Adversarial Training (AT) is known as an effective approach to enhance the robustness of deep neural networks. Recently researchers notice that robust models with AT have good generative ability and can synthesize realistic images, while the reason behind it is yet under-explored. In this paper, we demystify this phenomenon by developing a unified probabilistic framework, called Contrastive Energy-based Models (CEM). On the one hand, we provide the first probabilistic characterization of AT through a unified understanding of robustness and generative ability. On the other hand, our CEM can also naturally generalize AT to the unsupervised scenario and develop principled unsupervised AT methods. Based on these, we propose principled adversarial sampling algorithms in both supervised and unsupervised scenarios. Experiments show our sampling algorithms significantly improve the sampling quality and achieves an Inception score of 9.61 on CIFAR-10, which is superior to previous energy-based models and comparable to state-of-the-art generative models.