Today's deep models are often unable to detect inputs which do not belong to the training distribution. This gives rise to confident incorrect predictions which could lead to devastating consequences in many important application fields such as healthcare and autonomous driving. Interestingly, both discriminative and generative models appear to be equally affected. Consequently, this vulnerability represents an important research challenge. We consider an outlier detection approach based on discriminative training with jointly learned synthetic outliers. We obtain the synthetic outliers by sampling an RNVP model which is jointly trained to generate datapoints at the border of the training distribution. We show that this approach can be adapted for simultaneous semantic segmentation and dense outlier detection. We present image classification experiments on CIFAR-10, as well as semantic segmentation experiments on three existing datasets (StreetHazards, WD-Pascal, Fishyscapes Lost & Found), and one contributed dataset. Our models perform competitively with respect to the state of the art despite producing predictions with only one forward pass.