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.1, 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.

翻译：本文提出双扩散（DoubleDiffusion）这一新颖框架，该框架结合热耗散扩散与去噪扩散过程，直接在三维网格表面进行生成式学习。我们的方法解决了在曲线流形表面生成连续信号分布的挑战。与以往依赖将三维网格展开为二维或采用场表示的方法不同，双扩散利用拉普拉斯-贝尔特拉米算子处理遵循网格结构的特征。这种结合实现了沿底层几何结构的有效几何感知信号扩散。如图1所示，我们证明双扩散能够在复杂三维网格表面生成RGB信号分布，并实现跨不同形状几何的按类别形状条件纹理生成。本工作为三维表面上的扩散生成式建模开辟了新方向，在三维资产生成领域具有潜在应用前景。