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We address the challenging problem of learning motion representations using deep models for video recognition. To this end, we make use of attention modules that learn to highlight regions in the video and aggregate features for recognition. Specifically, we propose to leverage output attention maps as a vehicle to transfer the learned representation from a motion (flow) network to an RGB network. We systematically study the design of attention modules, and develop a novel method for attention distillation. Our method is evaluated on major action benchmarks, and consistently improves the performance of the baseline RGB network by a significant margin. Moreover, we demonstrate that our attention maps can leverage motion cues in learning to identify the location of actions in video frames. We believe our method provides a step towards learning motion-aware representations in deep models. Our project page is available at https://aptx4869lm.github.io/AttentionDistillation/