This paper addresses the challenge of learning semantically and functionally meaningful 3D motion priors from real-world videos, in order to enable prediction of future 3D scene motion from a single input image. We propose a novel pixel-aligned Motion Map (MoMap) representation for 3D scene motion, which can be generated from existing generative image models to facilitate efficient and effective motion prediction. To learn meaningful distributions over motion, we create a large-scale database of MoMaps from over 50,000 real videos and train a diffusion model on these representations. Our motion generation not only synthesizes trajectories in 3D but also suggests a new pipeline for 2D video synthesis: first generate a MoMap, then warp an image accordingly and complete the warped point-based renderings. Experimental results demonstrate that our approach generates plausible and semantically consistent 3D scene motion.