Explore the connections between optimal transport and variational inference in this 58-minute talk by Francisco Vargas from Valence Labs. Delve into forward and reverse time stochastic differential equations and Girsanov transformations. Discover a principled framework for sampling and generative modeling centered on path space divergences. Learn about a novel score-based annealed flow technique and its connections to statistical physics concepts. Examine a regularized iterative proportional fitting objective that departs from standard sequential approaches. Follow along as the speaker demonstrates the potential of these methods through generative modeling examples and a double-well-based rare event task. Gain insights into hierarchical VAEs, entropic optimal transport, and the process of learning forward and backward transitions. Conclude with a Q&A session to further clarify concepts presented in this comprehensive exploration of advanced machine learning techniques.