Transport, VI, and Diffusions
Keywords: Entropic Optimal Transport, Variational Inference, Stochastic Control, Diffusion Models, Score Matching, Schroedinger Bridges, Foellmer Drift
TL;DR: 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.
Abstract: 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.
Submission Number: 88
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