ICML 2026 论文列表

Diffusion models show growing promise for generative modeling of physical systems, but enforcing partial differential equation (PDE) constraints directly is infeasible during the stochastic denoising process. Current methods apply constraints to the expected clean sample, incurring a Jensen’s Gap that forces a trade-off between PDE satisfaction and generative accuracy. To bridge this gap, we propose Physics-Informed Distillation of Diffusion Models (PIDDM), a simple yet effective post-hoc distillation strategy that enforces PDE constraints after training. PIDDM enables fast single-step generation while improving both physical consistency and sample quality, supporting forward/inverse problems and reconstruction from partial observations. Extensive experiments across PDE benchmarks show PIDDM outperforms recent baselines, such as PIDM, DiffusionPDE, and ECI-sampling, in both accuracy and constraint satisfaction, with lower computation and minimal hyperparameter tuning, offering a more efficient pathway to physics-informed diffusion models.

Sequence learning is dominated by Transformers and parallelizable recurrent neural networks (RNNs) such as state-space models, yet learning long-term dependencies remains challenging, and state-of-the-art designs trade power consumption for performance. The Bistable Memory Recurrent Unit (BMRU) was introduced to enable hardware-software co-design of ultra-low power RNNs: quantized states with hysteresis provide persistent memory while mapping directly to analog primitives. However, BMRU performance lags behind parallelizable RNNs on complex sequential tasks. In this paper, we identify gradient blocking during state updates as a key limitation and propose a cumulative update formulation that restores gradient flow while preserving persistent memory, creating skip-connections through time. This leads to the Cumulative Memory Recurrent Unit (CMRU) and its relaxed variant, the $\alpha$CMRU. Experiments show that the cumulative formulation dramatically improves convergence stability and reduces initialization sensitivity. The CMRU and $\alpha$CMRU match or outperform Linear Recurrent Units (LRUs) and minimal Gated Recurrent Units (minGRUs) across diverse benchmarks at small model sizes, with particular advantages on tasks requiring discrete long-range retention, while the CMRU retains quantized states, persistent memory, and noise-resilient dynamics essential for analog implementation.

Pre-trained vision language models do not have good intuitions about the physical world. Recent work has shown that supervised fine-tuning can improve model performance on simple physical tasks. However, fine-tuned models do not appear to learn robust physical rules that can generalize to new contexts. Based on research in cognitive science, we hypothesize that models need to interact with an environment to properly learn its physical dynamics. We train models that learn through interaction with a simulated environment using reinforcement learning. While learning from interaction allows models to improve their within-task performance, it fails to produce models with generalizable physical intuitions. We find that models trained on one task do not reliably generalize to related tasks, even if the tasks share visual statistics and physical principles, and regardless of whether the models are trained through interaction.

Flow-matching policies have recently emerged as a powerful class of generative models for offline reinforcement learning (RL), capable of capturing complex, multi-modal action distributions from static datasets. However, standard training objectives are largely agnostic to the global properties of the generative path, permitting learned vector fields that are irregular and unstable, which can hinder performance. In this work, we introduce PDE-regularized Q-Learning (PQL), a novel algorithm that addresses this limitation by imposing a principled structure on the entire probability flow. PQL makes two synergistic contributions: first, a partial differential equation based regularizer derived from the continuity equation promotes global smoothness and stability on the flow. Second, to solve the complex optimization problem introduced by this regularizer, we propose a Beta-distributed timestep sampling strategy that focuses learning on the critical trajectory segments where the trade-off between imitation and smoothness is most acute. Through extensive experiments, we demonstrate that by structuring the generative journey and not just its destination, PQL achieves state-of-the-art performance on a wide range of challenging offline RL tasks.

