  We present a novel method and analysis to train generative adversarial
networks (GAN) in a stable manner. As shown in recent analysis, training is
often undermined by the probability distribution of the data being zero on
neighborhoods of the data space. We notice that the distributions of real and
generated data should match even when they undergo the same filtering.
Therefore, to address the limited support problem we propose to train GANs by
using different filtered versions of the real and generated data distributions.
In this way, filtering does not prevent the exact matching of the data
distribution, while helping training by extending the support of both
distributions. As filtering we consider adding samples from an arbitrary
distribution to the data, which corresponds to a convolution of the data
distribution with the arbitrary one. We also propose to learn the generation of
these samples so as to challenge the discriminator in the adversarial training.
We show that our approach results in a stable and well-behaved training of even
the original minimax GAN formulation. Moreover, our technique can be
incorporated in most modern GAN formulations and leads to a consistent
improvement on several common datasets.
