  The effective application of neural networks in the real-world relies on
proficiently detecting out-of-distribution examples. Contemporary methods seek
to model the distribution of feature activations in the training data for
adequately distinguishing abnormalities, and the state-of-the-art method uses
Gaussian distribution models. In this work, we present a novel approach that
improves upon the state-of-the-art by leveraging an expressive density model
based on normalizing flows. We introduce the residual flow, a novel flow
architecture that learns the residual distribution from a base Gaussian
distribution. Our model is general, and can be applied to any data that is
approximately Gaussian. For out of distribution detection in image datasets,
our approach provides a principled improvement over the state-of-the-art.
Specifically, we demonstrate the effectiveness of our method in ResNet and
DenseNet architectures trained on various image datasets. For example, on a
ResNet trained on CIFAR-100 and evaluated on detection of out-of-distribution
samples from the ImageNet dataset, holding the true positive rate (TPR) at
$95\%$, we improve the true negative rate (TNR) from $56.7\%$ (current
state-of-the-art) to $77.5\%$ (ours).
