Abstract
Within a broad class of generative adversarial networks, we show that discriminator optimization process increases a lower bound of the dual cost function for the Wasserstein distance between the target distribution p and the generator distribution pG . It implies that the trained discriminator can approximate optimal transport (OT) from pG to p. Based on some experiments and a bit of OT theory, we propose discriminator optimal transport (DOT) scheme to improve generated images. We show that it improves inception score and FID calculated by unconditional GAN trained by CIFAR-10, STL-10 and a public pre-trained model of conditional GAN trained by ImageNet.