Generative Adversarial Nets (GAN) have been one of the most exciting developments in machine learning and AI. In this talk I will give an introduction to GAN, and discuss the difficulty of training a GAN. I'll propose a framework to learn deep generative models via Variational Gradient Flow (Vgrow) on probability measure spaces. Connections of our proposed VGrow method with other popular methods, such as VAE, GAN and flow-based methods, have been established in this framework, gaining new insights of deep generative learning.