On the inverse problem of flow matching in the one-dimensional and Gaussian cases

Abstract

This paper studies the inverse problem of flow matching (FM) between distributions with finite exponential moment, a problem motivated by modern generative AI applications such as the distillation of flow matching models. Uniqueness of the solution is established in two cases – the one-dimensional setting and the Gaussian case. The general multidimensional problem remains open for future studies.

Alexander Korotin

Researcher

My research interests include generative modeling, diffusion models, unpaired learning, optimal transport and Schrodinger bridges.