AI Safety is a major concern in many deep learning applications such as autonomous driving. Given a trained deep learning model, an important natural problem is how to reliably verify the model's prediction. In this paper, we propose a novel framework --- deep verifier networks (DVN) to detect unreliable inputs or predictions of deep discriminative models, using separately trained deep generative models. Our proposed model is based on conditional variational auto-encoders with disentanglement constraints to separate the label information from the latent representation. We give both intuitive and theoretical justifications for the model. Our verifier network is trained independently with the prediction model, which eliminates the need of retraining the verifier network for a new model. We test the verifier network on both out-of-distribution detection and adversarial example detection problems, as well as anomaly detection problems in structured prediction tasks such as image caption generation. We achieve state-of-the-art results in all of these problems.