Diffusion models have demonstrated impressive results in both data generation and downstream tasks such as inverse problems, text-based editing, classification, and more. However, training such models usually requires large amounts of clean signals which are often difficult or impossible to obtain. In this work, we propose a novel training technique for generative diffusion models based only on corrupted data. We introduce a loss function based on the Generalized Stein's Unbiased Risk Estimator (GSURE), and prove that under some conditions, it is equivalent to the training objective used in fully supervised diffusion models. We demonstrate our technique on face images as well as Magnetic Resonance Imaging (MRI), where the use of undersampled data significantly alleviates data collection costs. Our approach achieves generative performance comparable to its fully supervised counterpart without training on any clean signals. In addition, we deploy the resulting diffusion model in various downstream tasks beyond the degradation present in the training set, showcasing promising results.

翻译：扩散模型在数据生成以及逆问题、文本编辑、分类等下游任务中均展现出卓越性能。然而，训练此类模型通常需要大量干净信号，这在实践中往往难以甚至无法获得。本研究提出一种仅基于含噪数据的生成式扩散模型训练新方法。我们引入基于广义斯坦无偏风险估计（GSURE）的损失函数，并证明在特定条件下该函数与全监督扩散模型训练目标等价。我们在人脸图像与磁共振成像（MRI）数据上验证了该技术——采用欠采样数据可显著降低数据采集成本。本方法无需干净信号训练即可达到与全监督方法相当的生成性能。此外，我们将所得扩散模型应用于训练集退化类型之外的多项下游任务，展现出令人鼓舞的效果。