Topo-Diffusion: Topological Diffusion Model for Image and Point Cloud Generation
Primary Area: generative models
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Keywords: Topological data analysis, generative diffusion model, generative model
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.
Abstract: Diffusion models represent an emerging topic in generative models and have demonstrated remarkable results in generating data with high quality and diversity. However, diffusion models suffer from two limitations (1) the notorious problem of computational burden such as large sampling step and train step needed due to directly diffusion in Euclidean space and (2) a global-structure representation for each sample that is implicitly considered in the process due to their very limited access to topological information. To mitigate these limitations, recent studies have reported that topological descriptors, which encode shape information from datasets across different scales in a topological space, can significantly improve the performance and stability of deep learning (DL). In this study, inspired by the success of topological data analysis (TDA), we propose a novel denoising diffusion model, i.e., Topo-Diffusion, which improves classical diffusion models by diffusing data in topology domain and sampling from reconstructing topological features. Within the Topo-Diffusion framework, we investigate whether local topological properties and higher-order structural information, as captured via persistent homology, can serve as a reliable signal that provides complementary information for generating a high-quality sample. Theoretically, we analyze the stability properties of persistent homology allow to establish the stability of generated samples over diffusion timesteps. We empirically evaluate the proposed Topo-Diffusion method on seven real-world and synthetic datasets, and our experimental results show that Topo-Diffusion outperforms benchmark models across all the evaluation metrics in fidelity and diversity of sampled synthetic data.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 4288
Loading