We introduce GEM3D -- a new deep, topology-aware generative model of 3D
shapes. The key ingredient of our method is a neural skeleton-based
representation encoding information on both shape topology and geometry.
Through a denoising diffusion probabilistic model, our method first generates
skeleton-based representations following the Medial Axis Transform (MAT), then
generates surfaces through a skeleton-driven neural implicit formulation. The
neural implicit takes into account the topological and geometric information
stored in the generated skeleton representations to yield surfaces that are
more topologically and geometrically accurate compared to previous neural field
formulations. We discuss applications of our method in shape synthesis and
point cloud reconstruction tasks, and evaluate our method both qualitatively
and quantitatively. We demonstrate significantly more faithful surface
reconstruction and diverse shape generation results compared to the
state-of-the-art, also involving challenging scenarios of reconstructing and
synthesizing structurally complex, high-genus shape surfaces from Thingi10K and
ShapeNet.

GEM3D 是一种新的深度、拓扑感知的 3D 形状生成模型，通过神经骨架为基础的表示编码形状拓扑和几何信息，生成更准确的拓扑和几何信息的表面，并应用于形状综合和点云重建任务，取得了显著的表面重建和多样化形状生成结果。