Wasserstein Gradient Flows Enable Scalable Barycenter Computation

A new method using gradient flows in the space of probability measures achieves scalable and regularized Wasserstein barycenter computation. The approach relies on mini-batch optimal transport, accepts modular regularization through task-aware functions, and integrates supervised information into the ground-cost. It addresses limitations of existing discrete methods that require complete sample sets and neural network approaches with complex optimization. The method is validated on domain adaptation benchmarks in computer vision, neuroscience, and chemical engineering, establishing a new state-of-the-art.