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：本文探讨了最优输运与变分推断之间的联系，重点研究了正向和反向时间随机微分方程以及吉尔萨诺夫变换。我们围绕路径空间上的散度，建立了一个基于原则且系统化的采样与生成建模框架。本工作的最终成果包括：一种新颖的基于分数的退火流技术（与统计物理中的雅尔津斯基恒等式和克鲁克斯恒等式相关联），以及一种正则化的迭代比例拟合（IPF）型目标函数，它突破了标准IPF的序列化特性。通过一系列生成建模示例和一项基于双势阱的罕见事件任务，我们展示了所提出方法的潜力。