We present a unified framework for dense correspondence estimation, called Homography flow, to handle large photometric and geometric deformations in an efficient manner. Our algorithm is inspired by recent successes of the sparse to dense framework. The main intuition is that dense flows located in same plane can be represented as a single geometric transform. Tailored to dense correspondence task, the Homography flow differs from previous methods in the flow domain clustering and the trilateral interpolation. By estimating and propagating sparsely estimated transforms, dense flow field is estimated with very low computation time. The Homography flow highly improves the performance of dense correspondences, especially in flow discontinuous area. Experimental results on challenging image pairs show that our approach suppresses the state-of-the-art algorithms in both accuracy and computation time.