  Optical flow is inherently a 2D search problem, and thus the computational
complexity grows quadratically with respect to the search window, making large
displacements matching infeasible for high-resolution images. In this paper, we
take inspiration from Transformers and propose a new method for high-resolution
optical flow estimation with significantly less computation. Specifically, a 1D
attention operation is first applied in the vertical direction of the target
image, and then a simple 1D correlation in the horizontal direction of the
attended image is able to achieve 2D correspondence modeling effect. The
directions of attention and correlation can also be exchanged, resulting in two
3D cost volumes that are concatenated for optical flow estimation. The novel 1D
formulation empowers our method to scale to very high-resolution input images
while maintaining competitive performance. Extensive experiments on Sintel,
KITTI and real-world 4K ($2160 \times 3840$) resolution images demonstrated the
effectiveness and superiority of our proposed method. Code and models are
available at \url{https://github.com/haofeixu/flow1d}.
