ICLR 2026 论文列表

Modeling wind-driven object dynamics from video observations is highly challenging due to the invisibility and spatio–temporal variability of wind, as well as the complex deformations of objects. We present DiffWind, a physics-informed differentiable framework that unifies wind–object interaction modeling, video-based reconstruction, and forward simulation. Specifically, we represent wind as a grid-based physical field and objects as particle systems derived from 3D Gaussian Splatting, with their interaction modeled by the Material Point Method (MPM). To recover wind-driven object dynamics, we introduce a reconstruction framework that jointly optimizes the spatio–temporal wind force field and object motion through differentiable rendering and simulation. To ensure physical validity, we incorporate the Lattice Boltzmann Method (LBM) as a physics-informed constraint, enforcing compliance with fluid dynamics laws. Beyond reconstruction, our method naturally supports forward simulation under novel wind conditions and enable new applications such as wind retargeting. We further introduce WD-Objects, a dataset of synthetic and real-world wind-driven scenes. Extensive experiments demonstrate that our method significantly outperforms prior dynamic scene modeling approaches in both reconstruction accuracy and simulation fidelity, opening a new avenue for video-based wind–object interaction modeling. The project page is available at: [https://zju3dv.github.io/DiffWind/](https://zju3dv.github.io/DiffWind/).

The message passing–readout framework has become the de facto standard of graph neural networks (GNNs) for material property prediction. However, most existing readout functions are built on an atom-decomposable inductive bias, i.e. the material-level property or feature can be reasonably assigned to contributions of individual atoms. This is a strong bias and may not hold for all properties, limiting the application scenarios (e.g. gas adsorption or separation of Metal Organic Frameworks, MOFs). In this work, we propose a region-based decomposition perspective, reformulating material properties as integrals over space and pooling contributions from spatial regions rather than atoms. Specifically, we propose a novel readout function named SpatialRead. SpatialRead introduces additional spatial nodes to represent a voxelized space, transforming the atomic isomorphic graph into a heterogeneous atom–space graph with unidirectional message flow from atoms to spatial nodes. To combine the two types of inductive bias, multimodal methods can be used to fuse the features of atoms the spatial nodes. Such a region-based readout function is especially suited for spatial properties such as gas adsorption capacity, separation ratio. Extensive experiments demonstrate that a simple PaiNN–Transformer-based SpatialRead trained from scratch outperforms state-of-the-art pre-trained foundation models on these special tasks. Our results highlight the importance of designing physically grounded readout functions tailored to the target property. The code and dataset can be found in github https://github.com/nankusa/SpatialRead.

Finding the right initialisation for neural networks is crucial to ensure smooth training and good performance. In transformers, the wrong initialisation can lead to one of two failure modes of self-attention layers: rank collapse, where all tokens collapse into similar representations, and entropy collapse, where highly concentrated attention scores lead to training instability. While previous work has studied different scaling regimes for transformers, an asymptotically exact, down-to-the constant prescription for how to initialise transformers has so far been lacking. Here, we provide an analytical theory of signal propagation through deep transformers with self-attention, layer normalisation, skip connections and MLP. Our theory yields a simple algorithm to compute trainability diagrams that identify the correct choice of initialisation hyper-parameters for a given architecture. We overcome the key challenge, an exact treatment of the self-attention layer, by establishing a formal parallel with the Random Energy Model from statistical physics. We also analyse gradients in the backward path and determine the regime where gradients vanish at initialisation. We demonstrate the versatility of our framework through three case studies. Our theoretical framework gives a unified perspective on the two failure modes of self-attention and gives quantitative predictions on the scale of both weights and residual connections that guarantee smooth training.

