Title: Generalization of GANs and overparameterized models under Lipschitz continuity. Abstract: Generative adversarial networks (GANs)  are really complex, and  little has been known about their generalization. The existing learning theories lack efficient tools to analyze generalization of GANs. To fill this gap, we introduce a novel tool to analyze generalization: Lipschitz continuity. We demonstrate its simplicity by showing generalization and consistency of overparameterized neural networks. We then use this tool to derive Lipschitz-based generalization bounds for GANs. In particular, our bounds show that penalizing the zero- and first-order informations of the GAN loss will improve generalization. Therefore, this work provides a unified theory for answering the long mystery of why imposing a Lipschitz constraint can help GANs to generalize well in practice. 