DoubleDiffusion: Combining Heat Diffusion with Denoising Diffusion for Generative Learning on 3D Meshes

This paper proposes DoubleDiffusion, a novel framework that combines heat dissipation diffusion and denoising diffusion for direct generative learning on 3D mesh surfaces. Our approach addresses the challenges of generating continuous signal distributions residing on a curve manifold surface. Unlike previous methods that rely on unrolling 3D meshes into 2D or adopting field representations, DoubleDiffusion leverages the Laplacian-Beltrami operator to process features respecting the mesh structure. This combination enables effective geometry-aware signal diffusion across the underlying geometry. As shown in Fig.~\ref{fig:teaser}, we demonstrate that DoubleDiffusion has the ability to generate RGB signal distributions on complex 3D mesh surfaces and achieves per-category shape-conditioned texture generation across different shape geometry. Our work contributes a new direction in diffusion-based generative modeling on 3D surfaces, with potential applications in the field of 3D asset generation.