Temporal domain generalization is a promising yet extremely challenging area where the goal is to learn models under temporally changing data distributions and generalize to unseen data distributions following the trends of the change. The advancement of this area is challenged by: 1) characterizing data distribution drift and its impacts on models, 2) expressiveness in tracking the model dynamics, and 3) theoretical guarantee on the performance. To address them, we propose a Temporal Domain Generalization with Drift-Aware Dynamic Neural Network (DRAIN) framework. Specifically, we formulate the problem into a Bayesian framework that jointly models the relation between data and model dynamics. We then build a recurrent graph generation scenario to characterize the dynamic graph-structured neural networks learned across different time points. It captures the temporal drift of model parameters and data distributions and can predict models in the future without the presence of future data. In addition, we explore theoretical guarantees of the model performance under the challenging temporal DG setting and provide theoretical analysis, including uncertainty and generalization error. Finally, extensive experiments on several real-world benchmarks with temporal drift demonstrate the proposed method’s effectiveness and efficiency.