Optimal Acceleration Transport for Improved Flow Matching
AS6 Level 5
MR6, AS6-05-10
Abstract:
As a powerful technique in generative modeling, Flow Matching (FM) aims to learn velocity fields from noise to data, which is often explained and implemented as solving Optimal Transport (OT) problems. In this talk, we bridge FM and the recent theory of Optimal Acceleration Transport (OAT), proposing an improved FM method called OAT-FM and exploring its benefits in both theory and practice. In particular, we demonstrate that the straightening objective hidden in existing OT-based FM methods is mathematically equivalent to minimizing the physical action associated with acceleration defined by OAT. Accordingly, instead of enforcing constant velocity, OAT-FM optimizes the acceleration transport in the product space of sample and velocity, whose objective corresponds to a necessary and sufficient condition of flow straightness. An efficient algorithm is designed to achieve OAT-FM with low complexity. OAT-FM motivates a new two-phase FM paradigm: Given a generative model trained by an arbitrary FM method, whose velocity information has been relatively reliable, we can fine-tune and improve it via OAT-FM. This paradigm eliminates the risk of data distribution drift and the need to generate a large number of noise data pairs, which consistently improves model performance in various generative tasks.
Bio:
Hongteng Xu is an Associate Professor at Gaoling School of Artificial Intelligence, Renmin University of China. He got his Ph.D. degree from the School of Electrical and Computer Engineering, Georgia Tech. From 2018 to September 2020, he was a senior research scientist in Infinia ML, Inc. At the same time, he was a postdoctoral researcher in Prof. Lawrence Carin's research group, Duke University. Hongteng's research lies in Artificial General Intelligence (AGI). In particular, he is interested in broad topics in computational optimal transport, generative modeling, large language models, model architecture design, and their applications in AI4Math and AI4Science.