In this paper, we study solution operators of physical field equations on geometric meshes from a function-space perspective. We reveal that Hodge orthogonality fundamentally resolves spectral interference by isolating unlearnable topological degrees of freedom from learnable geometric dynamics, enabling an additive approximation confined to structure-preserving subspaces. Building on Hodge theory and operator splitting, we derive a principled operator-level decomposition. The result is a Hybrid Eulerian-Lagrangian architecture with an algebraic-level inductive bias we call Hodge Spectral Duality (HSD). In our framework, we use discrete differential forms to capture topology-dominated components and an orthogonal auxiliary ambient space to represent complex local dynamics. Our method achieves superior accuracy and efficiency on geometric graphs with enhanced fidelity to physical invariants.

Temporal graphs are ubiquitous in real-world applications and Temporal Graph Networks (TGNs) have achieved superior predictive accuracy. Understanding which historical events drive model predictions can enhance trustworthiness of TGNs. Existing explanation methods overlook the memory module, the core component that records and updates node histories, leaving the influence of past events unexplored. To address this, we attribute TGNs predictions through the topology attribution tree and memory backtracking tree. The topology attribution tree captures the influence of neighbors and their memory vectors, then the memory backtracking tree quantifies how historical events shape node memory vectors. We apply the LRP in TGNs, ensuring that the total contribution of events equals the model’s logits. Finally, top-k selection may be unfaithful due to the nonlinear mapping from logits to probabilities, we design optimization objectives to identify the important events. Experiments on nine temporal graph datasets, spanning node property prediction, link prediction tasks and graph classification tasks, show that our method provides faithful explanations and outperforms state-of-the-art baselines. The code is available at https://github.com/yazhengliu/MemExplainer.

Precise alignment is a prerequisite for hyperspectral and multispectral image fusion, yet existing methods struggle with complex non-rigid deformations. Existing techniques either suffer from inter-task error accumulation by treating registration and fusion as disjoint processes or neglect the geometric nature of distortions by relying on isotropic Euclidean metrics. We propose Structure-Aware Riemannian Flow Matching (SA-RFM), a geometry-informed framework for joint registration and fusion of hyperspectral and multispectral images. SA-RFM reformulates registration as dynamic optimal transport on a structure-induced Riemannian manifold, where anisotropic costs are derived from MSI structural cues. To circumvent the complexity of explicit OT solvers, we incorporate this geometry into a conditional flow matching framework via a local cost approximation. This formulation is realized through two synergistic mechanisms: a Riemannian Flow Matching objective that enforces structure-aware error measurement, and an optimal transport direction regularization that aligns the velocity field with the induced metric, thereby resolving the fundamental mismatch between anisotropic costs and conventional Euclidean supervision. Extensive experiments on four datasets demonstrate the superiority of our method. Code is available at: https://github.com/ZhangQuan-hub.

Controllable molecule generation is crucial for diverse scientific applications, such as drug discovery and materials design. While large language models (LLMs) show great promise, their dense and entangled representations impede precise control over the generation of molecules with bespoke substructures or properties. To address this, we propose Sparse Representation Editing (SpaRE), an interpretability-driven framework for fine-grained and precise control in LLM-based molecule generation. The crux of SpaRE is to learn an overcomplete sparse feature space that disentangles LLM representations into a compact set of latent features corresponding to chemically meaningful concepts. Within this space, we can directly manipulate these concept-aligned latent features to achieve (1) local control, by generating target atoms and functional groups at specified positions; and (2) global control, by customizing the overall structural and physicochemical properties within defined ranges. In this way, our framework advances interpretability from post-hoc analysis to actionable generative control. Experiments show that SpaRE can generate chemically desirable molecules under complex constraints in real-world scenarios, while offering mechanistic insights for quantitative structure–property analysis. The code and demo are available at https://github.com/WanyuGroup/ICML2026_SpaRE.

