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.

翻译：我们提出了一种结合潜在扩散与持续同调的新型生成模型，用于创建具有高度多样性的三维形状，尤其关注其拓扑特性。该方法将三维形状表示为隐式场，并利用持续同调提取包含贝蒂数和持续图在内的拓扑特征。形状生成过程分为两个步骤：首先，采用基于Transformer的自编码模块将每个三维形状的隐式表示嵌入到潜在向量集合中；随后，通过扩散模型在学得的潜在空间中进行导航。通过策略性地将拓扑特征融入扩散过程，本生成模块能够生成具有不同拓扑结构的更丰富多样的三维形状。此外，该框架具有灵活性，支持受稀疏点云、部分点云及草图等多种输入约束的生成任务。通过修改持续图，我们能够改变基于这些输入模态生成形状的拓扑结构。