  We introduce Kernel Density Discrimination GAN (KDD GAN), a novel method for
generative adversarial learning. KDD GAN formulates the training as a
likelihood ratio optimization problem where the data distributions are written
explicitly via (local) Kernel Density Estimates (KDE). This is inspired by the
recent progress in contrastive learning and its relation to KDE. We define the
KDEs directly in feature space and forgo the requirement of invertibility of
the kernel feature mappings. In our approach, features are no longer optimized
for linear separability, as in the original GAN formulation, but for the more
general discrimination of distributions in the feature space. We analyze the
gradient of our loss with respect to the feature representation and show that
it is better behaved than that of the original hinge loss. We perform
experiments with the proposed KDE-based loss, used either as a training loss or
a regularization term, on both CIFAR10 and scaled versions of ImageNet. We use
BigGAN/SA-GAN as a backbone and baseline, since our focus is not to design the
architecture of the networks. We show a boost in the quality of generated
samples with respect to FID from 10% to 40% compared to the baseline. Code will
be made available.
