  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.
