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Optical flow estimation is a basic task in self-driving and robotics systems, which enables to temporally interpret traffic scenes. Autonomous vehicles clearly benefit from the ultra-wide Field of View (FoV) offered by 360° panoramic sensors. However, due to the unique imaging process of panoramic cameras, models designed for pinhole images do not directly generalize satisfactorily to 360° panoramic images. In this paper, we put forward a novel network framework--PanoFlow, to learn optical flow for panoramic images. To overcome the distortions introduced by equirectangular projection in panoramic transformation, we design a Flow Distortion Augmentation (FDA) method, which contains radial flow distortion (FDA-R) or equirectangular flow distortion (FDA-E). We further look into the definition and properties of cyclic optical flow for panoramic videos, and hereby propose a Cyclic Flow Estimation (CFE) method by leveraging the cyclicity of spherical images to infer 360° optical flow and converting large displacement to relatively small displacement. PanoFlow is applicable to any existing flow estimation method and benefits from the progress of narrow-FoV flow estimation. In addition, we create and release a synthetic panoramic dataset FlowScape based on CARLA to facilitate training and quantitative analysis. PanoFlow achieves state-of-the-art performance on the public OmniFlowNet and the established FlowScape benchmarks. Our proposed approach reduces the End-Point-Error (EPE) on FlowScape by 27.3%. On OmniFlowNet, PanoFlow achieves a 55.5% error reduction from the best published result. We also qualitatively validate our method via a collection vehicle and a public real-world OmniPhotos dataset, indicating strong potential and robustness for real-world navigation applications. Code and dataset are publicly available at https://github.com/MasterHow/PanoFlow.