Solving General Noisy Inverse Problem via Posterior Sampling: A Policy Gradient Viewpoint

Solving image inverse problems (e.g., super-resolution and inpainting) requires generating a high fidelity image that matches the given input (the low-resolution image or the masked image). By using the input image as guidance, we can leverage a pretrained diffusion generative model to solve a wide range of image inverse tasks without task specific model fine-tuning. To precisely estimate the guidance score function of the input image, we propose Diffusion Policy Gradient (DPG), a tractable computation method by viewing the intermediate noisy images as policies and the target image as the states selected by the policy. Experiments show that our method is robust to both Gaussian and Poisson noise degradation on multiple linear and non-linear inverse tasks, resulting into a higher image restoration quality on FFHQ, ImageNet and LSUN datasets.
Comment: Accepted and to Appear, AISTATS 2024