  Recently it has been shown that using diffusion models for inverse problems
can lead to remarkable results. However, these approaches require a closed-form
expression of the degradation model and can not support complex degradations.
To overcome this limitation, we propose a method (INDigo) that combines
invertible neural networks (INN) and diffusion models for general inverse
problems. Specifically, we train the forward process of INN to simulate an
arbitrary degradation process and use the inverse as a reconstruction process.
During the diffusion sampling process, we impose an additional data-consistency
step that minimizes the distance between the intermediate result and the
INN-optimized result at every iteration, where the INN-optimized image is
composed of the coarse information given by the observed degraded image and the
details generated by the diffusion process. With the help of INN, our algorithm
effectively estimates the details lost in the degradation process and is no
longer limited by the requirement of knowing the closed-form expression of the
degradation model. Experiments demonstrate that our algorithm obtains
competitive results compared with recently leading methods both quantitatively
and visually. Moreover, our algorithm performs well on more complex degradation
models and real-world low-quality images.
