Optimal Flow Matching: Learning Straight Trajectories in Just One Step

Understand

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.