The design space of discrete-space diffusion or flow generative models are significantly less well-understood than their continuous-space counterparts, with many works focusing only on a simple masked construction. In this work, we aim to take a holistic approach to the construction of discrete generative models based on continuous-time Markov chains, and for the first time, allow the use of arbitrary discrete probability paths, or colloquially, corruption processes. Through the lens of optimizing the symmetric kinetic energy, we propose velocity formulas that can be applied to any given probability path, completely decoupling the probability and velocity, and giving the user the freedom to specify any desirable probability path based on expert knowledge specific to the data domain. Furthermore, we find that a special construction of mixture probability paths optimizes the symmetric kinetic energy for the discrete case. We empirically validate the usefulness of this new design space across multiple modalities: text generation, inorganic material generation, and image generation. We find that we can outperform the mask construction even in text with kinetic-optimal mixture paths, while we can make use of domain-specific constructions of the probability path over the visual domain.
KTH Royal Institute of Technology（皇家理工学院）；Nordita, Nordic Institute for Theoretical Physics（北欧理论物理研究所）；Hasso Plattner Institute, University of Potsdam（波茨坦大学哈索 Plattner 研究院）；Trinity College Dublin（都柏林三一学院）；Hangzhou Institute of Technology, Xidian University（西安电子科技大学杭州研究院）；The Hong Kong University of Science（香港科学大学）；Mohamed bin Zayed University of Artificial Intelligence（莫莫丁·本·扎耶德人工智能大学）
The Generation Phases of Flow Matching: a Denoising Perspective
ENS de Lyon, CNRS, Université Claude Bernard Lyon 1, Inria, LIP, UMR 5668（里昂大学、国家科学研究中心、克莱尔伯恩大学 Lyon 1、Inria、LIP、UMR 5668）；Technische Universität Berlin（柏林技术大学）；Inria, ENS de Lyon, CNRS, Université Claude Bernard Lyon 1, LIP, UMR 5668（Inria、里昂大学、国家科学研究中心、克莱尔伯恩大学 Lyon 1、LIP、UMR 5668）
An Explicit Surrogate for Gaussian Mixture Flow Matching with Wasserstein Gap Bounds
Université Paris-Saclay, Inria, CIAMS（巴黎-萨克雷大学, 法国国家信息与自动化研究所, CIAMS）；Department of Electrical Engineering and Computer Science, University of Quebec in Trois-Rivieres (UQTR)（魁北克大学三河城分校电气工程与计算机科学系）
Cross-View Feature Matching: Survey, Benchmarking, and Foundation-Model Perspectives
School of Automation, Southeast University（东南大学自动化学院）；School of Computer Science and Technology, Tongji University（同济大学计算机科学与技术学院）；Institute of Artificial Intelligence, University of Science and Technology Beijing（北京科技大学人工智能研究院）；School of Robotics, Wuhan University（武汉大学机器人学院）；Graduate School of Information, Production and Systems, Waseda University（早稻田大学信息生产系统研究科）
Rethinking Deep Research from the Perspective of Web Content Distribution Matching
School of Computer science and engineering, Sun Yat-sen University（计算机科学与工程学院，中山大学）；CSE, The Hong Kong University of Science and Technology（计算机科学与工程系，香港科学与技术大学）；Sydney AI Centre, The University of Sydney（悉尼人工智能中心，悉尼大学）；Department of Data Science and Artificial Intelligence, The Hong Kong Polytechnic University（数据科学与人工智能系，香港理工大学）；DSA Thrust, The Hong Kong University of Science and Technology (GuangZhou)（数据科学与技术 thrust，香港科学与技术大学（广州））；TMLR Group, Department of Computer Science, Hong Kong Baptist University（TMLR 组，计算机科学系，香港 Baptist 大学）
