This paper explores the connections between optimal transport and variational inference, with a focus on forward and reverse time stochastic differential equations and Girsanov transformations.We present a principled and systematic framework for sampling and generative modelling centred around divergences on path space. Our work culminates in the development of a novel score-based annealed flow technique (with connections to Jarzynski and Crooks identities from statistical physics) and a regularised iterative proportional fitting (IPF)-type objective, departing from the sequential nature of standard IPF. Through a series of generative modelling examples and a double-well-based rare event task, we showcase the potential of the proposed methods.

翻译：本文探讨了最优运输与变分推断之间的联系，重点研究了正向和反向随机微分方程以及Girsanov变换。我们提出了一套以路径空间散度为核心的、用于采样和生成建模的规范化系统框架。本研究最终发展出一种新型的基于得分的退火流技术（与统计物理学中的Jarzynski和Crooks恒等式相联系），以及一种正则化的迭代比例拟合（IPF）型目标函数，该函数突破了标准IPF的序贯性限制。通过一系列生成建模实例和基于双势阱的稀有事件任务，我们展示了所提方法的潜力。