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Few methods have been proposed to address generalization in the presence of unforeseen domain shifts. In particular, digital noise corruptions arise commonly in practice during the image acquisition stage and present a significant challenge for current methods. In this paper, we propose a diverse Gaussian noise consistency regularization method for improving robustness of image classifiers under a variety of corruptions while still maintaining high clean accuracy. We derive bounds to motivate and understand the behavior of our Gaussian noise consistency regularization using a local loss landscape analysis. Our approach improves robustness against unforeseen noise corruptions by 4.2-18.4% over adversarial training and other strong diverse data augmentation baselines across several benchmarks. 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