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Optimal Flow Matching: Learning Straight Trajectories in Just One Step

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arxiv 2403.13117 v3 pith:6D5GAC7W submitted 2024-03-19 stat.ML cs.LG

Optimal Flow Matching: Learning Straight Trajectories in Just One Step

Nikita Kornilov , Petr Mokrov , Alexander Gasnikov , Alexander Korotin This is my paper
classification stat.ML cs.LG
keywords flowmatchingoptimalstraightapproachjustmethodsstep
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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Cited by 3 Pith papers

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  2. Efficient Transferable Optimal Transport via Min-Sliced Transport Plans

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    Min-STP optimizes slicers for efficient OT that transfer under slight distributional shifts, with a minibatch formulation offering accuracy guarantees and empirical success in point cloud alignment and generative modeling.

  3. FlowCTS: On-policy Continuous Trajectory Supervision of Flow Models

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    Trajectory-derived, temporally weighted velocity matching from shared student states outperforms KL-based on-policy distillation for multi-reference flow model post-training.