Computational and Statistical Guarantees of the c-Rectified flow
Read the original on arXiv Statistics ML →The paper investigates the computational and statistical properties of c‑rectified flow, a cost‑aware variant of rectified flow that projects velocity fields onto a gradient class while preserving endpoint marginals. It shows that ordinary rectified flow can fail to recover optimal transport couplings, whereas iterative c‑rectified flow always converges to the optimal coupling under suitable regularity and uniform‑integrability assumptions, and provides quantitative contraction and exponential convergence guarantees. Additionally, the authors derive minimax‑optimal score estimation rates that, when combined with iterative c‑rectified flow, yield rate‑optimal estimators of optimal transport in high dimensions and nearly parametric rates in low dimensions.
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