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Optimization within a layer of a deep-net has emerged as a new direction for deep-net layer design. However, there are two main challenges when applying these layers to computer vision tasks:(a) which optimization problem within a layer is useful?;(b) how to ensure that computation within a layer remains efficient? To study question (a), in this work, we propose total variation (TV) minimization as a layer for computer vision. Motivated by the success of total variation in image processing, we hypothesize that TV as a layer provides useful inductive bias for deep-nets too. We study this hypothesis on five computer vision tasks: image classification, weakly-supervised object localization, edge-preserving smoothing, edge detection, and image denoising, improving over existing baselines. To achieve these results, we had to address question (b): we developed a GPU-based projected-Newton method which is 37x faster than existing solutions.