ICML 2026 Papers

Low-count Positron Emission Tomography (PET) reconstruction is severely hindered by the dissipative nature of prevailing generative models, where the inherent phase-space contraction leads to the numerical extinction (``wash-out'') of weak but diagnostically critical lesion signals. To overcome this geometric limitation, we propose \textbf{FlowPET}, a physics-informed framework that reformulates reconstruction as volume-preserving transport in a symplectic phase space. By parameterizing the posterior dynamics via a Separable Hamiltonian System, our approach guarantees a divergence-free vector field by construction, theoretically immunizing weak signals against probability mass collapse. To steer this conservative flow, we introduce conjugate boundary conditions based on the Range-Null space decomposition of the PET operator; this strictly enforces data consistency in the range space while confining stochastic uncertainty injection to the unobserved null space. We train the model via symplectic flow matching and perform inference using a symplectic leapfrog integrator. Extensive experiments on BrainWeb, clinical pediatric, and UDPET datasets demonstrate that \textbf{FlowPET} not only surpasses state-of-the-art deterministic and stochastic baselines in SSIM and PSNR but, more crucially, exhibits superior recovery of low-contrast lesions. The results confirm that imposing Hamiltonian structural constraints offers a robust geometric safeguard for medical inverse problems in high-noise regimes.

We propose Ambient Dataloops, an iterative framework for refining datasets that makes it easier for diffusion models to learn the underlying data distribution. Modern datasets contain samples of highly varying quality, and training directly on such heterogeneous data often yields suboptimal models. We propose a dataset-model co-evolution process; at each iteration of our method, the dataset becomes progressively higher quality, and the model improves accordingly. To avoid destructive self-consuming loops, at each generation, we treat the synthetically improved samples as noisy, but at a slightly lower noisy level than the previous iteration, and we use Ambient Diffusion techniques for learning under corruption. Empirically, Ambient Dataloops achieve state-of-the-art performance in unconditional and text-conditional image generation and de novo protein design. We further provide a theoretical justification for the proposed framework that captures the benefits of the data looping procedure.

Parallel decoding for diffusion LLMs (dLLMs) is difficult because each denoising step provides only token-wise marginal distributions, while unmasking multiple tokens simultaneously requires accounting for inter-token dependencies. We propose **D**ependency-**A**ware **P**arallel **D**ecoding (**DAPD**), a simple, training-free decoding method that uses self-attention to induce a conditional dependency graph over masked tokens. At each iteration, edges in this graph capture strong token interactions, while non-edges indicate weak dependence. Parallel decoding is then reduced to selecting an independent set on the graph and unmasking the selected tokens in parallel. This avoids co-updating strongly coupled tokens without auxiliary models or retraining. Experiments on LLaDA and Dream show that DAPD improves the accuracy–steps trade-off over existing methods and enables more globally distributed parallel updates that better exploit the any-order generation capability of dLLMs. The project is available at \url{https://ai-isl.github.io/dapd}

Time series forecasting can be viewed as a generative problem that requires both semantic understanding over contextual conditions and stochastic modeling of continuous temporal dynamics. Existing approaches typically rely on either autoregressive large language models (LLMs) for semantic context modeling or diffusion-like models for continuous probabilistic generation. However, neither method alone can adequately model both aspects simultaneously. In this work, we propose CoGenCast, a hybrid generative framework that couples pre-trained LLMs with flow-matching mechanism for effective time series forecasting. Specifically, we reconfigure pre-trained decoder-only LLMs into a native forecasting encoder–decoder backbone by modifying only the attention topology, enabling bidirectional context encoding and causal representation generation. Building on this, a flow-matching mechanism is further integrated to model temporal evolution, capturing continuous stochastic dynamics conditioned on the autoregressively generated representation. Notably, CoGenCast naturally supports multimodal forecasting and cross-domain unified training. Extensive experiments on multiple benchmarks show that CoGenCast achieves competitive performance compared to previous baselines. Code is available at \url{https://github.com/liuyaguo/_CoGenCast}.

Recovering radiometric fidelity from unknown dynamic range compression (UDRC), such as low-light enhancement and HDR reconstruction, is a challenging blind inverse problem, due to the unknown forward model and irreversible information loss introduced by compression. To address this challenge, we first identify monotonicity as the fundamental physical invariant shared across UDRC tasks. Leveraging this insight, we introduce the cascaded monotonic Bernstein (CaMB) operator to parameterize the unknown forward model. CaMB enforces monotonicity as a hard architectural inductive bias, constraining optimization to physically consistent mappings and enabling robust and stable operator estimation. We further integrate CaMB with a plug-and-play diffusion framework, proposing CaMB-Diff. Within this framework, the diffusion model serves as a powerful geometric prior for structural and semantic recovery, while CaMB explicitly models and corrects radiometric distortions through a physically grounded forward operator. Extensive experiments on a variety of zero-shot UDRC tasks, including low-light enhancement, low-field MRI enhancement, and HDR reconstruction, demonstrate that CaMB-Diff significantly outperforms state-of-the-art zero-shot baselines in terms of both signal fidelity and physical consistency. Moreover, we empirically validate the effectiveness of the proposed CaMB parameterization in accurately modeling the unknown forward operator.

