  This paper presents a stochastic differential equation (SDE) approach for
general-purpose image restoration. The key construction consists in a
mean-reverting SDE that transforms a high-quality image into a degraded
counterpart as a mean state with fixed Gaussian noise. Then, by simulating the
corresponding reverse-time SDE, we are able to restore the origin of the
low-quality image without relying on any task-specific prior knowledge.
Crucially, the proposed mean-reverting SDE has a closed-form solution, allowing
us to compute the ground truth time-dependent score and learn it with a neural
network. Moreover, we propose a maximum likelihood objective to learn an
optimal reverse trajectory that stabilizes the training and improves the
restoration results. The experiments show that our proposed method achieves
highly competitive performance in quantitative comparisons on image deraining,
deblurring, and denoising, setting a new state-of-the-art on two deraining
datasets. Finally, the general applicability of our approach is further
demonstrated via qualitative results on image super-resolution, inpainting, and
dehazing. Code is available at
https://github.com/Algolzw/image-restoration-sde.

Machine Learning;Computer Vision and Pattern Recognition