TopoDiffusionNet: A Topology-aware Diffusion Model
This addresses a limitation in diffusion models for applications like robotics and environmental modeling that require exact topological control.
The paper tackled the problem of diffusion models struggling to generate images with specified topology, such as Betti numbers, by proposing TopoDiffusionNet, which enforces topological constraints using persistent homology and a topology-based objective function, resulting in significant improvements in topological accuracy across four datasets.
Diffusion models excel at creating visually impressive images but often struggle to generate images with a specified topology. The Betti number, which represents the number of structures in an image, is a fundamental measure in topology. Yet, diffusion models fail to satisfy even this basic constraint. This limitation restricts their utility in applications requiring exact control, like robotics and environmental modeling. To address this, we propose TopoDiffusionNet (TDN), a novel approach that enforces diffusion models to maintain the desired topology. We leverage tools from topological data analysis, particularly persistent homology, to extract the topological structures within an image. We then design a topology-based objective function to guide the denoising process, preserving intended structures while suppressing noisy ones. Our experiments across four datasets demonstrate significant improvements in topological accuracy. TDN is the first to integrate topology with diffusion models, opening new avenues of research in this area. Code available at https://github.com/Saumya-Gupta-26/TopoDiffusionNet