Parallel Diffusion Models of Operator and Image for Blind Inverse Problems
This addresses the limitation of existing diffusion-based solvers to non-blind cases, enabling broader applicability in imaging and inverse problems, though it is incremental as it extends prior methods to blind settings.
The paper tackles blind inverse problems, where the forward operator is unknown, by constructing a diffusion prior for the operator and using parallel reverse diffusion to jointly estimate the operator and image, achieving state-of-the-art performance on tasks like blind deblurring and imaging through turbulence.
Diffusion model-based inverse problem solvers have demonstrated state-of-the-art performance in cases where the forward operator is known (i.e. non-blind). However, the applicability of the method to blind inverse problems has yet to be explored. In this work, we show that we can indeed solve a family of blind inverse problems by constructing another diffusion prior for the forward operator. Specifically, parallel reverse diffusion guided by gradients from the intermediate stages enables joint optimization of both the forward operator parameters as well as the image, such that both are jointly estimated at the end of the parallel reverse diffusion procedure. We show the efficacy of our method on two representative tasks -- blind deblurring, and imaging through turbulence -- and show that our method yields state-of-the-art performance, while also being flexible to be applicable to general blind inverse problems when we know the functional forms.