Blind Inverse Problem Solving Made Easy by Text-to-Image Latent Diffusion

Abstract: Blind inverse problems, where both the target data and forward operator are unknown, are crucial to many computer vision applications. Existing methods often depend on restrictive assumptions such as additional training, operator linearity, or narrow image distributions, thus limiting their generalizability. In this work, we present LADiBI, a training-free framework that uses large-scale text-to-image diffusion models to solve blind inverse problems with minimal assumptions. By leveraging natural language prompts, LADiBI jointly models priors for both the target image and operator, allowing for flexible adaptation across a variety of tasks. Additionally, we propose a novel posterior sampling approach that combines effective operator initialization with iterative refinement, enabling LADiBI to operate without predefined operator forms. Our experiments show that LADiBI is capable of solving a broad range of image restoration tasks, including both linear and nonlinear problems, on diverse target image distributions.