SUD$^2$: Supervision by Denoising Diffusion Models for Image Reconstruction

Many imaging inverse problems---such as image-dependent in-painting and dehazing---are challenging because their forward models are unknown or depend on unknown latent parameters. While one can solve such problems by training a neural network with vast quantities of paired training data, such paired training data is often unavailable. In this paper, we propose a generalized framework for training image reconstruction networks when paired training data is scarce. In particular, we demonstrate the ability of image denoising algorithms and, by extension, denoising diffusion models to supervise network training in the absence of paired training data. (The unabridged version of this manuscript is available at https://arxiv.org/abs/2303.09642}{https://arxiv.org/abs/2303.09642).