference during novel object generation in target video. Furthermore, we propose a large-scale, high-quality video editing dataset, i.e., ReCo-Data, comprising 500K instruction-video pairs. Extensive experiments conducted on four major instruction-based video editing tasks verify the superiority of ReCo. Code is available at https://github.com/HiDream-ai/ReCo.

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.

Sparse autoencoders (SAEs) interpret neural network representations by decomposing activations into sparse combinations of dictionary atoms. However, SAEs assume features combine additively through linear reconstruction, an assumption that cannot capture compositional structure: linear models cannot distinguish whether ''Starbucks'' arises from the composition of ''star'' and ''coffee'' features or merely their co-occurrence. This forces SAEs to allocate monolithic features for compound concepts rather than decomposing them into interpretable constituents. We introduce PolySAE, which extends the SAE decoder with higher-order terms to model feature interactions while preserving the linear encoder essential for interpretability. Through low-rank tensor factorization on a shared projection subspace, PolySAE captures pairwise and triple feature interactions with small parameter overhead (3\% on GPT2). Across four language models and three SAE variants, PolySAE achieves an average improvement of $\sim$8\% in probing F1 while maintaining comparable reconstruction error, and produces 2--10$\times$ larger Wasserstein distances between class-conditional feature distributions. Critically, learned interaction weights exhibit negligible correlation with co-occurrence frequency ($r = 0.06$ vs $r = 0.82$ for SAE feature covariance), suggesting that polynomial terms capture compositional structure largely independent of surface statistics. Finally, the learned interaction directions causally steer model outputs toward the corresponding compositional semantics.

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.