Hardware support for deep convolutional neural networks (CNNs) is critical to advanced computer vision in mobile and embedded devices. Current designs, however, accelerate generic CNNs; they do not exploit the unique characteristics of real-time vision. We propose to use the temporal redundancy in natural video to avoid unnecessary computation on most frames. A new algorithm, activation motion compensation, detects changes in the visual input and incrementally updates a previously-computed activation. The technique takes inspiration from video compression and applies well-known motion estimation techniques to adapt to visual changes. We use an adaptive key frame rate to control the trade-off between efficiency and vision quality as the input changes. We implement the technique in hardware as an extension to state-of-the-art CNN accelerator designs. The new unit reduces the average energy per frame by 54%, 62%, and 87% for three CNNs with less than 1% loss in vision accuracy.