Statistics seminar: Aram Pooladian

Aram Pooladian
Yale University

Room: M3 3127

Blind denoising diffusion models and the blessings of dimensionality

We provide a mathematical theory for blind denoising diffusion models (BDDMs)---generative models based on denoisers where, crucially, the denoiser is not given the noise level in either the training or sampling stage. We show that when sampling via BDDMs, the noise level can be accurately estimated from a single noisy sample, provided that the intrinsic dimension of the data is sufficiently small compared to the ambient dimension.

Consequently, we show that blind denoising diffusion models implicitly track a certain noise schedule along the diffusion, allowing us to justify their correctness as samplers. This joint work with Zahra Kadkhodaie, Sinho Chewi, and Eero Simoncelli (view on arXiv).