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.

翻译：在一类广泛的生成对抗网络中，我们证明判别器的优化过程会提高目标分布$p$与生成器分布$p_G$之间Wasserstein距离对偶代价函数的下界。这表明训练后的判别器能够近似实现从$p_G$到$p$的最优传输（OT）。基于部分实验和最优传输理论，我们提出一种判别器最优传输（DOT）方案以改进生成图像的质量。实验证明，该方法能够提升基于CIFAR-10、STL-10数据集训练的无条件生成对抗网络，以及基于ImageNet的预训练条件生成对抗网络模型的Inception得分和FID指标。