Diffusion models have become the dominant approach for generative tasks in images, videos, and other domains. However, diverse data properties in generation requests, which are critical for efficient serving, remain underexploited. To address this issue, we propose a diffusion model serving system ChituDiffusion. ChituDiffusion leverages the locality of data properties to recompose a diffusion pipeline into dGraphs with shared optimization opportunities, enabling thorough compile-time and runtime co-optimizations. During compilation, ChituDiffusion compiles each dGraph into multiple execution engines optimized for specific data properties. At runtime, heterogeneous requests are elaborately reorganized into fine-grained batching tasks with similar properties and then efficiently executed by matched engines. Evaluation on five diffusion applications shows that ChituDiffusion improves the throughput by up to 2.13$\times$ (1.58$\times$ on average) on A100 and 2.19$\times$ (1.51$\times$ on average) on H100 compared with existing frameworks. The code for ChituDiffusion and the production traces have been made open-source at https://github.com/thu-pacman/chitu/tree/Diffusion.