Transformers have achieved great success across a wide range of applications, yet the theoretical foundations underlying their success remain largely unexplored. To demystify the strong capacities of transformers applied to versatile scenarios and tasks, we theoretically investigate utilizing transformers as students to learn from a class of teacher models. Specifically, the teacher models covered in our analysis include convolution layers with average pooling, graph convolution layers, and various classic statistical learning models, including a variant of sparse token selection models [Sanford et al., 2023, Wang et al., 2024] and group-sparse linear predictors [Zhang et al., 2025]. When learning from this class of teacher models, we prove that one-layer transformers with simplified "position-only'' attention can successfully recover all parameter blocks of the teacher models, thus achieving the optimal population loss. Building upon the efficient mimicry of trained transformers towards teacher models, we further demonstrate that they can generalize well to a broad class of out-of-distribution data under mild assumptions. The key in our analysis is to identify a fundamental bilinear structure shared by various learning tasks, which enables us to establish unified learning guarantees for these tasks when treating them as teachers for transformers.

A key step in protein optimization is modeling the fitness landscape, which maps proteins to functional assay readouts. Existing methods typically either use property-agnostic likelihoods/embeddings from pretrained protein language models (PLMs) for fitness prediction, or assume independent mutational effects, limiting their ability to capture higher-order interactions. In this work, we introduce RankFlow, a conditional flow framework that refines PLM representations to be a property-aligned distribution via a tailored energy function and captures multi-mutation interactions through learnable embeddings. To align optimization with evaluation protocols, we propose the Rank-Consistent Conditional Flow Loss (RC$^2$), a differentiable ranking objective that enforces the correct order of mutants rather than absolute values, which improves out-of-distribution generalization. Finally, we introduce a Property-guided Steering Gate (PSG) that concentrates learning on positions carrying signals for the target property while suppressing unrelated evolutionary biases. Across ProteinGym, PEER, and FLIP benchmarks, RankFlow obtains state-of-the-art ranking accuracy and stronger generalization.

Small-molecule ligands extend protein functionality beyond natural amino acids, enabling sophisticated processes like catalysis, signal transduction, and light harvesting. However, designing proteins with high affinity and selectivity for arbitrary ligands remains a major challenge. We present Pallatom-Ligand, a diffusion model that performs end-to-end generation of ligand-binding proteins at atomic resolution. By directly learning the joint distribution of all atoms in the protein–ligand complexes, Pallatom-Ligand delivers state-of-the-art performance, achieving the highest *in silico* success rates in a comprehensive benchmark. In addition, Pallatom-Ligand's novel conditioning framework enables programmable control over global protein fold and atomic-level ligand solvent accessibility. With these capabilities, Pallatom-Ligand opens new opportunities for exploring the protein function space, advancing both generative modeling and computational protein engineering.

Many methods have been developed to predict static protein structures, however understanding the dynamics of protein structure is essential for elucidating biological function. While molecular dynamics (MD) simulations remain the in silico gold standard, its high computational cost limits scalability. We present DynaProt, a lightweight, SE(3)-invariant framework that predicts rich descriptors of protein dynamics directly from static structures. By casting the problem through the lens of multivariate Gaussians, DynaProt estimates dynamics at two complementary scales: (1) per-residue marginal anisotropy as covariance matrices capturing local flexibility, and (2) joint scalar covariances encoding pairwise dynamic coupling across residues. From these dynamics outputs, DynaProt achieves high accuracy in predicting residue-level flexibility (RMSF) and, remarkably, enables reasonable reconstruction of the full covariance matrix for fast ensemble generation. Notably, it does so using orders of magnitude fewer parameters than prior methods. Our results highlight the potential of direct protein dynamics prediction as a scalable alternative to existing methods.

We introduce FragFM, a novel hierarchical framework via fragment-level discrete flow matching for efficient molecular graph generation. FragFM generates molecules at the fragment level, leveraging a coarse-to-fine autoencoder to reconstruct details at the atom level. Together with a stochastic fragment bag strategy to effectively handle an extensive fragment space, our framework enables more efficient and scalable molecular generation. We demonstrate that our fragment-based approach achieves better property control than the atom-based method and additional flexibility through conditioning the fragment bag. We also propose a Natural Product Generation benchmark (NPGen) to evaluate modern molecular graph generative models' ability to generate natural product-like molecules. Since natural products are biologically prevalidated and differ from typical drug-like molecules, our benchmark provides a more challenging yet meaningful evaluation relevant to drug discovery. We conduct a FragFM comparative study against various models on diverse molecular generation benchmarks, including NPGen, demonstrating superior performance. The results highlight the potential of fragment-based generative modeling for large-scale, property-aware molecular design, paving the way for more efficient exploration of chemical space.

