FIR-SDE: fast image restoration via mean-reverting stochastic differential equation

In computer vision, zero-shot image restoration—a technique enabling degraded image restoration without large-scale paired training data—has emerged as a pivotal technique for scenarios where data is limited or paired training data is challenging to obtain. However, existing methods face two key limitations: data consistency preservation remains challenging for out-of-domain data, and degradation process alignment is difficult when the degradation mechanism is not mathematically predetermined. To address these issues, this paper presents a novel zero-shot image restoration method (FIR-SDE). Traditional generation-oriented diffusion models (designed for image creation) are replaced with restoration-oriented models (specialized for degradation repair), expanding the range of effectively restorable images. To mitigate the noise offset (discrepancies between real and model-simulated degradation) and to enhance the alignment, a multi-step optimization strategy is employed, which evaluates the distance between real and simulated degraded images via frequency domain distribution. Experiments were conducted on two image restoration tasks (image deraining and inpainting) using three public datasets (AFHQ-dog, CelebA, and FFHQ), with Gaussian blur and motion blur superimposed as noise offsets. Results demonstrate that FIR-SDE method outperforms competitive methods in restoration quality and noise resistance. By eliminating data space constraints and exhibiting robustness against noise offsets, FIR-SDE offers a more flexible and efficient solution to broaden the practical applicability of zero-shot image restoration.