Title: Mutual Calibration between Explicit and Implicit Deep Generative Models. Abstract: Deep generative models are generally categorized into explicit models and implicit models. The former defines an explicit density form that allows likelihood inference; while the latter targets a flexible transformation from random noise to generated samples. To take full advantages of both models, we propose Stein Bridging, a novel joint training framework that connects an explicit (unnormalized) density estimator and an implicit sample generator via Stein discrepancy. We show that the Stein bridge 1) induces novel mutual regularization via kernel Sobolev norm penalization and Moreau-Yosida regularization, and 2) stabilizes the training dynamics. Empirically, we demonstrate that Stein Bridging can facilitate the density estimator to accurately identify data modes and guide the sample generator to output more high-quality samples especially when the training samples are contaminated or limited.