2025 Noether Early Career Scholar Award - To Intrinsic Dimension and Beyond: Efficient Sampling in Diffusion Models

Music City Center 

The denoising diffusion probabilistic model (DDPM) has become a cornerstone of generative AI. While sharp convergence guarantees have been established for DDPM, the iteration complexity typically scales with the ambient data dimension of target distributions, leading to overly conservative theory that fails to explain its practical efficiency. This has sparked recent efforts to understand how DDPM can achieve sampling speed-ups through automatic exploitation of intrinsic low dimensionality of data. This talk explores two key scenarios: (1) For a broad class of data distributions with intrinsic dimension k, we prove that the iteration complexity of the DDPM scales nearly linearly with k, which is optimal under the KL divergence metric; (2) For mixtures of Gaussian distributions with k components, we show that DDPM learns the distribution with iteration complexity that grows only logarithmically in k. These results provide theoretical justification for the practical efficiency of diffusion models.