Title: Variational Invariant Learning for Bayesian Domain Generalization. Abstract: Domain generalization addresses the out-of-distribution problem, which is challenging due to the domain shift and the uncertainty caused by the inaccessibility to data from the target domains. In this paper, we propose variational invariant learning, a probabilistic inference framework that jointly models domain invariance and uncertainty. We introduce variational Bayesian approximation into both the feature representation and classifier layers to facilitate invariant learning for better generalization across domains. In the probabilistic modeling framework, we introduce a domain-invariant principle to explore invariance across domains in a unified way. We incorporate the principle into the variational Bayesian layers in neural networks, achieving domain-invariant representations and classifier. We empirically demonstrate the effectiveness of our proposal on four widely used cross-domain visual recognition benchmarks. Ablation studies demonstrate the benefits of our proposal and on all benchmarks our variational invariant learning consistently delivers state-of-the-art performance. 