Thanks to my collaborators Maojiang Su, Jerry Yao-Chieh Hu, and Prof. Han Liu for their work on this project. My part was mostly on the empirical side: implementing and running the numerical experiments that validate the KL identities and error bounds.
It was a nice change of pace to do more numerical work while still leaning on the theory — a good complement to my other projects, which sit much further toward the pencil-and-paper end of the spectrum.
Abstract
We investigate KL divergence identities and error bounds for flow-matching objectives, establishing theoretical identities that connect the flow-matching objective to KL divergence and deriving error bounds that characterize approximation quality.
The theory is paired with empirical validation from controlled numerical experiments. We check the identities and bounds both with and without learned velocity fields, using controlled perturbations in the latter case to stress-test the theoretical results.