Real-world physical systems are inherently complex, often involving the coupling of multiple physics, making their simulation both highly valuable and challenging. Many mainstream approaches face challenges when dealing with decoupled data. Besides, they also suffer from low efficiency and fidelity in strongly coupled spatio-temporal physical systems. Here we propose GenCP, a novel and elegant generative paradigm for coupled multiphysics simulation. By formulating coupled-physics modeling as a probability modeling problem, our key innovation is to integrate probability density evolution in generative modeling with iterative multiphysics coupling, thereby enabling training on data from decoupled simulation and inferring coupled physics during sampling. We also utilize operator-splitting theory in the space of probability evolution to establish error controllability guarantees for this “conditional-to-joint” sampling scheme. We evaluate our paradigm on a synthetic setting and three challenging multiphysics scenarios to demonstrate both principled insight and superior application performance of GenCP. Code is available at this repo: https://github.com/AI4Science-WestlakeU/GenCP.

Recent advances in multimodal large language models (MLLMs) have opened new opportunities for embodied intelligence, enabling multimodal understanding, reasoning, and interaction, as well as continuous spatial decision-making. Nevertheless, current MLLM-based embodied systems face two critical limitations. First, **Geometric Adaptability Gap:** models trained solely on 2D inputs or with hard-coded 3D geometry injection suffer from either insufficient spatial information or restricted 2D generalization, leading to poor adaptability across tasks with diverse spatial demands. Second, **Embodiment Constraint Gap**: prior work often neglects the physical constraints of real robots, resulting in task plans that are theoretically valid but practically infeasible.To address these gaps, we introduce **OmniEVA** -- an embodied versatile planner that enables advanced embodied reasoning and task planning through two pivotal innovations: (1) a **Task-Adaptive 3D Grounding** mechanism, which uses a gated router to dynamically inject 3D features based on task context, enabling selective geometric reasoning. (2) an **Embodiment-Aware Reasoning** framework that incorporates task goals and physical constraints into the reasoning loop, ensuring executable plans. Extensive experiments show that OmniEVA achieves state-of-the-art performance on 7 of 8 embodied reasoning benchmarks and excels in downstream tasks such as object navigation and mobile manipulation. Evaluations on proposed primitive and composite benchmarks confirm its robust and versatile planning capabilities.

Developing effective representations of protein structures is essential for advancing protein science, particularly for protein generative modeling. Current approaches often grapple with the complexities of the $\operatorname{SE}(3)$ manifold, rely on discrete tokenization, or the need for multiple training objectives, all of which can hinder the model optimization and generalization. We introduce ProteinAE, a novel and streamlined protein diffusion autoencoder designed to overcome these challenges by directly mapping protein backbone coordinates from $\operatorname{E}(3)$ into a continuous, compact latent space. ProteinAE employs a non-equivariant Diffusion Transformer with a bottleneck design for efficient compression and is trained end-to-end with a single flow matching objective, substantially simplifying the optimization pipeline. We demonstrate that ProteinAE achieves state-of-the-art reconstruction quality, outperforming existing autoencoders. The resulting latent space serves as a powerful foundation for a latent diffusion model that bypasses the need for explicit equivariance. This enables efficient, high-quality structure generation that is competitive with leading structure-based approaches and significantly outperforms prior latent-based methods.

We present a deep learning model for high-resolution probabilistic precipitation forecasting over an 8-hour horizon in Europe, overcoming the limitations of radar-only deep learning models with short forecast lead times. Our model efficiently integrates multiple data sources - including radar, satellite, and physics-based numerical weather prediction (NWP) - while capturing long-range interactions, resulting in accurate forecasts with robust uncertainty quantification through consistent probabilistic maps. Featuring a compact architecture, it enables more efficient training and faster inference than existing models. Extensive experiments demonstrate that our model surpasses current operational NWP systems, extrapolation-based methods, and deep-learning nowcasting models, setting a new standard for high-resolution precipitation forecasting in Europe, ensuring a balance between accuracy, interpretability, and computational efficiency.

