A Discrete Index Graph Diffusion Model for 3D Meshes Synthesis

The generation of 3D meshes is critical in numerous applications, evidenced by the growing popularity and attention towards interactive generative models. Although diffusion models currently stand out as powerful interactive generative models, they are confined to the 2D domain. Performing direct diffusion and denoising on complex 3D meshes with dense vertices and faces is impractical, time-consuming, and resource-intensive. In this work, we discretize the 3D space and incorporate the intricate 3D mesh topology within the Truncated-Signed Distance Fields (T-SDFs) of each discrete cell vertex and propose an efficient discrete index graph diffusion model for T-SDFs. We further divide T-SDFs into multiple local shapes and encode the complete object as a discretized 3D grid based on codebook indices, with each index labeled for its position to preserve its discretization while reducing the input dimensionality. A graph neural network is trained on these latent spaces to jointly denoise the diffusion process on continuous coordinates and discrete codebook indices to incorporate local and global information. As we delete the most frequently repeated codebook indices in the 3D grid, the input size of the diffusion model becomes variable. We employ diverse conditional embeddings from task-specific autoencoders to estimate the quantity of codebook indices in various 3D grids and achieve interactive conditional synthesis by utilizing classifier-free guidance to sample from diverse normal distributions. Our model exhibits exceptional generative performance, supported by experimental results showcasing its effectiveness in various generative tasks, including shape completion, single-view 3D generation, and text-driven generation.