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Diffusion models have demonstrated impressive results in both data generationand downstream tasks such as inverse problems, text-based editing,classification, and more. However, training such models usually requires largeamounts of clean signals which are often difficult or impossible to obtain. Inthis work, we propose a novel training technique for generative diffusionmodels based only on corrupted data. We introduce a loss function based on theGeneralized Stein's Unbiased Risk Estimator (GSURE), and prove that under someconditions, it is equivalent to the training objective used in fully superviseddiffusion models. We demonstrate our technique on face images as well asMagnetic Resonance Imaging (MRI), where the use of undersampled datasignificantly alleviates data collection costs. Our approach achievesgenerative performance comparable to its fully supervised counterpart withouttraining on any clean signals. In addition, we deploy the resulting diffusionmodel in various downstream tasks beyond the degradation present in thetraining set, showcasing promising results.

GSURE-Based Diffusion Model Training with Corrupted Data