In this work, we formulate a novel framework for adversarial robustness using the manifold hypothesis. This framework provides sufficient conditions for defending against adversarial examples. We develop an adversarial purification method with this framework. Our method combines manifold learning with variational inference to provide adversarial robustness without the need for expensive adversarial training. Experimentally, our approach can provide adversarial robustness even if attackers are aware of the existence of the defense. In addition, our method can also serve as a test-time defense mechanism for variational autoencoders.