Bayesian Optimal Latent Projection for Noisy Image Restoration

In recent years, image restoration using large-scale la-tent diffusion generative models (DGM) has attracted in-creasing attention and achieved significant progress. Most of these latent DGM-based image restoration methods re-quire predicting the original clean image in each iteration, which is then used to estimate the image for the next iter-ation. However, these predicted original clean images are often inaccurate, leading to errors in the subsequent im-age estimation. In other words, there is a significant devi-ation between the final sampling restoration trajectory and the ground truth trajectory. The purpose of this paper is to narrow the gap between these two trajectories and en-hance the performance of image restoration. We propose the Bayesian Optimal Latent Projection (BOLP) algorithm, which identifies the optimal random noise within the Gaus-sian distribution to iteratively correct the estimated image at each step, thereby minimizing the distance to the ground truth image. Experiments in deblurring, super-resolution, and inpainting on FFHQ and ImageNet datasets demon-strate that the BOLP outperforms the previously established best algorithms and sets a new state of the art.