Polysomnography (PSG) provides the gold standard for sleep assessment but suffers from substantial heterogeneity across recording devices and cohorts. There have been growing efforts to build general-purpose foundation models (FMs) for sleep physiology, but lack an in-depth understanding of the pre-training process and scaling patterns that lead to more generalizable sleep FMs. To fill this gap, we curate a massive corpus of 166,500 hours of sleep recordings from nine public sources and establish SleepBench, a comprehensive, fully open-source benchmark. Leveraging SleepBench, we systematically evaluate four families of self-supervised pre-training objectives and uncover three critical findings: (1) existing FMs fail to generalize to missing channels at inference; (2) channel-invariant feature learning is essential for pre-training; and (3) scaling sample size, model capacity, and multi-source data mixture consistently improves downstream performance. With an enhanced pre-training and scaling recipe, we introduce OSF, a family of sleep FMs that achieves state-of-the-art performance across nine datasets on diverse sleep and disease prediction tasks. Further analysis of OSF also reveals intriguing properties in sample efficiency, hierarchical aggregation, and cross-dataset scaling. Codes are available at: https://github.com/yang-ai-lab/OSF-Open-Sleep-FM.

Multimodal sentiment analysis (MSA) aims to predict human sentiments by integrating signals from different modalities such as text, video, and audio. However, raw multimodal sequences often suffer from semantic inconsistency--exhibiting redundancy or conflicts within and across modalities--which hinders robust understanding and increases computational cost. To this end, we introduce ConsMSA, which explicitly formalizes semantic distribution consistency across both $\textit{intra}$- and $\textit{inter}$-modality, providing a consistency-aware mechanism for robust and efficient multimodal sentiment prediction. Specifically, ConsMSA projects multimodal token features into a shared sentiment space to compute an Intra- and Inter-modality Consistency Score ($I^2CS$). By coupling this score with predictive relevance, we formulate consistency-aware importance signals that are utilized: (i) as a consistency regularizer to align latent distributions during training, (ii) to derive semantic-aware weights for adaptive multimodal token reweighting, and (iii) as a practical criterion to prune redundant or conflicting tokens. Extensive experiments on CMU-MOSI, CMU-MOSEI, and CH-SIMS demonstrate that ConsMSA achieves state-of-the-art performance while remaining robust under aggressive token compression--retaining only 10\% of tokens yields comparable accuracy. These results establish semantic distribution consistency as a promising foundation for synergizing predictive robustness with computational efficiency.

Mixtures of Bernoulli product distributions are a simple and widely used latent-variable model, with applications in e.g.\ recommendation systems, crowdsourcing, and medical data analysis. We consider the problem of reconstructing the mixture parameters from oracle access to its probability generating polynomial (PGP), for instance represented by a probabilistic generating circuit (PGC). We show that the parameters are uniquely identifiable for almost all mixtures, and give a randomized algorithm that exactly recovers the mixture weights and component marginals for mixtures of $r$ Bernoulli product distributions over $n$ variables using only $O(nr^2)$ oracle queries. The algorithm repeatedly applies restrictions to $O(r)$ variables, extracts low-degree coefficients, and then recovers the parameters using a moment-based tensor decomposition. To the best of our knowledge, this is the {\em first} exact reconstruction algorithm in this PGP oracle model with query complexity linear in $n$ and polynomial in $r$.

Graph Neural Networks (GNNs) have shown remarkable capabilities in learning from graph-structured data with various applications such as social analysis and bioinformatics. However, the presence of label noise in real scenarios poses a significant challenge in learning robust GNNs, and their effectiveness can be severely impacted when dealing with noisy labels on graphs, often stemming from annotation errors or inconsistencies. To address this, in this paper we propose a novel approach called ICGNN that harnesses the structure information of the graph to effectively alleviate the challenges posed by noisy labels. Specifically, we first design a novel noise indicator that measures the influence contradiction score (ICS) based on the graph diffusion matrix to quantify the credibility of nodes with clean labels, such that nodes with higher ICS values are more likely to be detected as having noisy labels. Then we leverage the Gaussian mixture model to precisely detect whether the label of a node is noisy or not. Additionally, we develop a soft strategy to combine the predictions from neighboring nodes on the graph to correct the detected noisy labels. At last, pseudo-labeling for abundant unlabeled nodes is incorporated to provide auxiliary supervision signals and guide the model optimization. Experiments on benchmark datasets show the superiority of our approach over competitive baselines in noisy label scenarios. The source code is available at: https://github.com/wayc04/ICGNN.

