Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matching

arXiv:2403.18705v1 Announce Type: new
Abstract: In inverse problems, many conditional generative models approximate the posterior measure by minimizing a distance between the joint measure and its learned approximation. While this approach also controls the distance between the posterior measures in the case of the Kullback--Leibler divergence, this is in general not hold true for the Wasserstein distance. In this paper, we introduce a conditional Wasserstein distance via a set of restricted couplings that equals the expected Wasserstein distance of the …

abstract applications approximation arxiv bayesian case cs.lg divergence flow general generative generative models math.oc posterior type