The Geometry of Diffusion Models: Tubular Neighbourhoods and Singularities
Abstract
Diffusion generative models have been a leading approach for generating high-dimensional data. The current research aims to investigate the relation between the dynamics of diffusion models and the tubular neighbourhoods of a data manifold. We propose an algorithm to estimate the injectivity radius, the supremum of radii of tubular neighbourhoods. Our research relates geometric objects such as curvatures of data manifolds and dimensions of ambient spaces, to singularities of the generative dynamics such as emergent critical phenomena or spontaneous symmetry breaking.
Cite
Text
Sakamoto et al. "The Geometry of Diffusion Models: Tubular Neighbourhoods and Singularities." ICML 2024 Workshops: GRaM, 2024.Markdown
[Sakamoto et al. "The Geometry of Diffusion Models: Tubular Neighbourhoods and Singularities." ICML 2024 Workshops: GRaM, 2024.](https://mlanthology.org/icmlw/2024/sakamoto2024icmlw-geometry/)BibTeX
@inproceedings{sakamoto2024icmlw-geometry,
title = {{The Geometry of Diffusion Models: Tubular Neighbourhoods and Singularities}},
author = {Sakamoto, Kotaro and Sakamoto, Ryosuke and Tanabe, Masato and Akagawa, Masatomo and Hayashi, Yusuke and Yaguchi, Manato and Suzuki, Masahiro and Matsuo, Yutaka},
booktitle = {ICML 2024 Workshops: GRaM},
year = {2024},
url = {https://mlanthology.org/icmlw/2024/sakamoto2024icmlw-geometry/}
}