Wasserstein Gradient Flows for Scalable and Regularized Barycenter Computation

ArXi:2510.04602v3 Announce Type: replace-cross Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space. Existing discrete methods are not scalable as they assume access to the complete set of samples from the input measures. Meanwhile, neural network approaches do scale well, but rely on complex optimization problems and cannot easily incorporate label information. We address these limitations through gradient flows in the space of probability measures.