Optimal transport and probability flows

In this talk, I will present some recent work at the intersection of optimal transport (OT) and probability flows. Optimal transport is an elegant theory that has diverse downstream applications. For likelihood estimation in particular, there has been a recent interest in using parametric invertible models (aka normalizing flows) to approximate the data distribution of interest. I will present my recent work on parameterizing flows using a neural convex potential, which is inspired by Brenier's theorem. In addition, I will cover a few other recently proposed probability flow models related to OT.