Flows for Flows: Training Normalizing Flows Between Arbitrary Distributions with Maximum Likelihood Estimation

TL;DR

This paper introduces a method to train normalizing flows between any two distributions using maximum likelihood estimation, enhancing flexibility especially for conditional flows and optimal transport applications.

Contribution

It proposes a novel approach where the base distribution of a normalizing flow is itself modeled by a flow, enabling mappings between arbitrary distributions.

Findings

Effective training of flows between arbitrary distributions

Enhanced conditional flow modeling capabilities

Incorporation of optimal transport constraints

Abstract

Normalizing flows are constructed from a base distribution with a known density and a diffeomorphism with a tractable Jacobian. The base density of a normalizing flow can be parameterised by a different normalizing flow, thus allowing maps to be found between arbitrary distributions. We demonstrate and explore the utility of this approach and show it is particularly interesting in the case of conditional normalizing flows and for introducing optimal transport constraints on maps that are constructed using normalizing flows.