Blind denoising diffusion models and the blessings of dimensionality

TL;DR

This paper demonstrates that blind denoising diffusion models can effectively learn and sample from data distributions with low intrinsic dimensionality without explicit noise schedule information, outperforming traditional models.

Contribution

The paper provides a theoretical analysis and empirical validation showing blind denoising diffusion models automatically track an implicit noise schedule and produce higher quality samples without explicit schedule information.

Findings

BDDMs accurately estimate noise variance from noisy images

Schedule-free BDDMs generate higher quality samples

BDDMs can sample efficiently in polynomial steps of intrinsic dimension

Abstract

We analyze, theoretically and empirically, the performance of generative diffusion models based on \emph{blind denoisers}, in which the denoiser is not given the noise amplitude in either the training or sampling processes. Assuming that the data distribution has low intrinsic dimensionality, we prove that blind denoising diffusion models (BDDMs), despite not having access to the noise amplitude, \emph{automatically} track a particular \emph{implicit} noise schedule along the reverse process. Our analysis shows that BDDMs can accurately sample from the data distribution in polynomially many steps as a function of the intrinsic dimension. Empirical results corroborate these mathematical findings on both synthetic and image data, demonstrating that the noise variance is accurately estimated from the noisy image. Remarkably, we observe that schedule-free BDDMs produce samples of higher quality compared to their non-blind counterparts. We provide evidence that this performance gain arises because BDDMs correct the mismatch between the true residual noise (of the image) and the noise assumed by the schedule used in non-blind diffusion models.