  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.
