用连续对应嵌入生成逼真手物操作动作，实现物理合理且精细的交互。

Dynamic and dexterous manipulation of objects presents a complex challenge, requiring the synchronization of hand motions with the trajectories of objects to achieve seamless and physically plausible interactions. In this work, we introduce ManiDext, a unified hierarchical diffusion-based framework for generating hand manipulation and grasp poses based on 3D object trajectories. Our key insight is that accurately modeling the contact correspondences between objects and hands during interactions is crucial. Therefore, we propose a continuous correspondence embedding representation that specifies detailed hand correspondences at the vertex level between the object and the hand. This embedding is optimized directly on the hand mesh in a self-supervised manner, with the distance between embeddings reflecting the geodesic distance. Our framework first generates contact maps and correspondence embeddings on the object's surface. Based on these fine-grained correspondences, we introduce a novel approach that integrates the iterative refinement process into the diffusion process during the second stage of hand pose generation. At each step of the denoising process, we incorporate the current hand pose residual as a refinement target into the network, guiding the network to correct inaccurate hand poses. Introducing residuals into each denoising step inherently aligns with traditional optimization process, effectively merging generation and refinement into a single unified framework. Extensive experiments demonstrate that our approach can generate physically plausible and highly realistic motions for various tasks, including single and bimanual hand grasping as well as manipulating both rigid and articulated objects. Code will be available for research purposes.