Title: Robust saliency maps with distribution-preserving decoys. Abstract: Saliency methods help to make deep neural network predictions more interpretable by identifying particular features, such as pixels in an image, that contribute most strongly to the network's prediction. Unfortunately, recent evidence suggests that many saliency methods perform poorly when gradients are saturated or in the presence of strong inter-feature dependence or noise injected by an adversarial attack. In this work, we propose a data-driven technique that uses the distribution-preserving decoys to infer robust saliency scores in conjunction with a pre-trained convolutional neural network classifier and any off-the-shelf saliency method.  We formulate the generation of decoys as an optimization problem, potentially applicable to any convolutional network architecture. We also propose a novel decoy-enhanced saliency score, which provably compensates for gradient saturation and considers joint activation patterns of pixels in a single-layer convolutional neural network. Empirical results on the ImageNet data set using three different deep neural network architectures---VGGNet, AlexNet and ResNet---show both qualitatively and quantitatively that decoy-enhanced saliency scores outperform raw scores produced by three existing saliency methods.