  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.
