Modern neural networks excel at image classification, yet they remain vulnerable to common image corruptions such as blur, speckle noise or fog. Recent methods that focus on this problem, such as AugMix and DeepAugment, introduce defenses that operate in expectation over a distribution of image corruptions. In contrast, the literature on Lp-norm bounded perturbations focuses on defenses against worst-case corruptions. In this work, we reconcile both approaches by proposing AdversarialAugment, a technique which optimizes the parameters of image-to-image models to generate adversarially corrupted augmented images. We theoretically motivate our method and give sufficient conditions for the consistency of its idealized version as well as that of DeepAugment. Our classifiers improve upon the state-of-the-art on common image corruption benchmarks conducted in expectation on CIFAR-10-C and improve worst-case performance against Lp-norm bounded perturbations on both CIFAR-10 and ImageNet.