Correspondences between frames encode rich information about dynamic content in videos. However, it is challenging to effectively capture and learn those due to their irregular structure and complex dynamics. In this paper, we propose a novel neural network that learns video representations by aggregating information from potential correspondences. This network, named $CPNet$CPNet, can learn evolving 2D fields with temporal consistency. In particular, it can effectively learn representations for videos by mixing appearance and long-range motion with an RGB-only input. We provide extensive ablation experiments to validate our model. CPNet shows stronger performance than existing methods on Kinetics and achieves the state-of-the-art performance on Something-Something and Jester. We provide analysis towards the behavior of our model and show its robustness to errors in proposals.