让扩散模型生成图像时保持指定拓扑结构，提升精确控制能力。
TopoDiffusionNet: A Topology-aware Diffusion Model
- 用持久同调提取图像拓扑结构，设计拓扑损失函数。
- 在4个数据集上显著提升生成图像的贝蒂数准确率。
- 适合需要精确拓扑控制的机器人、环境建模等场景。
扩散模型虽能生成视觉逼真的图像，但难以生成具有指定拓扑结构的图像。贝蒂数是拓扑学中衡量图像结构数量的基本指标，而现有扩散模型无法满足这一基本约束，限制了其在机器人、环境建模等需精确控制领域的应用。为此，本文提出拓扑感知扩散模型 TopoDiffusionNet（TDN），利用拓扑数据分析工具——持久同调，提取图像中的拓扑结构，并设计基于拓扑的损失函数，在去噪过程中保留目标结构、抑制噪声结构。在四个数据集上的实验表明，该方法显著提升了生成图像的拓扑准确性。TDN是首个将拓扑信息融入扩散模型的工作，为该领域开辟了新方向。代码已公开于 https://github.com/Saumya-Gupta-26/TopoDiffusionNet。
原文摘要 · Abstract (English)
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
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