Noisy Image Restoration Based on Conditional Acceleration Score Approximation

Ziqiang Shi, Rujie Liu

Abstract: In recent years, score-based generative models (SGM) have achieved state-of-the-art (SOTA) performance in noisy image restoration [1], [2]. But at present, most of these methods are performed in the position space, and there is a lack in modeling of the velocity and acceleration of the image on the restoration path. In this paper, we propose a new image restoration method called conditional acceleration score approximation (CASA), which introduces velocity and acceleration variables on top of the data position along the recovery path. Guided by the degraded image, CASA can effectively and dynamically control the direction and speed of motion along the diffusion path in the reverse-time stochastic differential equation. Therefore, the key to this process is how to inject the degraded image as a guidance into the third-order reverse-time process in this position-velocity-acceleration space, especially in the evolution direction of the diffusion path. We propose a strategy for approximating the conditional acceleration score by decomposing the true posterior CAS into a priori CAS and an observed acceleration score for the measurement at the current moment. Experiments on 3 different datasets and 7 kinds of restoration tasks show that CASA is better than other methods and achieves a new SOTA.