Understanding Guidance Scale in Diffusion Models from a Geometric Perspective

Zhiyuan Zhan, Liuzhuozheng Li, Masashi Sugiyama

Abstract: Conditional diffusion models have become a leading approach for generating condition-consistent samples, such as class-specific images. In practice, the guidance scale is a key hyperparameter in conditional diffusion models, used to adjust the strength of the guidance term. While empirical studies have demonstrated that appropriately choosing the scale can significantly enhance generation quality, the theoretical understanding of its role remains limited. In this work, we analyze the probabilistic guidance term from a geometric view under the linear manifold assumption and, based on this analysis, construct a geometric guidance model that enables tractable theoretical study. To address regularity issues arising from multi-modal data, we introduce a mollification technique that ensures well-posed dynamics. Our theoretical results show that increasing the guidance scale improves alignment with the target data manifold, thereby enhancing generation performance. We further extend our framework to nonlinear manifolds, and empirical results on real-world datasets validate the effectiveness of the proposed model and are consistent with our theories.

Submission Type: Long submission (more than 12 pages of main content)

Code: https://github.com/liuzhuozheng-LI/Guidance-Scale-of-Diffusion

Assigned Action Editor: ~Mauricio_Delbracio1

Submission Number: 6530