Blind denoising diffusion models and the blessings of dimensionality
This work addresses a fundamental challenge in generative modeling for machine learning by proposing a more robust and efficient approach to diffusion models, with potential broad applications in image synthesis and beyond.
The paper tackles the problem of generative diffusion models by analyzing blind denoising diffusion models (BDDMs) that do not require noise amplitude information, showing they automatically track an implicit noise schedule and can sample accurately in polynomially many steps based on intrinsic dimensionality. Empirical results on synthetic and image data demonstrate that BDDMs produce higher quality samples than non-blind counterparts by correcting noise mismatch issues.
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.