Data-to-Energy Stochastic Dynamics

The Schrödinger bridge problem is concerned with finding the optimal transportation dynamics between two distributions. Existing algorithms allow to infer such dynamics only for cases where samples from both distributions are available. We propose a novel method that allows to model Schrödinger bridges when one (or both) distributions are given by their unnormalised densities. We apply the newly developed method to the problem of sampling posterior distributions in latent spaces of generative models, creating a scalable data-free image-to-image translation method.