In this talk, I will discuss how state-of-the-art discriminative deep networks can be turned into likelihood-based density models. Further, I will discuss how such models give rise to an alternative viewpoint on adversarial examples. Under this viewpoint adversarial examples are a consequence of excessive invariances learned by the classifier, manifesting themselves in striking failures when evaluating the model on out of distribution inputs. I will discuss how the commonly used cross-entropy objective encourages such overly invariant representations. Finally, I will present an extension to cross-entropy that, by exploiting properties of invertible deep networks, enables control of erroneous invariances in theory and practice.