Residual Denoising Diffusion Models
Authors: Jiawei Liu, Qiang Wang, Huijie Fan, Yinong Wang, Yandong Tang, Liangqiong Qu

We propose residual denoising diffusion models (RDDM) a novel dual diffusion process that decouples the traditional single denoising diffusion process into residual diffusion and noise diffusion. This dual diffusion framework expands the denoising-based diffusion models initially uninterpretable for image restoration into a unified and interpretable model for both image generation and restoration by introducing residuals. Specifically our residual diffusion represents directional diffusion from the target image to the degraded input image and explicitly guides the reverse generation process for image restoration while noise diffusion represents random perturbations in the diffusion process. The residual prioritizes certainty while the noise emphasizes diversity enabling RDDM to effectively unify tasks with varying certainty or diversity requirements such as image generation and restoration. We demonstrate that our sampling process is consistent with that of DDPM and DDIM through coefficient transformation and propose a partially path-independent generation process to better understand the reverse process. Notably our RDDM enables a generic UNet trained with only an L1 loss and a batch size of 1 to compete with state-of-the-art image restoration methods. We provide code and pre-trained models to encourage further exploration application and development of our innovative framework (https://github.com/nachifur/RDDM).