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.
@article{arxiv.2512.23265,
title = {On the Inverse Flow Matching Problem in the One-Dimensional and Gaussian Cases},
author = {Alexander Korotin and Gudmund Pammer},
journal= {arXiv preprint arXiv:2512.23265},
year = {2025}
}