In embodied vision, Goal-Oriented Navigation (GON) requires robots to locate a specific goal within an unexplored environment. The primary challenge of GON arises from the need to construct a Bird's-Eye-View (BEV) map to understand the environment while simultaneously localizing an unobserved goal. Existing map-based methods typically employ self-centered semantic maps, often facing challenges such as reliance on complete maps or inconsistent semantic association. To this end, we propose Plug-and-Play Label Map Diffusion (PLMD), which defines a novel map completion diffusion model based on Denoising Diffusion Probabilistic Models (DDPM). PLMD generates obstacle and semantic labels for unobserved regions through a diffusion-based completion process, thereby enabling goal localization even in partially observed environments. Moreover, it mitigates inconsistent semantic association by leveraging structural consistency between known and unknown obstacle layouts and integrating obstacle priors into the semantic denoising process. By substituting predicted labels for unobserved regions, robots can accurately localize the specified objects. Extensive experiments demonstrate that PLMD **(I)** effectively expands the region of unknown maps, **(II)** integrates seamlessly into existing navigation strategies that rely on semantic maps, **(III)** achieves state-of-the-art performance on three GON tasks. Code is available at: <https://github.com/FrankZxShen/PLMD>.

Current video diffusion models generate visually compelling content but often struggle with physical motion, producing subtle artifacts like rubber-sheet deformations and inconsistent object motion. We introduce a frequency-domain physics prior that improves motion plausibility without modifying model architectures. Our method decomposes common motion patterns (translation, rotation, scaling) into lightweight spectral losses. Applied to Open-Sora, MVDIT, and Hunyuan, our approach improves both motion accuracy and action recognition by ∼11\% on average on OpenVID-1M (relative), while maintaining visual quality. Additional results on Wan 2.1-14B show consistent gains on video-quality and physics-oriented metrics. User studies show 74-83\% preference for our physics-enhanced videos. It also reduces warping error by 22-37\% (depending on the backbone) and improves temporal consistency scores. These results indicate that simple, global spectral cues are an effective drop-in regularizer for physically plausible motion in video diffusion.

Current computer-aided synthesis planning (CASP) methods often treat retrosynthesis as solved once a single feasible route is identified, focusing primarily on convergence or shortest-path metrics. This view is misaligned with real-world practice, where chemists must balance competing objectives such as cost, sustainability, toxicity, and overall yield. To address this, we formulate synthesis planning as a multi-objective search problem and introduce MORetro$^\ast$, an algorithm that generates a Pareto front of synthesis routes to explicitly capture trade-offs between user-defined criteria. MORetro$^\ast$ uses weighted scalarization and solution-informed sampling to efficiently navigate the combinatorial search space and prioritize promising trade-offs. Building on multi-objective A$^\ast$-search, we provide optimality guarantees showing that, for a fixed single-step model, MORetro$^\ast$ recovers the true Pareto front under admissibility. Across multiple retrosynthesis benchmarks, MORetro$^\ast$ produces diverse, high-quality Pareto fronts, uncovering solutions overlooked by single-objective approaches and better aligning CASP outputs with industrial decision-making.

Most spatio-temporal forecasting models assume in-distribution data and can degrade sharply under non-stationary environments. Existing methods for handling distribution shift largely rely on discrete graph inference, making it difficult to disentangle universal dynamics from environment-specific changes and to respect the continuous physical nature of spatio-temporal fields. To this end, we propose STPDE, a general framework that reformulates spatio-temporal dynamics as the evolution of inhomogeneous partial differential equations. STPDE explicitly decomposes dynamics into an Invariant Diffusion Operator that captures universal mechanisms and an Environment Basis Manifold that parameterizes local heterogeneous media. We show that the Green's function of the Laplacian can be effectively approximated by linear attention, enabling global diffusion at scale. Combined with stochastic environment perturbations, STPDE improves robustness under heterogeneous and shifting environments. Extensive experiments on in-distribution forecasting, out-of-distribution generalization, few-shot cross-city transfer, and continual learning demonstrate consistent improvements over state-of-the-art baselines with competitive computational efficiency.

