  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).
