Most existing 3D assembly methods treat the problem as pure pose estimation, rearranging observed parts via rigid transformations. In contrast, human assembly naturally couples structural reasoning with holistic shape inference. Inspired by this intuition, we reformulate 3D assembly as a joint problem of assembly and generation. We show that these two processes are mutually reinforcing: assembly provides part-level structural priors for generation, while generation injects holistic shape context that resolves ambiguities in assembly. Unlike prior methods that cannot synthesize missing geometry, we propose CRAG, which simultaneously generates plausible complete shapes and predicts poses for input parts. Extensive experiments demonstrate state-of-the-art performance across in-the-wild objects with diverse geometries, varying part counts, and missing pieces. Project Page: https://ai4ce.github.io/CRAG/

翻译：大多数现有3D装配方法将问题视为纯姿态估计，通过刚性变换重新排列观测到的部件。相比之下，人类装配自然地将结构推理与整体形状推断相结合。受此启发，我们将3D装配重新定义为装配与生成的联合问题。我们证明这两个过程相互促进：装配为生成提供部件级结构先验，而生成为装配注入消除歧义的整体形状上下文。与无法合成缺失几何结构的现有方法不同，我们提出CRAG，该方法能同时生成合理的完整形状并预测输入部件的姿态。大量实验表明，该方法在具有多样化几何结构、不同部件数量及缺失部件的野外物体上均达到最先进性能。项目主页：https://ai4ce.github.io/CRAG/