Abstract:
This talk connects learned flow models with optimal transport and Wasserstein gradient flows. In the first part,
we consider flow matching and rectified flows as fixed point iterations in the space of couplings. We will examine
under which conditions limits of these iterations resamble optimal transport. In the second part, we train a
generative model for sampling from unnormalized probability density functions by simulating a Wasserstein
gradient flow. To this end, we iteratively solve the steps of the Jordan-Kinderlehrer-Otto (JKO) scheme by
continuous normalizing flows with regularized velocity fields. We combine the Wasserstein gradient flow with
importance weighting and show the effectiveness of the method by numerical examples.