On Flow Matching KL Divergence

I'm grateful to my collaborators Maojiang Su, Jerry Yao-Chieh Hu, and Prof. Han Liu for their work on this project. For this paper, I primarily focused on implementing and running numerical experiments to empirically validate the KL identities and error bounds. It was a great experience doing more numerical work while still strengthening my theoretical foundations—a nice complement to my other projects that lean more heavily on theory.

Abstract

We investigate KL divergence identities and error bounds for flow-matching objectives. We establish theoretical identities connecting flow-matching objectives to KL divergence and derive error bounds that characterize approximation quality.

Our work provides both theoretical guarantees and empirical validation through controlled numerical experiments. We validate KL identities and error bounds both with and without learned velocity fields, using controlled perturbations in the latter case to stress-test the theoretical results.