Denoising Diffusion Probabilistic Models Are Optimally Adaptive to Unknown Low Dimensionality

• 成果类型: Article; Early Access
• 署名作者: Huang, Zhihan; Wei, Yuting; Chen, Yuxin
• 署名单位: University of Pennsylvania
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2024.0769
• 发表日期: 2026-03-13
• 关键词: diffusion models; denoising diffusion probabilistic models; nonasymptotic theory; low-dimensional structures

摘要

The denoising diffusion probabilistic model (DDPM) has emerged as a mainstream generative model in generative artificial intelligence. Although sharp convergence guarantees have been established for the DDPM, the iteration complexity is, in general, proportional to the ambient data dimension, resulting in overly conservative theory that fails to explain its practical efficiency. This has motivated the recent work to investigate how the DDPM can achieve sampling speed-ups through automatic exploitation of intrinsic low dimensionality of data. We strengthen this line of work by demonstrating, in some sense, optimal adaptivity to unknown low dimensionality. For a broad class of data distributions, we prove that the iteration complexity of the DDPM scales nearly linearly with its intrinsic dimension, which is optimal when using the Kullback-Leibler divergence to measure distributional discrepancy.