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.

我们介绍了一种在 3D 形状表面上直接操作的基于内在隐性扩散模型的框架，旨在合成高质量的纹理。通过对网格顶点上的离散矢量场编码纹理的隐式表示和学习在表面上的学习隐空间中去噪扩散过程的隐性扩散模型，我们的方法具有两个贡献。我们考虑了一种单一纹理网格范式，其中我们的模型被训练为在网格上生成给定纹理的变化。我们展示了合成的纹理与现有的单一纹理网格生成模型相比，具有较高的保真度。我们的模型还可以用于用户控制的编辑任务，例如修复缺失和标签引导的生成。我们提出的框架具有在等价变换下的等变性，这部分有助于我们方法的有效性，使我们的模型能够在局部相似区域之间无缝复现细节，并打开了生成纹理迁移的可能性。