We introduce a framework for intrinsic latent diffusion models operating directly on the surfaces of 3D shapes, with the goal of synthesizing high-quality textures. Our approach is underpinned by two contributions: field latents, a latent representation encoding textures as discrete vector fields on the mesh vertices, and field latent diffusion models, which learn to denoise a diffusion process in the learned latent space on the surface. We consider a single-textured-mesh paradigm, where our models are trained to generate variations of a given texture on a mesh. We show the synthesized textures are of superior fidelity compared those from existing single-textured-mesh generative models. Our models can also be adapted for user-controlled editing tasks such as inpainting and label-guided generation. The efficacy of our approach is due in part to the equivariance of our proposed framework under isometries, allowing our models to seamlessly reproduce details across locally similar regions and opening the door to a notion of generative texture transfer.

翻译：我们提出了一种直接在三维形状表面进行内蕴潜变量扩散的框架，旨在合成高质量纹理。该方法基于两项核心贡献：场潜变量——一种将纹理编码为网格顶点离散向量场的潜变量表示，以及场潜变量扩散模型——通过学习在表面潜变量空间中对扩散过程进行去噪。我们采用单纹理网格范式，训练模型生成网格上给定纹理的变体。实验表明，与现有单纹理网格生成模型相比，我们的方法合成的纹理具有更优保真度。该模型还可适用于用户控制编辑任务，如修复和标签引导生成。方法的部分有效性源于所提框架在等距变换下的等变性，这使得模型能够无缝地在局部相似区域重现细节，并开创了生成式纹理迁移的概念。