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We introduce a new diffusion-based approach for shape completion on 3D range scans. Compared with prior deterministic and probabilistic methods, we strike a balance between realism, multi-modality, and high fidelity. We propose DiffComplete by casting shape completion as a generative task conditioned on the incomplete shape. Our key designs are two-fold. First, we devise a hierarchical feature aggregation mechanism to inject conditional features in a spatially-consistent manner. So, we can capture both local details and broader contexts of the conditional inputs fusion strate to control gy in the our shape model completion.