Compositional video generation aims to synthesize multiple instances with diverse appearance and motion. However, current approaches mainly focus on binding semantics, neglecting to understand diverse motion categories specified in prompts. In this paper, we propose a motion factorization framework that decomposes complex motion into three primary categories: motionlessness, rigid motion, and non-rigid motion. Specifically, our framework follows a planning before generation paradigm. (1) During planning, we reason about motion laws on the motion graph to obtain frame-wise changes in the shape and position of each instance. This alleviates semantic ambiguities in the user prompt by organizing it into a structured representation of instances and their interactions. (2) During generation, we modulate the synthesis of distinct motion categories in a disentangled manner. Conditioned on the motion cues, guidance branches stabilize appearance in motionless regions, preserve rigid-body geometry, and regularize local non-rigid deformations. Crucially, our two modules are model-agnostic, which can be seamlessly incorporated into various diffusion model architectures. Extensive experiments demonstrate that our framework achieves impressive performance in motion synthesis on real-world benchmarks. Code is available at https://github.com/ZixuanWang0525/MF-CVG.
@article{arxiv.2603.09104,
title = {Training-free Motion Factorization for Compositional Video Generation},
author = {Zixuan Wang and Ziqin Zhou and Feng Chen and Duo Peng and Yixin Hu and Changsheng Li and Yinjie Lei},
journal= {arXiv preprint arXiv:2603.09104},
year = {2026}
}