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.
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