The discovery of novel catalytic materials is a cornerstone of chemical engineering and sustainable energy, yet it remains a complex, knowledge-intensive process. While Large Language Models (LLMs) have demonstrated remarkable potential in various scientific domains, their application to catalysis is hindered by the lack of specialized, multi-dimensional benchmarks to guide their development and evaluation. To bridge the critical gap, we introduce CatalystBench, a comprehensive and challenging benchmark meticulously constructed from scientific literature and public datasets, specifically designed to assess the capabilities of LLMs in the nuanced domain of catalyst design. The tasks covered by this benchmark dataset encompass the entire closed-loop process of catalyst development, including reading comprehension, experimental analysis, and scheme reasoning. Based on this benchmark, we propose a Multi-head Full-task (MFT) domain-specific fine-tuning method that employs coupling task-specific output heads. We systematically compare with other three distinct fine-tuning strategies: Single-Task (ST), Full-Task (FT) and Multi-head Single-Task (MST). The extensive experiments demonstrate that the MFT strategy consistently achieves the most substantial performance improvements across all tasks, underscoring the effectiveness of explicit multi-task architectures in complex scientific reasoning. The resulting CatalystLLM significantly outperforms a wide array of state-of-the-art open-source and closed-source models on CatalystBench. We will publicly release both the CatalystBench benchmark and the CatalystLLM model, providing the community with a robust evaluation framework and a powerful new tool to accelerate AI-driven research in catalytic materials science.

Physics-constrained generative modeling aims to produce high-dimensional samples that are both physically consistent and distributionally accurate, a task that remains challenging due to often conflicting optimization objectives. Recent advances in flow matching and diffusion models have enabled efficient generative modeling, but integrating physical constraints often degrades generative fidelity or requires costly inference-time corrections. Our work is the first to recognize the trade-off between distributional and physical accuracy. Based on the insight of inherently conflicting objectives, we introduce Physics-Based Flow Matching (PBFM) a method that enforces physical constraints at training time using conflict-free gradient updates and unrolling to mitigate Jensen's gap. Our approach avoids manual loss balancing and enables simultaneous optimization of generative and physical objectives. As a consequence, physics constraints do not impede inference performance. We benchmark our method across three representative PDE benchmarks. PBFM achieves a Pareto-optimal trade-off, competitive inference speed, and generalizes to a wide range of physics-constrained generative tasks, providing a practical tool for scientific machine learning. Code and datasets available at [https://github.com/tum-pbs/PBFM](https://github.com/tum-pbs/PBFM).

Biological profiling technologies, such as imaging mass cytometry (IMC) and spatial transcriptomics (ST), generate multi-channel data with strong spatial alignment and complex inter-channel relationships. Modeling such data requires generative frameworks that can jointly model spatial structure and channel relationships, while also generalizing across arbitrary combinations of observed and missing channels for practical applications. Existing generative models typically assume low-dimensional inputs (e.g., RGB images) and rely on simple conditioning mechanisms that break spatial correspondence and overlook inter-channel dependencies. This work proposes a unified multi-channel diffusion (MCD) framework for controllable generation of structured biological data with intricate inter-channel relationships. Our model introduces two key innovations: (1) a hierarchical feature injection mechanism that enables multi-resolution conditioning on spatially aligned observed channels, and (2) two complementary channel attention modules to capture inter-channel relationships and recalibrate latent features. To support flexible conditioning and generalization to arbitrary sets of observed channels, we train the model using a random channel masking strategy, enabling it to reconstruct missing channels from any combination of observed channels as the spatial condition. We demonstrate state-of-the-art performance across both spatial and non-spatial biological data generation tasks, including imputation in spatial proteomics and clinical imaging, as well as gene-to-protein prediction in single-cell datasets, and show strong generalizability to unseen conditional configurations.

