Expected Batch Optimal Transport Plans and Consequences for Flow Matching

arXiv:2605.12174v1 Announce Type: new Abstract: Solving optimal transport (OT) on random minibatches is a common surrogate for exact OT in large-scale learning. In flow matching (FM), this surrogate is used to obtain OT-like couplings that can straighten probability paths and reduce numerical integration cost. Yet, the population-level coupling induced by repeated minibatch OT remains only partially understood. We formalize this coupling as the expected batch OT plan overline{pi}{k}, obtained by averaging empirical OT plans over independent minibatches of size k. We then establish its large-batch consistency and, in the semidiscrete case relevant to generative modeling, derive rates for both the transport-cost bias and the convergence of overline{pi}{k} to the OT plan. For FM, this yields a population coupling whose induced velocity field is regular enough to define a unique flow from the source to the discrete target. We finally quantify how OT batch size interacts with numerical integration in a tractable two-atom model and in synthetic and image experiments.

Source: arXiv cs.LG | 2026-05-13