Title: Model-Based Robust Deep Learning: Generalizing to Natural, Out-of-Distribution Data. Abstract: While deep learning (DL) has resulted in major breakthroughs in many applications, the frameworks commonly used in DL remain fragile to seemingly innocuous changes in the data. In response, adversarial training has emerged as a principled approach for improving the robustness of DL against norm-bounded perturbations.  Despite this progress, DL is also known to be fragile to unbounded shifts in the data distribution due to many forms of natural variation, including changes in weather or lighting in images.  However, there are remarkably few techniques that can address robustness to natural, out-of-distribution shifts in the data distribution in a general context.  To address this gap, we propose a paradigm shift from perturbation-based adversarial robustness to model-based robust deep learning.  Critical to our paradigm is to obtain models of natural variation, which vary data over a range of natural conditions.  Then by exploiting these models, we develop three novel model-based robust training algorithms that improve the robustness of DL with respect to natural variation. Our extensive experiments show that across a variety of natural conditions in twelve distinct datasets, classifiers trained with our algorithms significantly outperform classifiers trained via ERM, adversarial training, and domain adaptation techniques.  Specifically, when training on ImageNet and testing on various subsets of ImageNet-c, our algorithms improve over baseline methods by up to 30 percentage points in top-1 accuracy.  Further, we show that our methods provide robustness (1) against natural, out-of-distribution data, (2) against multiple simultaneous distributional shifts, and (3) to domains entirely unseen during training.