Diffusion Models Adapt to Low-Dimensional Structure Under Flexible Coefficient Choices
2026-06-22 • Machine Learning
Machine Learning
AI summaryⓘ
The authors studied diffusion models, which are used to generate data samples efficiently by taking advantage of simpler underlying patterns. They found that these models work well across many different settings, not just specific ones previously studied. Their math shows that the number of steps needed to get a good sample depends mostly on the true underlying complexity, not on the full data size. This means diffusion models are reliably effective even when using a variety of parameter choices.
diffusion modelssamplinglow-dimensional structureconvergence theorytotal variation distanceupdate coefficientsiteration complexityhigh-dimensional data
Authors
Changxiao Cai, Yuchen Jiao, Gen Li
Abstract
Diffusion models are known to exploit unknown low-dimensional structure to accelerate sampling. However, existing convergence theory under low-dimensional data structure has largely focused on update rules with narrowly prescribed coefficient choices. This raises a fundamental question: is adaptation to low-dimensional structure sensitive to the precise choice of update coefficients? In this paper, we show that such adaptation is a robust property of diffusion models. For a broad class of update coefficients, we prove that $\widetilde{O}(k/\varepsilon)$ iterations suffice to generate an $\varepsilon$-accurate sample in total variation (TV) distance, independently of the ambient dimension. Our framework substantially broadens the class of diffusion samplers known to enjoy low dimensional adaptation and applies to several commonly used methods in practice. These results provide a theoretical justification for the empirical effectiveness of diffusion samplers across different coefficient choices when applied to structured, high-dimensional data.