  Natural images may lie on a union of disjoint manifolds rather than one
globally connected manifold, and this can cause several difficulties for the
training of common Generative Adversarial Networks (GANs). In this work, we
first show that single generator GANs are unable to correctly model a
distribution supported on a disconnected manifold, and investigate how sample
quality, mode dropping and local convergence are affected by this. Next, we
show how using a collection of generators can address this problem, providing
new insights into the success of such multi-generator GANs. Finally, we explain
the serious issues caused by considering a fixed prior over the collection of
generators and propose a novel approach for learning the prior and inferring
the necessary number of generators without any supervision. Our proposed
modifications can be applied on top of any other GAN model to enable learning
of distributions supported on disconnected manifolds. We conduct several
experiments to illustrate the aforementioned shortcoming of GANs, its
consequences in practice, and the effectiveness of our proposed modifications
in alleviating these issues.
