Title: Directional Domain Generalization. Abstract: Domain generalization aims to learn a predictive model from multiple different but related source tasks that can generalize well to a target task without the need of accessing any target data. Existing domain generalization methods ignore the relation between tasks, implicitly assuming that all the tasks are sampled from a stationary environment. Therefore, they can fail when deployed in an evolving environment. To this end, we formulate and study the \emph{directional domain generalization} (DDG) scenario, which exploits not only the source data but also their evolving pattern to generate a model for the unseen task. Our theoretical result reveals the benefits of modeling the relation between two consecutive tasks by learning a globally consistent directional mapping function. In practice, our analysis also suggest solving the DDG problem in a meta-learning manner, which leads to \emph{directional prototypical network}, the first method for the DDG problem. Empirical evaluation on both synthetic and real-world data sets validates the effectiveness of our approach.