  Generating samples given a specific label requires estimating conditional
distributions. We derive a tractable upper bound of the Wasserstein distance
between conditional distributions to lay the theoretical groundwork to learn
conditional distributions. Based on this result, we propose a novel conditional
generation algorithm where conditional distributions are fully characterized by
a metric space defined by a statistical distance. We employ optimal transport
theory to propose the Wasserstein geodesic generator, a new conditional
generator that learns the Wasserstein geodesic. The proposed method learns both
conditional distributions for observed domains and optimal transport maps
between them. The conditional distributions given unobserved intermediate
domains are on the Wasserstein geodesic between conditional distributions given
two observed domain labels. Experiments on face images with light conditions as
domain labels demonstrate the efficacy of the proposed method.

Machine Learning;Machine Learning