The Geometry of Phase Transitions in Diffusion Models: Tubular Neighbourhoods and Singularities
Abstract
Diffusion models undergo phase transitions during the generative process where data features suddenly emerge in the final stages. The current study aims to elucidate this critical phenomenon from the geometrical perspective. We employ the concept of ``injectivity radius'', a quantity that characterises the structure of the data manifold. Through theoretical and empirical evidence, we demonstrate that phase transitions in the generative process of diffusion models are closely related to the injectivity radius. Our findings offer a novel perspective on phase transitions in diffusion models, with potential implications for improving performance and sampling efficiency.
Cite
Text
Yaguchi et al. "The Geometry of Phase Transitions in Diffusion Models: Tubular Neighbourhoods and Singularities." Transactions on Machine Learning Research, 2025.Markdown
[Yaguchi et al. "The Geometry of Phase Transitions in Diffusion Models: Tubular Neighbourhoods and Singularities." Transactions on Machine Learning Research, 2025.](https://mlanthology.org/tmlr/2025/yaguchi2025tmlr-geometry/)BibTeX
@article{yaguchi2025tmlr-geometry,
title = {{The Geometry of Phase Transitions in Diffusion Models: Tubular Neighbourhoods and Singularities}},
author = {Yaguchi, Manato and Sakamoto, Kotaro and Sakamoto, Ryosuke and Tanabe, Masato and Akagawa, Masatomo and Hayashi, Yusuke and Suzuki, Masahiro and Matsuo, Yutaka},
journal = {Transactions on Machine Learning Research},
year = {2025},
url = {https://mlanthology.org/tmlr/2025/yaguchi2025tmlr-geometry/}
}