Title: Test Time Robustification of Deep Models via Adaptation and Augmentation. Abstract: While deep neural networks can attain good accuracy on in-distribution test points, many applications require robustness even in the face of unexpected perturbations in the input, changes in the domain, or other sources of distribution shift. We study the problem of test time robustification, i.e., using the test input to improve model robustness. Recent prior works have proposed methods for test time adaptation, however, they each introduce additional assumptions, such as access to multiple test points, that prevent widespread adoption. In this work, we aim to study and devise methods that make no assumptions about the model training process and are broadly applicable at test time. We propose a simple approach that can be used in any test setting where the model is probabilistic and adaptable: when presented with a test example, perform different data augmentations on the data point, and then adapt (all of) the model parameters by minimizing the entropy of the model's average, or marginal, output distribution across the augmentations. Intuitively, this objective encourages the model to make the same prediction across different augmentations, thus enforcing the invariances encoded in these augmentations, while also maintaining confidence in its predictions. In our experiments, we demonstrate that this approach consistently improves robust ResNet and vision transformer models, achieving accuracy gains of 1-8% over standard model evaluation and also generally outperforming prior augmentation and adaptation strategies. We achieve state-of-the-art results for test shifts caused by image corruptions (ImageNet-C), renditions of common objects (ImageNet-R), and, among ResNet-50 models, adversarially chosen natural examples (ImageNet-A).