Incomplete Multi-View Clustering (IMVC) is affected not only by missing feature values, but also by the degradation of relational structure induced by missing views. Many graph-based approaches either rely on costly data imputation or adopt first-order fusion mechanisms, which can be viewed as shallow low-pass filters with limited spectral selectivity. As a result, they may be insufficient to distinguish latent consensus structure from view-specific structural variations. To address this limitation, we reformulate IMVC from a spectral filtering perspective and propose \textbf{C}ontractive \textbf{A}nchor \textbf{R}esolvent \textbf{D}iffusion (\textbf{CARD}), a scalable framework for structural refinement without explicit view imputation. CARD constructs a unified anchor-induced hypergraph from observed sample--anchor relations and derives a high-order resolvent diffusion operator that acts as a rational spectral filter. This operator enhances the relative response of consensus-dominant modes while attenuating view-specific variations. We further derive a compact implicit solver that couples similarity learning and clustering without materializing dense matrices, and provide a conditional local refinement analysis under spectral-gap and local-stability assumptions. Extensive experiments on eight benchmarks, including large-scale datasets, show that CARD achieves competitive performance while scaling linearly in \(N\) for a fixed anchor budget. The code for our method is publicly available at \url{https://github.com/Whale-Waves/CARD}.

Smoothing a signal based on local neighborhoods is a core operation in machine learning and geometry processing. On well-structured domains such as vector spaces and manifolds, the Laplace operator derived from differential geometry offers a principled approach to smoothing via heat diffusion, with strong theoretical guarantees. However, constructing such Laplacians requires a carefully defined domain structure, which is not always available. Most practitioners thus rely on simple convolution kernels and message-passing layers, which are biased against the boundaries of the domain. We bridge this gap by introducing a broad class of smoothing operators, derived from general similarity or adjacency matrices, and demonstrate that they can be normalized into diffusion-like operators that inherit desirable properties from Laplacians. Our approach relies on a symmetric variant of the Sinkhorn algorithm, which rescales positive smoothing operators to match the structural behavior of heat diffusion. This construction enables Laplacian-like smoothing and processing of irregular data such as point clouds, sparse voxel grids or mixture of Gaussians. We show that the resulting operators not only approximate heat diffusion but also retain spectral information from the Laplacian itself, with applications to shape analysis and matching.

Latent diffusion models excel at generating high-quality images but lose the benefits of end-to-end modeling. They discard information during image encoding, require a separately trained decoder, and model an auxiliary distribution to the raw data. In this paper, we propose Latent Forcing, a simple modification to existing architectures that achieves the efficiency of latent diffusion while operating on raw natural images. Our approach orders the denoising trajectory by jointly processing latents and pixels with separately tuned noise schedules. This allows the latents to act as a scratchpad for intermediate computation before high-frequency pixel features are generated. We find that the order of conditioning signals is critical, and we analyze this to explain differences between REPA distillation in the tokenizer and the diffusion model, as well as conditional and unconditional generation. Applied to pixel-space diffusion on ImageNet, Latent Forcing achieves a new state of the art for diffusion transformer-based pixel generation at our compute scale. Code and checkpoints at https://github.com/AlanBaade/LatentForcing

Sequence models typically operate at a fixed temporal or spatial scale and struggle to generalize to substantially longer horizons or higher resolutions without retraining. Existing hierarchical architectures expand receptive fields but rely on scale-specific parameters and lack mechanisms to enforce consistent dynamics across scales. We propose Dynamic Fractal Mamba (DF-Mamba), a recursive state-space model that applies a single shared operator across multiple scales. By sharing parameters across recursion depths and exponentially scaling the effective time step, DF-Mamba achieves an exponentially expanding receptive field while preserving linear computational complexity. A learned content-aware coarse-graining module aggregates representations across scales. Auxiliary reconstruction and cross-scale consistency objectives stabilize recursive training. We evaluate DF-Mamba on long-range time-series forecasting, spatial transcriptomics, and computational pathology. Across all tasks, DF-Mamba consistently outperforms Transformers and flat Mamba baselines while using fewer parameters and maintaining linear-time scalability. Importantly, models trained on short sequences or low-resolution inputs generalize in a zero-shot manner to substantially larger temporal and spatial scales unseen during training. These results demonstrate that recursive parameter sharing provides an effective inductive bias for learning scale-consistent and efficient sequence representations.

Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their statistical efficiency remains limited. Existing theories typically rely on strong regularity assumptions, such as uniformly bounded densities or globally smooth score functions, which fail to capture such intrinsic structures. In this work, we study the sample complexity of diffusion models for learning distributions supported on a union of low-dimensional subspaces. Assuming that the data distribution within each subspace is subgaussian, we show that diffusion models require at most the order of $\widetilde{O}(\varepsilon^{-k \vee 2})$ (up to some logarithmic factor) samples to achieve $\varepsilon$ sampling error in 1-Wasserstein distance, where $k$ is the intrinsic dimension. This near-optimal convergence rate depends only on the intrinsic dimension and significantly improves upon prior theoretical guarantees that suffer from the curse of dimensionality. Notably, our analysis applies to a broad collection of distributions without imposing smoothness, bounded-density, or log-concavity assumptions. Overall, our results show that diffusion models can statistically adapt to intrinsic low-dimensional structure while naturally accommodating multi-modal data, offering a rigorous theoretical justification for their success in complex high-dimensional learning tasks.

Preference alignment aims to guide generative models by learning from comparisons between preferred and non-preferred samples. In practice, most existing approaches rely on preference pairs constructed from model-generated images. Such supervision is inherently relative and can be ambiguous when both samples exhibit artifacts or limited visual quality, making it difficult to infer what constitutes a truly desirable output. In this work, we investigate whether real data can serve as an alternative source of supervision for preference alignment. We adopt a data-centric perspective and study a curation strategy that treats real images as reference points and constructs preference signals by contrasting them with generated or perturbed samples, without requiring manually annotated preference pairs. Through empirical analysis, we show that real-data-based supervision provides effective guidance for aligning diffusion models and achieves performance comparable to existing preference-based methods. Our results suggest that real data offers a practical and complementary source of supervision for preference alignment and highlight directions of label-efficient alignment strategies. Code and models are available at https://cwyxx.github.io/RealAlign.

Unpaired domain translation remains a challenging task due to the need of finding a balance between faithfulness and realism. In this paper, we propose a method called Regularized Distribution Matching Distillation (RDMD) that combines the best properties of Optimal Transport (OT) and diffusion-based domain translation methods. Instead of the conventional adversarial training, RDMD utilizes diffusion-based distribution matching, addressing the common shortcomings of OT methods and providing a strong initialization for the trained models. RDMD provides efficient one-step inference, explicitly controls the input-output alignment via regularization of the transport cost and maintains high faithfulness similar to the OT methods. We prove that in theory RDMD approximates the OT map and demonstrate its empirical performance on several tasks, including unpaired image-to-image translation in pixel and latent space and unpaired text detoxification. Empirical results show that RDMD achieves a comparable or better faithfulness-realism trade-off compared to the diffusion and OT baselines.

Large-scale text-to-image (T2I) diffusion models have enabled unprecedented creative applications, but their unauthorized use has raised serious intellectual property concerns, making model ownership verification (MOV) increasingly critical. We find that existing backdoor-based diffusion watermarking methods often (implicitly) assume a "faithful" verification process, namely, that the verifier can query a suspicious model and obtain the faithful watermark response to complete MOV. However, in practice, adversaries may intentionally or unintentionally damage potential watermark signals, significantly degrading verification reliability. To address this issue, we propose Cert-LAS, the first certified MOV method for T2I models based on layer-adaptive smoothing. In general, Cert-LAS embeds specified watermarks using diffusion classifiers and an LFS-guided layer-adaptive noise, and verifies ownership by examining whether the suspected model exhibits significantly stronger watermark responses compared to unwatermarked references through hypothesis testing. We further prove that, under certain conditions, our Cert-LAS can still achieve reliable verification even in the presence of malicious removal attacks. Extensive experiments validate the effectiveness of Cert-LAS and its resistance to adaptive attacks. Our code is available at https://github.com/Leyi-Qi/Cert-LAS.

Image dehazing, an important image restoration problem, aims to recover clear scene content from images degraded by atmospheric haze. Existing dehazing methods rely on observing the distribution of hazy images during training: supervised approaches typically depend on synthetic datasets, leading to poor generalization in real-world scenarios; unsupervised methods are constrained by the limited diversity of observed haze conditions due to the difficulty of collecting real hazy images, and fail to generalize to unseen haze types. To address these challenges, we propose the first fully zero-shot dehazing framework that is trained without any hazy images. The framework is built upon a set of representations that remain invariant across clean and hazy images to bridge the two domains, which is both theoretically derived and experimentally validated. Consequently, we formulate dehazing as a conditional generative modeling problem and train a diffusion model solely with the invariant representations of the abundant and readily available clean images. During testing, the same representations extracted from hazy images serve as the conditional input to guide the diffusion process toward the clean image distribution. Quantitative analyses verify the effectiveness of the proposed representations, and extensive experiments across various real-world hazy datasets demonstrate our framework’s remarkable generalization ability, significantly outperforming existing methods. Our code will be available after the review process.

