  Inversion by Direct Iteration (InDI) is a new formulation for supervised
image restoration that avoids the so-called ``regression to the mean'' effect
and produces more realistic and detailed images than existing regression-based
methods. It does this by gradually improving image quality in small steps,
similar to generative denoising diffusion models. Image restoration is an
ill-posed problem where multiple high-quality images are plausible
reconstructions of a given low-quality input. Therefore, the outcome of a
single step regression model is typically an aggregate of all possible
explanations, therefore lacking details and realism. The main advantage of InDI
is that it does not try to predict the clean target image in a single step but
instead gradually improves the image in small steps, resulting in better
perceptual quality. While generative denoising diffusion models also work in
small steps, our formulation is distinct in that it does not require knowledge
of any analytic form of the degradation process. Instead, we directly learn an
iterative restoration process from low-quality and high-quality paired
examples. InDI can be applied to virtually any image degradation, given paired
training data. In conditional denoising diffusion image restoration the
denoising network generates the restored image by repeatedly denoising an
initial image of pure noise, conditioned on the degraded input. Contrary to
conditional denoising formulations, InDI directly proceeds by iteratively
restoring the input low-quality image, producing high-quality results on a
variety of image restoration tasks, including motion and out-of-focus
deblurring, super-resolution, compression artifact removal, and denoising.

Image and Video Processing;Computer Vision and Pattern Recognition;Machine Learning