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).

翻译：我们提出残差去噪扩散模型（RDDM），这是一种新颖的双扩散过程，将传统的单去噪扩散过程解耦为残差扩散和噪声扩散。该双扩散框架通过引入残差，将最初对图像修复缺乏可解释性的基于去噪的扩散模型扩展为既适用于图像生成又适用于图像修复的统一且可解释的模型。具体而言，我们的残差扩散代表从目标图像到退化输入图像的方向性扩散，并显式引导图像修复的反向生成过程，而噪声扩散则代表扩散过程中的随机扰动。残差优先考虑确定性，而噪声则强调多样性，使RDDM能够有效统一具有不同确定性或多样性需求的任务（如图像生成和修复）。我们通过系数变换证明，所提采样过程与DDPM和DDIM一致，并提出部分路径无关的生成过程以更好地理解反向过程。值得注意的是，我们的RDDM使得仅以L1损失和批量大小1训练的通用UNet能够与最先进的图像修复方法相竞争。我们提供代码和预训练模型以鼓励对该创新框架的进一步探索、应用和发展（https://github.com/nachifur/RDDM）。