Optimal Transport Flow Matching by Design
Quick Answer
The study presents a novel approach to optimal transport (OT) flow matching, reformulating the problem by treating the prior as a design choice.
Quick Take
This method achieves over 2x reduction in trajectory curvature compared to existing methods, improving generation quality in few-step regimes without altering the flow model. The approach integrates seamlessly with latent-space models and classifier-free guidance.
Key Points
- Reformulates OT flow matching by treating prior as a design choice.
- Achieves over 2x reduction in trajectory curvature compared to existing methods.
- Empirically shows identity coupling between data and low-frequency representation is OT-optimal.
- Improves generation quality by interpolating the prior with Gaussian noise.
- Integrates naturally with latent-space models and one-step generation frameworks.
Paper Resources
Source Excerpt
From the original publisher, up to about 700 charactersFlow 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
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