Video coding focuses on reducing the data size of videos. Video stabilization targets at removing shaky camera motions. In this paper, we enable video coding for video stabilization by constructing the camera motions based on the motion vectors employed in the video coding. The existing stabilization methods rely heavily on image features for the recovery of camera motions. However, feature tracking is time-consuming and prone to errors. On the other hand, nearly all captured videos have been compressed before any further processing and such a compression has produced a rich set of block-based motion vectors that can be utilized for estimating the camera motion. More specifically, video stabilization requires camera motions between two adjacent frames. However, motion vectors extracted from video coding may refer to non-adjacent frames. We first show that these non-adjacent motions can be transformed into adjacent motions such that each coding block within a frame contains a motion vector referring to its adjacent previous frame. Then, we regularize these motion vectors to yield a spatially-smoothed motion field at each frame, named as CodingFlow, which is optimized for a spatially-variant motion compensation. Based on CodingFlow, we finally design a grid-based 2D method to accomplish the video stabilization. Our method is evaluated in terms of efficiency and stabilization quality, both quantitatively and qualitatively, which shows that our method can achieve high-quality results compared with the state-of-the-art methods (feature-based).