这篇论文告诉你：扩散模型采样快慢不挑超参数，只需O(k/ε)步就能出高质量样本，环境维度再高也不怕。
该论文证明扩散模型在低维数据结构下自适应采样的鲁棒性，对于宽泛的更新系数，仅需O(k/ε)步迭代即可生成TV距离ε准确的样本，且与数据环境维度无关。该结果显著扩展了已知具有低维适应性的扩散采样器类别，并适用于多种常用实践方法。研究为扩散采样器在不同系数选择下处理结构化高维数据时的经验有效性提供了理论支撑。
Diffusion Models Adapt to Low-Dimensional Structure Under Flexible Coefficient Choices
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.