Optimal Transport Flow Matching by Design
Quick Take
The study presents a novel approach to optimal transport (OT) flow matching, reformulating the problem by treating the prior as a design choice. 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.
Article Content
From source RSS / original summaryarXiv: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.
The identity coupling between data and its low-frequency representation is empirically OT-optimal, the prior is structured enough to be sampled by a lightweight model at inference, and the remaining flow-matching task reduces to synthesizing high-frequency detail. Interpolating the prior with Gaussian noise further improves generation quality while preserving the OT coupling.
The approach requires no modifications to the flow model itself, and integrates naturally with latent-space models, classifier-free guidance, and one-step generation frameworks. Across all benchmarks, our method reduces trajectory curvature by more than $2\times$ compared to existing flow matching methods, yielding better generation quality in the few-step regime.
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