We present the first diffusion-based framework that can learn an unknown distribution using only highly-corrupted samples. This problem arises in scientific applications where access to uncorrupted samples is impossible or expensive to acquire. Another benefit of our approach is the ability to train generative models that are less likely to memorize individual training samples since they never observe clean training data. Our main idea is to introduce additional measurement distortion during the diffusion process and require the model to predict the original corrupted image from the further corrupted image. We prove that our method leads to models that learn the conditional expectation of the full uncorrupted image given this additional measurement corruption. This holds for any corruption process that satisfies some technical conditions (and in particular includes inpainting and compressed sensing). We train models on standard benchmarks (CelebA, CIFAR-10 and AFHQ) and show that we can learn the distribution even when all the training samples have $90\%$ of their pixels missing. We also show that we can finetune foundation models on small corrupted datasets (e.g. MRI scans with block corruptions) and learn the clean distribution without memorizing the training set.

介绍了一种基于扩散的框架，可以使用高度损坏的样本学习未知分布，通过在扩散过程中引入附加的测量损坏，并要求模型从进一步损坏的图像中预测原始损坏的图像，来学习完整未损坏图像的条件期望。

环境扩散：从损坏的数据中学习干净的分布