GRIFDIR: Graph Resolution-Invariant Diffusion Models over Irregular Domains
University of Cambridge（剑桥大学）；Technical University of Denmark（丹麦技术大学）；Simon Fraser University（西蒙弗雷泽大学）；Helmholtz Imaging（亥姆霍兹成像中心）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器研究所）
James Rowbottom, Elizabeth L. Baker, Nick Huang, Ben Adcock, Carola-Bibiane Schönlieb, Alexander Denker
Score-based diffusion models in infinite-dimensional function spaces provide a mathematically principled framework for modelling function-valued data, offering key advantages such as resolution invariance and the ability to handle irregular discretisations. However, practical implementations have struggled to fully realise these benefits. Existing backbones like Fourier neural operators are often biased towards regular grids and fail to generalise to complex domain topologies. We introduce an architecture, GRIFDIR, for function-space diffusion models that represents generalised graph convolutional kernels as finite element functions, allowing the score network to operate directly on unstructured meshes over domains of arbitrary shape. We demonstrate the efficacy of our network architecture through a series of unconditional and conditional sampling experiments across diverse geometries, including non-convex and multiply-connected domains. Our results show that the proposed method maintains resolution invariance and achieves high fidelity in capturing functional distributions on non-trivial geometries.
Generating Full-field Evolution of Physical Dynamics from Irregular Sparse Observations
College of Information Science and Electronic Engineering, Zhejiang University（浙江大学信息科学与电子工程学院）；Zhejiang Provincial Key Laboratory of Multi-Modal Communication Networks and Intelligent Information Processing（浙江省多模态通信网络与智能信息处理重点实验室）；College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）；Microsoft Research Asia（微软亚洲研究院）
Out-of-Distribution Detection in Molecular Complexes via Diffusion Models for Irregular Graphs
Seminar for Applied Mathematics, Department of Mathematics and ETH AI Center, ETH Zurich（应用数学研讨会，数学系和ETH人工智能中心，瑞士苏黎世ETH学院）；Institute for Computational Life Sciences, Zurich University of Applied Sciences（计算生命科学研究所，苏黎世应用科学大学）；Department of Chemistry, Biochemistry and Pharmaceutical Sciences, University of Bern（化学、生物化学和药学系，伯尔尼大学）
StreamPhy: Streaming Inference of High-Dimensional Physical Dynamics via State Space Models
College of Information Science and Electronic Engineering, Zhejiang University（浙江大学信息科学与电子工程学院）；School of EECS,Oregon State University（俄勒冈州立大学电子工程与计算机科学学院）
