We establish a theoretical link between the recently proposed "drifting" generative dynamics and gradient flows induced by the Sinkhorn divergence. In a particle discretization, the drift field admits a cross-minus-self decomposition: an attractive term toward the target distribution and a repulsive/self-correction term toward the current model, both expressed via one-sided normalized Gibbs kernels. We show that Sinkhorn divergence yields an analogous cross-minus-self structure, but with each term defined by entropic optimal-transport couplings obtained through two-sided Sinkhorn scaling (i.e., enforcing both marginals). This provides a precise sense in which drifting acts as a surrogate for a Sinkhorn-divergence gradient flow, interpolating between one-sided normalization and full two-sided Sinkhorn scaling. Crucially, this connection resolves an identifiability gap in prior drifting formulations: leveraging the definiteness of the Sinkhorn divergence, we show that zero drift (equilibrium of the dynamics) implies that the model and target measures match. Experiments show that Sinkhorn drifting reduces sensitivity to kernel temperature and improves one-step generative quality, trading off additional training time for a more stable optimization, without altering the inference procedure used by drift methods. These theoretical gains translate to strong low-temperature improvements in practice: on FFHQ-ALAE at the lowest temperature setting we evaluate, Sinkhorn drifting reduces mean FID from 187.7 to 37.1 and mean latent EMD from 453.3 to 144.4, while on MNIST it preserves full class coverage across the temperature sweep. Project page: https://mint-vu.github.io/SinkhornDrifting/
Convergence rates for generative drifting flows: fixed-scale obstructions and multihead acceleration
Centre de recherche en économie et statistique（经济与统计研究中心）；ENSAE, IP Paris（ENSAE，巴黎综合理工学院）；Département de Mathématiques et Applications（数学与应用数学系）；CNRS, École Normale Supérieure, PSL（法国国家科学研究中心，巴黎高等师范学院，巴黎文理研究大学）
Gaussian entropic optimal transport: Schrödinger bridges and the Sinkhorn algorithm
Department of Mathematics, Imperial College London, UK；Centre de Recherche Inria Bordeaux Sud-Ouest, Talence, France；Department of Signal Theory \& Communications, Universidad Carlos III de Madrid, Spain
Department of Applied Mathematics and Theoretical Physics, University of Cambridge（应用数学与理论物理系，剑桥大学）；Nonlinear Systems Laboratory, Massachusetts Institute of Technology（非线性系统实验室，麻省理工学院）
Center for Machine Learning (ZML)（机器学习中心（ZML））；Institute for Flow in Additively Manufactured Porous Structures (ISAPS)（添加剂制造多孔结构流动研究所（ISAPS））；Heilbronn University of Applied Sciences（海德堡应用科学大学）
Generative Neural Networks for Sinkhorn Distributionally Robust Hypothesis Testing
School of Artificial Intelligence, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）人工智能学院）；College of Business, City University of Hong Kong（香港城市大学商学院）；School of Data Science, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）数据科学学院）
Discrete Wasserstein Flows for One-Step Generative Modeling
Imperial College London（帝国理工学院）；Aalborg University（奥尔堡大学）；Centre for Frontier AI Research (CFAR)（前沿人工智能研究中心）；Institute of Advanced Intelligence and Computing (IAIC)（先进智能与计算研究所）；A*STAR（新加坡科技研究局）；University of Copenhagen（哥本哈根大学）
University of California, Irvine（加州大学伊万斯堡分校）；University of Virginia（弗吉尼亚大学）；University of Alabama at Birmingham（阿拉巴马大学伯明翰分校）；Northeastern University（东北大学）
