Does optimal-transport forward dynamics remain best for robustness under imperfect velocity-field estimation?

Determine whether choosing the forward diffusion process to follow optimal transport dynamics—i.e., geodesics in the space endowed with the 2-Wasserstein distance—yields the best robustness of data generation when the reverse/estimated velocity field is not perfectly learned (so that the estimated velocity field differs from the true forward-process velocity field).

Background

The paper derives a speed-accuracy trade-off for diffusion models that upper-bounds a robustness metric of data generation—the response of the final 1-Wasserstein error to perturbations in the initial estimated distribution—by quantities determined solely by the forward process. When the forward process follows the geodesic in the 2-Wasserstein space (optimal transport) and the reverse/estimated dynamics perfectly reconstruct the true forward velocity field, this bound is minimized, motivating optimal transport as an ideal forward protocol.

However, in practical settings the estimated velocity field is learned and may be inaccurate. The authors note that corrections to their trade-off would then be necessary, and explicitly raise the open question of whether optimal-transport forward dynamics still confer the best robustness of data generation under such imperfect estimation.