基于学习的有限维空间吉布斯分布采样方法已快速发展，但无穷维函数空间的理论与算法设计仍有限，尽管这类空间在采样条件扩散过程路径方面潜力巨大，可实现对满足稀有事件或边界约束的扩散过程轨迹的高效模拟。本研究提出针对无穷维函数空间的伴随采样器，这是一种基于随机最优控制的扩散采样器，在函数空间中运行，目标是无穷维希尔伯特空间上的吉布斯型分布。我们的功能伴随采样器（Functional Adjoint Sampler，FAS）基于名为随机最大值原理（stochastic maximum principle）的随机最优控制理论，将伴随采样（Adjoint Sampling，Havens等人，2025）推广到希尔伯特空间，得到了一个用于函数表示的简单且可扩展的匹配型目标函数。我们表明，FAS在合成势和真实分子系统（包括丙氨酸二肽（Alanine Dipeptide）和Chignolin）上实现了更优的转移路径采样性能。
英文摘要：
Learning-based methods for sampling from the Gibbs distribution in finite-dimensional spaces have progressed quickly, yet theory and algorithmic design for infinite-dimensional function spaces remain limited. This gap persists despite their strong potential for sampling the paths of conditional diffusion processes, enabling efficient simulation of trajectories of diffusion processes that respect rare events or boundary constraints. In this work, we present the adjoint sampler for infinite-dimensional function spaces, a stochastic optimal control-based diffusion sampler that operates in function space and targets Gibbs-type distributions on infinite-dimensional Hilbert spaces. Our Functional Adjoint Sampler (FAS) generalizes Adjoint Sampling (Havens et al., 2025) to Hilbert spaces based on a SOC theory called stochastic maximum principle, yielding a simple and scalable matching-type objective for a functional representation. We show that FAS achieves superior transition path sampling performance across synthetic potential and real molecular systems, including Alanine Dipeptide and Chignolin.
Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physics
ELLIS Unit Linz, LIT AI Lab, Johannes Kepler University Linz, Austria（林茨ELLIS单元、LIT AI实验室、林茨约瑟夫·冯·海德里希大学，奥地利）；Department of Electrical & Computer Engineering, Georgia Institute of Technology（电气与计算机工程系，佐治亚理工学院）；NXAI Lab & NXAI GmbH, Linz, Austria（NXAI实验室及NXAI GmbH，林茨，奥地利）
Iterated Denoising Energy Matching for Sampling from Boltzmann Densities
Mila – Québec AI Institute（米拉-魁北克人工智能研究所）；McGill University（麦吉尔大学）；Dreamfold；Université de Montréal（蒙特利尔大学）；University of Oxford（牛津大学）；Ciela Institute（Ciela研究所）；Center for Computational Astrophysics, Flatiron Institute（弗拉铁隆研究所计算天体物理中心）；Jagiellonian University（雅盖隆大学）；CIFAR（加拿大高级研究所）
Scalable Logistic Gaussian Process Density Regression with Kinetic Langevin Sampling
Nanyang Technological University（南洋理工大学）；Eötvös Loránd University (ELTE)（厄特沃什·罗兰大学（ELTE））；HUN-REN Institute for Computer Science and Control (SZTAKI)（匈牙利国家研究网络计算机科学与控制研究所（SZTAKI））
