Deep networks for computer vision are not reliable when they encounter adversarial examples. In this paper, we introduce a framework that uses the dense intrinsic constraints in natural images to robustify inference. By introducing constraints at inference time, we can shift the burden of robustness from training to testing, thereby allowing the model to dynamically adjust to each individual image's unique and potentially novel characteristics at inference time. Our theoretical results show the importance of having dense constraints at inference time. In contrast to existing single-constraint methods, we propose to use equivariance, which naturally allows dense constraints at a fine-grained level in the feature space. Our empirical experiments show that restoring feature equivariance at inference time defends against worst-case adversarial perturbations. The method obtains improved adversarial robustness on four datasets (ImageNet, Cityscapes, PASCAL VOC, and MS-COCO) on image recognition, semantic segmentation, and instance segmentation tasks.