Novelty detection, a fundamental task in machine learning, has drawn a lot of recent attention due to its wide-ranging applications and the rise of neural approaches. In this work, we present a general framework for neural novelty detection that centers around a multivariate extension of the univariate quantile function. Our framework unifies and extends many classical and recent novelty detection algorithms, and opens the way to exploit recent advances in flow-based neural density estimation. We adapt the multiple gradient descent algorithm to obtain the first efficient end-to-end implementation of our framework that is free of tuning hyperparameters. Extensive experiments over a number of real datasets confirm the efficacy of our proposed method against state-of-the-art alternatives.