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Various blur distortions in video will cause negative impact on both human viewing and video-based applications, which makes motion-robust deblurring methods urgently needed. Most existing works have strong dataset dependency and limited generalization ability in handling challenging scenarios, like blur in low contrast or severe motion areas, and non-uniform blur. Therefore, we propose a PRiOr-enlightened and MOTION-robust video deblurring model (PROMOTION) suitable for challenging blurs. On the one hand, we use 3D group convolution to efficiently encode heterogeneous prior information, explicitly enhancing the scenes' perception while mitigating the output's artifacts. On the other hand, we design the priors representing blur distribution, to better handle non-uniform blur in spatio-temporal domain. Besides the classical camera shake caused global blurry, we also prove the generalization for the downstream task suffering from local blur. Extensive experiments demonstrate we can achieve the state-of-the-art performance on well-known REDS and GoPro datasets, and bring machine task gain.