Optimal Flow Matching: Learning Straight Trajectories in Just One Step
This addresses a bottleneck in generative modeling for researchers and practitioners by providing a more efficient and accurate method for flow straightening, though it is incremental as it builds on existing flow matching techniques.
The paper tackled the problem of learning straight trajectories in flow matching for generative modeling, which is crucial for fast inference, by developing Optimal Flow Matching (OFM) that recovers straight Optimal Transport displacements for quadratic transport in just one step, eliminating errors from iterative methods.
Over the several recent years, there has been a boom in development of Flow Matching (FM) methods for generative modeling. One intriguing property pursued by the community is the ability to learn flows with straight trajectories which realize the Optimal Transport (OT) displacements. Straightness is crucial for the fast integration (inference) of the learned flow's paths. Unfortunately, most existing flow straightening methods are based on non-trivial iterative FM procedures which accumulate the error during training or exploit heuristics based on minibatch OT. To address these issues, we develop and theoretically justify the novel \textbf{Optimal Flow Matching} (OFM) approach which allows recovering the straight OT displacement for the quadratic transport in just one FM step. The main idea of our approach is the employment of vector field for FM which are parameterized by convex functions.