FlowMatcher: Heteroscedastic Conditional Transport for Dense Correspondence

A dense matcher should report not only where each pixel corresponds, but how reliable that correspondence is. Coarse-to-fine matchers expose this reliability at the coarse stage, where matching scores spread across candidate regions, yet de- code a single warp and refine it deterministically. We introduce FlowMatcher, a stochastic refiner that makes this coarse ambiguity the source of a transport pro- cess: candidate target coordinates are drawn from a Gaussian centered on the coarse warp, with a per-pixel scale predicted from the coarse matching scores, and a time-conditioned multiscale refiner moves each candidate toward the cor- rect correspondence. Samples converge where the evidence is decisive and stay apart where it is not, so their disagreement serves as an uncertainty signal. Built on the frozen RoMaV2 coarse matcher, FlowMatcher remains competitive with RoMaV2 in accuracy, while its sample spread ranks errors better than a RoMaV2- style precision head trained on our architecture, improves relative pose as residual weights, and yields held-out 90% regions after split-conformal calibration. The samples also contain correct answers that a single prediction misses: an oracle choosing among them raises one-pixel accuracy by 5–10 points over their mean, and a ground-truth-free cycle-consistency criterion recovers part of this gain in dense accuracy and pose. Although both refiners are trained at 640 × 640, when both methods are run directly at 1024 × 1024, FlowMatcher exceeds RoMaV2 in one-pixel accuracy on all dense benchmarks tested.