  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 $p_G$. It implies that the trained discriminator can
approximate optimal transport (OT) from $p_G$ to $p$.Based on some experiments
and a bit of OT theory, we propose a discriminator optimal transport (DOT)
scheme to improve generated images. We show that it improves inception score
and FID calculated by un-conditional GAN trained by CIFAR-10, STL-10 and a
public pre-trained model of conditional GAN by ImageNet.
