Learning normalizing flows from Entropy-Kantorovich potentials

TL;DR

This paper introduces a novel method for learning continuous normalizing flows by leveraging entropy-regularized optimal transport, enabling training through scalar potential functions without explicitly computing the flows.

Contribution

It proposes a dual formulation that trains scalar potential functions to implicitly define normalizing flows, simplifying the training process and improving efficiency.

Findings

Effective training of normalizing flows via scalar potentials

Elimination of explicit flow computation during training

Potential for improved scalability and flexibility

Abstract

We approach the problem of learning continuous normalizing flows from a dual perspective motivated by entropy-regularized optimal transport, in which continuous normalizing flows are cast as gradients of scalar potential functions. This formulation allows us to train a dual objective comprised only of the scalar potential functions, and removes the burden of explicitly computing normalizing flows during training. After training, the normalizing flow is easily recovered from the potential functions.