Title: Stein Bridging: Enabling Mutual Reinforcement between Explicit and Implicit Generative Models. Abstract: Deep generative models are generally categorized into explicit models and implicit models. The former assumes an explicit density form whose normalizing constant is often unknown; while the latter, including generative adversarial networks (GANs), generates samples using a push-forward mapping. In spite of substantial recent advances demonstrating the power of the two classes of generative models in many applications, both of them, when used alone, suffer from respective limitations and drawbacks. To mitigate these issues, we propose Stein Bridging, a novel joint training framework that connects an explicit density estimator and an implicit sample generator with Stein discrepancy. We show that the Stein Bridge induces new regularization schemes for both explicit and implicit models. Convergence analysis and extensive experiments demonstrate that the Stein Bridging i) improves the stability and sample quality of the GAN training, and ii) facilitates the density estimator to seek more modes in data and alleviate the mode-collapse issue. Additionally, we discuss several applications of Stein Bridging and useful tricks in practical implementation used in our experiments.