Title: Uncertain Out-of-Domain Generalization. Abstract: We study a worst-case scenario in generalization: Out-of-domain generalization from a single source. The goal is to learn a robust model from a single source and expect it to generalize over many unknown distributions. This challenging problem has been seldom investigated while existing solutions suffer from various limitations. In this paper, we propose a new solution. The key idea is to augment the source capacity in both input and label spaces, while the augmentation is guided by uncertainty assessment. To the best of our knowledge, this is the first work to (1) access the generalization uncertainty from a single source and (2) leverage it to guide both input and label augmentation for robust generalization. The model training and deployment are effectively organized in a Bayesian meta-learning framework. We conduct extensive comparisons and ablation study to validate our approach. The results prove our superior performance in a wide scope of tasks including image classification, text classification, and speech recognition.