Potential Matching Optimal Transport: Continuous Normalizing Flows for Exact $p$-Wasserstein Dynamics
We introduce Potential Matching Optimal Transport (PMOT), a potential-flow framework for general $p$-cost optimal transport with $c_p(x,y)=\|x-y\|^p$. PMOT parameterizes the CNF velocity field with a scalar potential in the generalized Benamou--Brenier form for the chosen exponent $p$. It trains the potential gradient with a self-induced matching loss along straight bridges determined by the model's own endpoints, while allowing flexible terminal distribution matching. Our main result establishes zero-loss exactness: under the stated regularity, exact terminal matching, and uniqueness assumptions, any zero-loss solution satisfies the generalized Benamou--Brenier optimality system and reco...
| Authors | Lishuo Zhang, Ruizhi Huang, Yang Yu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 6 August 2026 |
| Last updated at source | 6 August 2026 |
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