This paper introduces *Composable Part-Based Manipulation* (CPM), a novel approach that leverages object-part decomposition and part-part correspondences to enhance the learning and generalization of robotic manipulation skills. CPM models functional actions, such as pouring and constrained placing, as combinations of different correspondence constraints between object parts. It comprises a collection of composable diffusion models, each capturing a specific inter-object correspondence. These models generate parameters for manipulation skills based on the specific object parts, enabling strong generalization to novel objects and object categories. The approach is validated in both simulated and real-world scenarios, demonstrating robust and generalized manipulation capabilities. Key contributions include the proposal of CPM and the development of diffusion models trained to capture primitive functional correspondences, which can be flexibly recombined during inference. The paper also discusses related work, experimental setup, and limitations, highlighting the potential for future extensions and improvements.This paper introduces *Composable Part-Based Manipulation* (CPM), a novel approach that leverages object-part decomposition and part-part correspondences to enhance the learning and generalization of robotic manipulation skills. CPM models functional actions, such as pouring and constrained placing, as combinations of different correspondence constraints between object parts. It comprises a collection of composable diffusion models, each capturing a specific inter-object correspondence. These models generate parameters for manipulation skills based on the specific object parts, enabling strong generalization to novel objects and object categories. The approach is validated in both simulated and real-world scenarios, demonstrating robust and generalized manipulation capabilities. Key contributions include the proposal of CPM and the development of diffusion models trained to capture primitive functional correspondences, which can be flexibly recombined during inference. The paper also discusses related work, experimental setup, and limitations, highlighting the potential for future extensions and improvements.