Optical flow estimation is a fundamental and ill-posed problem in computer vision. To recover a dense flow field, appropriate spatial constraints have to be enforced. Recent advances exploit higher order spatial regularization, and achieve the top performance on the Middlebury benchmark. In this work, we revisit learning-based approach, and propose a learned sparse model to patch-wisely regularize the flow field. In particular, our method is based on multi-scale spatial regularization, which benefits from first-order spatial regularity and our learned, higher order sparse model. To obtain accurate flow estimation, we propose a sequential optimization scheme to solve the corresponding energy minimization problem. Moreover, as the errors in intermediate flow estimates are usually dense with large variations, we further propose flow-driven and image-driven approaches to address the problem of outliers. Experiments on the Middlebury benchmark show that our method is competitive ...