Machine-learned (ML) XC functionals aim to replace human-designed density functional approximations by learning directly from reference data, but they still do not consistently outperform traditional $\mathcal{O}(N^4)$-scaling hybrid functionals. We therefore study a hybrid-distillation setting, where $\mathcal{O}(N^3)$-scaling semilocal ML-XC functionals are trained to reproduce B3LYP/def2-SVP targets. We introduce Derivative Informed XC-Loss (DI-Loss), a loss that incorporates additional information from the reference hybrid functional by supervising first and second derivatives of the energy on the Grassmannian of admissible density matrices. Rather than only matching the self-consistent fixed point, DI-Loss aligns the local first- and second-order response of the learned functional with that of the target functional. Across four evaluated architectures, DI-Loss consistently improves the main energy metrics. Averaged uniformly across architectures, the total-energy MAE decreases by 66% relative to energy and density supervision alone. The density-sensitive mean-field energy metric $E_\rho$ improves from 1.2 to 0.8 mEh on average, while dipole and $\mathcal{L}_2$ density errors do not improve uniformly. We further show that densities from the distilled functionals reduce hybrid-functional SCF iterations by up to 55%. In downstream TDDFT calculations, Hessian supervision improves excited-state predictions, with XCdiff reducing the mean excitation-energy MAE by 24-35% across molecule sizes on QM40.

Computational protein design typically employs a sequential workflow of structure generation followed by sequence (re)design. While structure generators can be explicitly conditioned on functional objectives, inverse folding models are constrained by their function-agnostic nature and sequence-structure degeneracy. More critically, the associated training objectives do not account for the *Best-of-N* (BoN) inference protocol, resulting in a fundamental training-inference misalignment. Here, we propose FIDIA, a reinforcement learning framework that enables **F**unction-**I**nformed sequence **D**esign via **I**nference-**A**ligned policy optimization. Specifically, FIDIA integrates functional constraints into composite rewards and explicitly optimize the induced policy under BoN toward high-fitness sequence regions. We achieve this via a grounded gradient estimator that directly maximizes the expected maximum reward. FIDIA consistently outperforms both standard and RL-optimized baselines in success rate and precision on a general motif scaffolding benchmark. Further experiments on realworld cases including vaccine and affinity-enhancing enzyme design validate FIDIA’s efficacy in complex therapeutic and biocatalytic contexts.

In the AI4Chemistry scenario, utilizing heterogeneous data at different fidelity levels is a common and core issue. High-fidelity data is accurate but scarce, while low-fidelity data is abundant but biased. Traditional multi-fidelity methods typically identify cross-fidelity biases based on paired samples under different fidelity labels. However, due to the mismatch in dataset input distribution and the complexity of the biases themselves, these methods are difficult to implement in real-world scientific environments. To address this, we propose a trusted information subset decomposition framework that can efficiently utilize multi-fidelity data without requiring paired samples. Multi-fidelity label supervision is decomposed into three complementary subsets: a trusted information subset based on the absolute value of high-fidelity labels; a trusted subset that captures the reliability of the high-fidelity and medium-fidelity label intervals through adaptive constraints; and an ordered trusted subset representing the numerical relationships within the same fidelity level. These subsets are then integrated into a unified end-to-end model, enabling the reasonable utilization of medium- and low-fidelity information. Extensive experiments on various molecular and material property benchmarks demonstrate that our method consistently outperforms state-of-the-art multifidelity and singlefidelity baseline methods, and exhibits good robustness under real-world unpaired multifidelity conditions.