Solving Inverse Problems using Diffusion with Iterative Colored Renoising
This work improves the efficiency and accuracy of solving inverse problems in imaging, such as medical or scientific reconstruction, by enhancing diffusion-based methods, though it is incremental as it builds on existing diffusion frameworks.
The paper tackles the problem of solving imaging inverse problems using pre-trained diffusion models by addressing poor approximations of the measurement-conditional score function, proposing a new iterative renoising method called FIRE that injects colored noise to maintain white noise conditions. The result is a state-of-the-art method, DDfire, which achieves high accuracy and runtime on linear inverse problems and phase retrieval.
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