Optimal Transport Flow Matching by Design 文章

arXiv:2606.04092v1 Announce Type: new Abstract: Flow matching models learn to transport samples from a simple prior distribution to a complex data distribution. When prior-data pairs are coupled via optimal transport (OT), the learned trajectories are straight and non-crossing, enabling fast, even single-step, generation. However, computing the OT coupling in high dimensions is intractable, and existing methods attempt to solve the OT problem, at the cost of persistent bias or significant overhead. Rather than solving for the OT coupling, we reformulate the problem. Once the prior is treated as a design choice rather than a fixed input, the OT coupling between prior and data is no longer unique. Many priors admit an OT-optimal identity coupling to the data, leaving us free to choose one that is also tractable to sample. We identify low-frequency projection of natural images as such a choice.