The speed of optical flow algorithm is crucial for many video editing tasks such as slow motion synthesis, selection propagation, tone adjustment propagation, and so on. Variational coarse-to-fine optical flow algorithms can generally produce high-quality results but cannot fulfil the speed requirement of many practical applications. Besides, large motions in real-world videos also pose a difficult problem to coarse-to-fine variational approaches. We, in this paper, present a fast optical flow algorithm that can handle large displacement motions. Our algorithm is inspired by recent successes of local methods in visual correspondence searching as well as approximate nearest neighbor field algorithms. The main novelty is a fast randomized edge-preserving approximate nearest neighbor field algorithm, which propagates self-similarity patterns in addition to offsets. Experimental results on public optical flow benchmarks show that our method is significantly faster than state-of-the-art methods without compromising on quality, especially when scenes contain large motions. Finally, we show some demo applications by applying our technique into real-world video editing tasks.