An Unconditional Representation of the Conditional Score in Infinite-Dimensional Linear Inverse Problems
School of Engineering Science（工程科学学院）；Lappeenranta-Lahti University of Technology（拉普兰塔-拉赫蒂技术大学）；Vienna University of Technology (TU Wien)（维也纳技术大学）；Department of Mathematics and Statistics（数学与统计学系）；University of Helsinki（赫尔辛基大学）；Department of Computational and Applied Mathematics（计算与应用数学系）；Rice University（里士满大学）
Fabian Schneider, Duc-Lam Duong, Matti Lassas, Maarten V. de Hoop, Tapio Helin
备注：
37 pages, 13 figures, 3 tables. Accepted in TMLR November 2025
Score-based diffusion models (SDMs) have emerged as a powerful tool for sampling from the posterior distribution in Bayesian inverse problems. However, existing methods often require multiple evaluations of the forward mapping to generate a single sample, resulting in significant computational costs for large-scale inverse problems. To address this, we propose an unconditional representation of the conditional score function (UCoS) tailored to linear inverse problems, which avoids forward model evaluations during sampling by shifting computational effort to an offline training phase. In this phase, a \emph{task-dependent} score function is learned based on the linear forward operator. Crucially, we show that the conditional score can be derived \emph{exactly} from a trained (unconditional) score using affine transformations, eliminating the need for conditional score approximations. Our approach is formulated in infinite-dimensional function spaces, making it inherently discretization-invariant. We support this formulation with a rigorous convergence analysis that justifies UCoS beyond any specific discretization. Finally we validate UCoS through high-dimensional computed tomography (CT) and image deblurring experiments, demonstrating both scalability and accuracy.
From Conditional to Unconditional Independence: Testing Conditional Independence via Transport Maps
Institute of Statistics and Big Data, Renmin University of China（中国人民大学统计与大数据研究院）；Department of Data Science and Artificial Intelligence, The Hong Kong Polytechnic University（香港理工大学数据科学与人工智能学院）；Department of Applied Mathematics, The Hong Kong Polytechnic University（香港理工大学应用数学系）
Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecasting
School of Computation, Information and Technology, Technical University of Munich（计算、信息与技术学院，慕尼黑技术大学）；Munich Data Science Institute（慕尼黑数据科学研究所）；Munich Center for Machine Learning（慕尼黑机器学习中心）
Guided Unconditional and Conditional Generative Models for Super-Resolution and Inference of Quasi-Geostrophic Turbulence
Massachusetts Institute of Technology（麻省理工学院）；Department of Mechanical Engineering, Massachusetts Institute of Technology（麻省理工学院机械工程系）；Center for Computational Science and Engineering, Massachusetts Institute of Technology（麻省理工学院计算科学与工程中心）
Score Mismatch and Set-Constrained Sampling in Zero-Shot Conditional Discrete Diffusion
University of California, Davis（加州大学戴维斯分校）；Luddy School of Informatics, Computing, and Engineering, Indiana University Indianapolis（印第安纳大学印第安纳波利斯分校卢迪信息学、计算与工程学院）；The Ohio State University（俄亥俄州立大学）
Verifiable Regularity Criterion for Conditional Expectation Operators and Conditional Mean Embeddings with Applications to Nonparametric Regression, Bayesian Inverse Problems, and Koopman Operators
Technische Universität Ilmenau（伊尔梅瑙工业大学）；Freie Universität Berlin（柏林自由大学）；Chemnitz University of Technology（开姆尼茨工业大学）
Diverse capability and scaling of diffusion and auto-regressive models when learning abstract rules
Kempner Institute, Harvard University（哈佛大学肯普纳研究所）；Harvard Medical School（哈佛医学院）；Center for Brain Science, Harvard University（哈佛大学脑科学中心）；Edmond and Lily Safra Center for Brain Sciences, Hebrew University（希伯来大学埃德蒙与莉莉·萨夫拉脑科学中心）
