We introduce Primal-Dual Wasserstein GAN, a new learning algorithm for building latent variable models of the data distribution based on the primal and the dual formulations of the optimal transport (OT) problem. We utilize the primal formulation to learn a flexible inference mechanism and to create an optimal approximate coupling between the data distribution and the generative model. In order to learn the generative model, we use the dual formulation and train the decoder adversarially through a critic network that is regularized by the approximate coupling obtained from the primal. Unlike previous methods that violate various properties of the optimal critic, we regularize the norm and the direction of the gradients of the critic function. Our model shares many of the desirable properties of auto-encoding models in terms of mode coverage and latent structure, while avoiding their undesirable averaging properties, e.g. their inability to capture sharp visual features when modeling real images. We compare our algorithm with several other generative modeling techniques that utilize Wasserstein distances on Frechet Inception Distance (FID) and Inception Scores (IS).

我们引入了Primal-Dual Wasserstein GAN作为一种新的学习算法，用于基于最优输运问题的原始和对偶公式建立数据分布的潜在变量模型，同时通过对偶公式训练解码器实现生成模型，通过适当的正则化来保留最优批评者的性质，实现比以前的方法更好的图像生成效果。

原始对偶Wasserstein GAN