Motivated by recent progress in natural image statistics, we use newly available datasets with ground truth optical flow to learn the local statistics of optical flow and compare the learned models to prior models assumed by computer vision researchers. We find that a Gaussian mixture model (GMM) with 64 components provides a significantly better model for local flow statistics when compared to commonly used models. We investigate the source of the GMM's success and show it is related to an explicit representation of flow boundaries. We also learn a model that jointly models the local intensity pattern and the local optical flow. In accordance with the assumptions often made in computer vision, the model learns that flow boundaries are more likely at intensity boundaries. However, when evaluated on a large dataset, this dependency is very weak and the benefit of conditioning flow estimation on the local intensity pattern is marginal.