Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality

Understand

The denoising diffusion probabilistic model (DDPM) has emerged as a mainstream generative model in generative AI.

• While 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 Li and Yan (2024a) 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.