This paper introduces EnergyFlow, a framework that unifies generative action modeling with inverse reinforcement learning by parameterizing a scalar energy function whose gradient is the denoising field. We establish that under maximum-entropy optimality, the score function learned via denoising score matching recovers the gradient of the expert's soft Q-function, enabling reward extraction without adversarial training. Formally, we prove that constraining the learned field to be conservative reduces hypothesis complexity and tightens out-of-distribution generalization bounds. We further characterize the identifiability of recovered rewards and bound how score estimation errors propagate to action preferences. Empirically, EnergyFlow achieves state-of-the-art imitation performance on various manipulation tasks while providing an effective reward signal for downstream reinforcement learning that outperforms both adversarial IRL methods and likelihood-based alternatives. These results show that the structural constraints required for valid reward extraction simultaneously serve as beneficial inductive biases for policy generalization. The code is available at https://github.com/sotaagi/EnergyFlow.

Tabular synthesis is critical for privacy-preserving sharing and augmentation, yet diffusion models rely on implicit mechanisms to capture inter-column relationships. We introduce Geometry-Aware Tabular Diffusion (GATD), which augments tabular diffusion denoisers with pairwise angles and lengths computed from column value differences and used as inputs and auxiliary targets. Our MLP instantiation achieves state-of-the-art benchmark performance while using $3.5\times$ fewer parameters on average (up to $25\times$ for classification tasks): on ten datasets, it wins 8/10 Shape, 7/10 Trend, and 9/10 downstream utility (F1/RMSE), reducing Shape and Trend error by 27\% and 20\%. Default loss weights transfer to GNN and Transformer denoisers, improving Shape on 27/30 and Trend on 25/30 architecture-dataset cells. A matched ablation shows supervision (not extra inputs or capacity) drives the gain. This shows explicit relational supervision is a portable inductive bias for tabular diffusion.

Simulation-based inference (SBI) is transforming experimental sciences by enabling parameter estimation in complex non-linear models from simulated data. A persistent challenge, however, is model misspecification. In a Bayesian setting, targeting posterior distributions, errors may arise from the simulator, the noise or prior modelling. These model components are only approximations of reality, and severe mismatches can yield biased or overconfident posteriors. We address this issue by introducing Flow Matching Corrected Posterior Estimation (FMCPE), a framework that leverages the flow matching paradigm to refine simulation-trained posterior estimators using a small set of calibration samples. Our approach proceeds in two stages: first, a posterior approximator is trained on abundant simulated data; second, flow matching transports its predictions toward the true posterior supported by calibration observations. We rely on the later to guide the correction, without requiring explicit knowledge of the misspecification form or of which model components are affected. This design enables FMCPE to combine the scalability of SBI with robustness to distributional shift. Across synthetic benchmarks and real-world datasets, we show that our proposal consistently mitigates the effects of misspecification, delivering improved inference accuracy and uncertainty quantification compared to standard SBI baselines, while remaining computationally efficient.

Steering intermediate representations has emerged as a powerful strategy for controlling generative models. However, despite its empirical success, it currently lacks a comprehensive theoretical framework. In this paper, we bridge this gap by formalizing the theory of concept steering. First, we establish a link between steering and affine concept erasure, proving that the standard approach for removing unwanted behaviors is a special case of LEACE (a closed-form method for affine erasure). Next, we formulate a principled theoretical framework for concept switching, LEACE-Switch, and characterize the assumptions under which it provides an optimal affine solution. Building on this analysis, we then introduce MidSteer (Minimal Disturbance concept Steering), a more general affine framework for concept manipulation that relaxes these assumptions and enables directed, minimal-disturbance transformations. We empirically demonstrate that MidSteer performs favorably across a range of tasks, modalities, and architectures, including vision diffusion models and large language models.

High-dimensional datasets often concentrate near low-dimensional structures, but estimating their geometry from samples typically relies on graphs and kernels that scale poorly with dataset size and dimension. We propose **Riemannian metric matching**: a denoising probabilistic framework for learning the Riemannian geometry of data using neural networks. Specifically, we learn the *carré du champ* operator, which, using diffusion geometry, gives us access to the Riemannian geometry toolkit for downstream machine learning and statistical tasks. Our key observation is that the carré du champ operator can be formulated as a conditional expectation over random perturbations of the data, which can be exploited for sample-wise training and constant cost, amortized inference without explicit kernel construction. Empirically, metric matching rivals or improves the accuracy of $k$-NN-based diffusion geometry estimators, while enabling amortized inference that is up to $400\times$ faster, and supports graph-free geometric analysis on high-dimensional images where nearest neighbors break down.