Mathematical modeling is the process of understanding and predicting complex real-world phenomena. Traditionally, it is a time-intensive effort reliant on deep human expertise and iterative refinement. Automating this intricate process, therefore, offers the potential to significantly accelerate discovery and broaden the application of mathematical modeling across diverse domains. Such automation, however, must address inherent challenges, including fundamental modeling uncertainty, balancing multiple conflicting objectives, and incorporating subjective qualities into assessing model utility. We approach this by conceptualizing mathematical modeling as a sequential decision-making problem under uncertainty. In response, we introduce $\texttt{MATHMO}$, a novel adaptive search method designed to automatically navigate the complex decisions in selecting mathematical frameworks, specifying model formulations, and defining algorithmic procedures. Specifically, $\texttt{MATHMO}$ employs a principled bi-level search strategy---combining high-level exploration across diverse frameworks and local intra-framework model refinements---leveraging Large Language Models for exploration, surrogate evaluations, and incorporating subjective preferences into the automated process. We demonstrate $\texttt{MATHMO}$'s efficacy on diverse real-world tasks, where it successfully discovers Pareto-efficient frontiers of models that balance varied objectives, including subjective criteria.

Accurate crowd simulation is crucial for public safety management, emergency evacuation planning, and intelligent transportation systems. However, existing methods, which typically model crowds as a collection of independent individual trajectories, are limited in their ability to capture macroscopic physical laws. This microscopic approach often leads to error accumulation and compromises simulation stability. Furthermore, deep learning-driven methods tend to suffer from low inference efficiency and high computational overhead, making them impractical for large-scale, efficient simulations. To address these challenges, we propose the Spatio-Temporal Decoupled Differential Equation Network (STDDN), a novel framework that guides microscopic trajectory prediction with macroscopic physics. We innovatively introduce the continuity equation from fluid dynamics as a strong physical constraint. A Neural Ordinary Differential Equation (Neural ODE) is employed to model the macroscopic density evolution driven by individual movements, thereby physically regularizing the microscopic trajectory prediction model. We design a density-velocity coupled dynamic graph learning module to formulate the derivative of the density field within the Neural ODE, effectively mitigating error accumulation. We also propose a differentiable density mapping module to eliminate discontinuous gradients caused by discretization and introduce a cross-grid detection module to accurately model the impact of individual cross-grid movements on local density changes. The proposed STDDN method has demonstrated significantly superior simulation performance compared to state-of-the-art methods on long-term tasks across four real-world datasets, as well as a major reduction in inference latency.

Uniform sampling is a highly efficient method for data summarization. However, its effectiveness in producing coresets for clustering problems is not yet well understood, primarily because it generally does not yield a strong coreset, which is the prevailing notion in the literature. We formulate \emph{stable coresets}, a notion that is intermediate between the standard notions of weak and strong coresets, and effectively combines the broad applicability of strong coresets with highly efficient constructions, through uniform sampling, of weak coresets. Our main result is that a uniform sample of size $O(\epsilon^{-2}\log d)$ yields, with high constant probability, a stable coreset for $1$-median in $\mathbb{R}^d$ under the $\ell_1$ metric. We then leverage the powerful properties of stable coresets to easily derive new coreset constructions, all through uniform sampling, for $\ell_1$ and related metrics, such as Kendall-tau and Jaccard. We also show applications to fair rank aggregation and to approximation algorithms for $k$-median problem in these metric spaces. Our experiments validate the benefits of stable coresets in practice, in terms of both construction time and approximation quality.

Biomolecular interaction modeling has been substantially advanced by foundation models, yet they often produce all-atom structures that violate basic steric feasibility. We address this limitation by enforcing physical validity as a strict constraint during both training and inference with a unified module. At its core is a differentiable projection that maps the provisional atom coordinates from the diffusion model to the nearest physically valid configuration. This projection is achieved using a Gauss-Seidel scheme, which exploits the locality and sparsity of the constraints to ensure stable and fast convergence at scale. By implicit differentiation to obtain gradients, our module integrates seamlessly into existing frameworks for end-to-end finetuning. With our Gauss-Seidel projection module in place, two denoising steps are sufficient to produce biomolecular complexes that are both physically valid and structurally accurate. Across six benchmarks, our $2$-step model achieves the same structural accuracy as state-of-the-art $200$-step diffusion baselines, delivering ${\sim}10\times$ wall-clock speedups while guaranteeing physical validity.