ArXiv

Diffusion Models Adapt to Low-Dimensional Structure Under Flexible Coefficient Choices

2026-06-22 · 17:20 UTC ·Changxiao Cai, Yuchen Jiao, Gen Li ·1 min read
Authors
Changxiao Cai, Yuchen Jiao, Gen Li
Categories
stat.ML, cs.LG, math.ST
arXiv
https://arxiv.org/abs/2606.23627v1
PDF
https://arxiv.org/pdf/2606.23627v1

Brief

Diffusion models are analyzed for sensitivity of low-dimensional adaptation to update-coefficient choices: the authors prove that, for a broad family of coefficient schemes, only O~(k/ε) iterations are needed to obtain an ε-accurate sample in total variation, independently of ambient dimension. The result (Cai, Jiao, Li, 2026) broadens prior narrowly tuned convergence theory and explains empirical robustness; summary based on the abstract.

Why it matters

Proves that for a broad class of update coefficients, O~(k/ε) iterations suffice to produce an ε-accurate sample in total variation (TV) distance, with the guarantee independent of the ambient dimension.

Key details

  • Establishes that adaptation to unknown k-dimensional structure is robust to coefficient choices (extending prior theory that required narrowly prescribed coefficients) and covers several commonly used diffusion samplers (Cai, Jiao, Li; 2026-06-22).
Source evidence

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.