Unsupervised domain adaptive person re-identification (UDA re-ID) aims at transferring the labeled source domain's knowledge to improve the model's discriminability on the unlabeled target domain. From a novel perspective, we argue that the bridging between the source and target domains can be utilized to tackle the UDA re-ID task, and we focus on explicitly modeling appropriate intermediate domains to characterize this bridging. Specifically, we propose an Intermediate Domain Module (IDM) to generate intermediate domains' representations on-the-fly by mixing the source and target domains' hidden representations using two domain factors. Based on the “shortest geodesic path” definition, i.e., the intermediate domains along the shortest geodesic path between the two extreme domains can play a better bridging role, we propose two properties that these intermediate domains should satisfy. To ensure these two properties to better characterize appropriate intermediate domains, we enforce the bridge losses on intermediate domains' prediction space and feature space, and enforce a diversity loss on the two domain factors. The bridge losses aim at guiding the distribution of appropriate intermediate domains to keep the right distance to the source and target domains. The diversity loss serves as a regularization to prevent the generated intermediate domains from being over-fitting to either of the source and target domains. Our proposed method outperforms the state-of-the-arts by a large margin in all the common UDA re-ID tasks, and the mAP gain is up to 7.7% on the challenging MSMT17 benchmark. Code is available at https://github.com/SikaStar/IDM.