Topology-Aware Latent Diffusion for 3D Shape Generation

TL;DR

This paper presents a topology-aware latent diffusion model that generates diverse 3D shapes with controllable topological features by integrating persistent homology into the diffusion process.

Contribution

It introduces a novel method combining latent diffusion with persistent homology for topologically controllable 3D shape generation.

Findings

Produces diverse 3D shapes with varied topologies

Supports constrained generation from sparse inputs

Allows topology modification via persistence diagrams

Abstract

We introduce a new generative model that combines latent diffusion with persistent homology to create 3D shapes with high diversity, with a special emphasis on their topological characteristics. Our method involves representing 3D shapes as implicit fields, then employing persistent homology to extract topological features, including Betti numbers and persistence diagrams. The shape generation process consists of two steps. Initially, we employ a transformer-based autoencoding module to embed the implicit representation of each 3D shape into a set of latent vectors. Subsequently, we navigate through the learned latent space via a diffusion model. By strategically incorporating topological features into the diffusion process, our generative module is able to produce a richer variety of 3D shapes with different topological structures. Furthermore, our framework is flexible, supporting generation tasks constrained by a variety of inputs, including sparse and partial point clouds, as well as sketches. By modifying the persistence diagrams, we can alter the topology of the shapes generated from these input modalities.