Diffusion models have been widely adopted in image and language generation and are now being applied to reinforcement learning. However, the application of diffusion models in offline cooperative Multi-Agent Reinforcement Learning (MARL) remains limited. Although existing studies explore this direction, they suffer from scalability or poor cooperation issues due to the lack of design principles for diffusion-based MARL. The Individual-Global-Max (IGM) principle is a popular design principle for cooperative MARL. By satisfying this principle, MARL algorithms achieve remarkable performance with good scalability. In this work, we extend the IGM principle to the Individual-Global-identically-Distributed (IGD) principle. This principle stipulates that the generated outcome of a multi-agent diffusion model should be identically distributed as the collective outcomes from multiple individual-agent diffusion models. We propose DoF, a diffusion factorization framework for Offline MARL. It uses noise factorization function to factorize a centralized diffusion model into multiple diffusion models. We theoretically show that the noise factorization functions satisfy the IGD principle. Furthermore, DoF uses data factorization function to model the complex relationship among data generated by multiple diffusion models. Through extensive experiments, we demonstrate the effectiveness of DoF. The source code is available at https://github.com/xmu-rl-3dv/DoF.