Diffusion Models for High-Dimensional Clustered Data: Intrinsic-Dimension Adaptivity via Bayesian Classification
Provides theoretical foundations for diffusion model performance on clustered data, advancing mathematical understanding for researchers working on generative model theory.
AI Summary
New arXiv paper proves diffusion models adapt to high-dimensional data by interpreting denoising as Bayesian classification, improving KL error bounds to depend linearly on cluster intrinsic dimension.
Excerpt
The empirical success of diffusion models in generative modelling has motivated theoretical work, including quantitative error bounds and qualitative analyses that characterise the different phases of denoising. We bring these two areas together by studying the adaptivity of diffusion models to the structured geometry of multimodal high-dimensional data that consists of multiple clusters in $\mathbb{R}^D$, each with its own low-dimensional structure, and inter-cluster separation depending on $D$