  Wasserstein barycenters have become popular due to their ability to represent
the average of probability measures in a geometrically meaningful way. In this
paper, we present an algorithm to approximate the Wasserstein-2 barycenters of
continuous measures via a generative model. Previous approaches rely on
regularization (entropic/quadratic) which introduces bias or on input convex
neural networks which are not expressive enough for large-scale tasks. In
contrast, our algorithm does not introduce bias and allows using arbitrary
neural networks. In addition, based on the celebrity faces dataset, we
construct Ave, celeba! dataset which can be used for quantitative evaluation of
barycenter algorithms by using standard metrics of generative models such as
FID.
