KTH Royal Institute of Technology（皇家理工学院）；University of Amsterdam（阿姆斯特丹大学）；University of Cambridge（剑桥大学）；University of California, Los Angeles（加州大学洛杉矶分校）；Delft University of Technology（代尔夫特理工大学）
Friso de Kruiff, Erik Bekkers, Ozan Öktem, Carola-Bibiane Schönlieb, Willem Diepeveen
We propose Pullback Flow Matching (PFM), a novel framework for generative modeling on data manifolds. Unlike existing methods that assume or learn restrictive closed-form manifold mappings for training Riemannian Flow Matching (RFM) models, PFM leverages pullback geometry and isometric learning to preserve the underlying manifold's geometry while enabling efficient generation and precise interpolation in latent space. This approach not only facilitates closed-form mappings on the data manifold but also allows for designable latent spaces, using assumed metrics on both data and latent manifolds. By enhancing isometric learning through Neural ODEs and proposing a scalable training objective, we achieve a latent space more suitable for interpolation, leading to improved manifold learning and generative performance. We demonstrate PFM's effectiveness through applications in synthetic data, protein dynamics and protein sequence data, generating novel proteins with specific properties. This method shows strong potential for drug discovery and materials science, where generating novel samples with specific properties is of great interest.
University of North Carolina Charlotte（北卡罗来纳大学夏洛特分校）；Montreal Institute for Learning Algorithms（蒙特利尔学习算法研究所）；Carnegie Mellon University（卡内基梅隆大学）；University of Maryland College Park（马里兰大学学院公园分校）；Korea University（高丽大学）；IIIT Delhi（德里印度理工学院）；Electronics and Telecommunications Research Institute（电子与电信研究院）
Score-based Pullback Riemannian Geometry: Extracting the Data Manifold Geometry using Anisotropic Flows
Department of Mathematics University of California, Los Angeles（数学系，加州大学洛杉矶分校）；Department of Engineering University of Cambridge（工程系，剑桥大学）；Faculty of Mathematics University of Cambridge（数学系，剑桥大学）
Booth School of Business, University of Chicago（芝加哥大学布斯商学院）；Department of Statistics, University of Michigan（密歇根大学统计系）；Department of Mathematics, University of Maryland, College Park（马里兰大学帕克分校数学系）
Riemannian AmbientFlow: Towards Simultaneous Manifold Learning and Generative Modeling from Corrupted Data
Department of Mathematics, University of California, Los Angeles（数学系，加州大学洛杉矶分校）；Department of Statistics and Data Science, University of California, Los Angeles（统计与数据科学系，加州大学洛杉矶分校）
Unveiling Transformer Perception by Exploring Input Manifolds
Department of Environmental Science and Policy（环境科学与政策系）；Department of Computer Science（计算机科学系）；Department of Mathematics（数学系）；Department of Control and Computer Engineering（控制与计算机工程系）
Emergent Riemannian geometry over learning discrete computations on continuous manifolds
School of Informatics University of Edinburgh（信息学院爱丁堡大学）；Département d’Etudes Cognitives Ecole Normale Supérieure PSL（认知研究部巴黎高等师范学院PSL）；Gastsby Unit University College London（加斯特比单位伦敦大学学院）；Data Science Center Ecole Normale Supérieure PSL（数据科学中心巴黎高等师范学院PSL）
