Solving Inverse Problems using Diffusion with Iterative Colored Renoising
Journal:
arXiv
Published Date:
Jan 29, 2025
Abstract
Imaging inverse problems can be solved in an unsupervised manner using
pre-trained diffusion models, but doing so requires approximating the gradient
of the measurement-conditional score function in the diffusion reverse process.
We show that the approximations produced by existing methods are relatively
poor, especially early in the reverse process, and so we propose a new approach
that iteratively reestimates and "renoises" the estimate several times per
diffusion step. This iterative approach, which we call Fast Iterative REnoising
(FIRE), injects colored noise that is shaped to ensure that the pre-trained
diffusion model always sees white noise, in accordance with how it was trained.
We then embed FIRE into the DDIM reverse process and show that the resulting
"DDfire" offers state-of-the-art accuracy and runtime on several linear inverse
problems, as well as phase retrieval. Our implementation is at
https://github.com/matt-bendel/DDfire
