Full-motion cost volumes play a central role in current state-of-the-art optical flow methods. However, constructed using simple feature correlations, they lack the ability to encapsulate prior, or even non-local, knowledge. This creates artifacts in poorly constrained, ambiguous regions, such as occluded and textureless areas. We propose a separable cost volume module, a drop-in replacement to correlation cost volumes, that uses non-local aggregation layers to exploit global context cues and prior knowledge, in order to disambiguate motions in these regions. Our method leads both the now standard Sintel and KITTI optical flow benchmarks in terms of accuracy, and is also shown to generalize better from synthetic to real data.