The Fundamental Limits of Valid Transport Map Estimation
Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map. In applications like generative modeling, the transport cost itself is irrelevant, and this makes it natural to target maps which are more tractable from either a statistical or computational standpoint. In this short note, we formalize the task of estimating any valid transport map in a rigorous minimax framework. One consequence of this framing is that it yields sample complexity lower bounds for any method whose learned object is evaluated as a transport map or plan, ...
| Authors | Sivaraman Balakrishnan |
|---|---|
| Primary category | cs.LG |
| Published | 29 June 2026 |
| Last updated at source | 29 June 2026 |
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