Maximum Likelihood Estimation for Flow Matching by Direct Second-order Trace Objective

Daiki Miyake, Masahiro Suzuki, Yutaka Matsuo

Keywords: flow matching, generative models

TL;DR: We proposed a method to maximize likelihood more directly in flow matching.

Abstract:

Flow matching, one of the attractive deep generative models, has recently been used in wide modality.
Despite the remarkable success, the flow matching objective of the vector field is insufficient for maximum likelihood estimation.
Previous works show that adding the vector field's high-order gradient objectives further improves likelihood.
However, their method only minimizes the upper bound of the high-order objectives, hence it is not guaranteed that the objectives themselves are indeed minimized, resulting in likelihood maximization becoming less effective.
In this paper, we propose a method to directly minimize the high-order objective.
Since our method guarantees that the objective is indeed minimized, our method is expected to improve likelihood compared to previous works.
We verify that our proposed method achieves better likelihood in practice through experiments on 2D synthetic datasets and high-dimensional image datasets.

Primary Area: generative models

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 13274