Wasserstein Geodesic Generator for Conditional Distributions

Understand

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.