从噪声观测中学习干净图像生成过程的扩散方法
Learning Clean Generative Processes from Noisy Measurements
没有干净数据也能训练扩散模型，CIFAR-10、显微镜、SAR 上都验证了，做图像恢复的可以看看这套一致性思路。
这篇 arXiv 论文研究只使用带噪声观测来训练生成模型的问题。作者先用 Noise2Noise 回归学习各噪声水平的后验预测，但仅能覆盖训练噪声水平以上的范围。为生成干净图像，他们引入一致性约束：预测应等于继续采样后的期望，并在 Poisson、binomial、Gamma 和 negative-binomial 测量下验证了该条件。实验覆盖 CIFAR-10、光子计数显微镜和合成孔径雷达，结果表明一致性约束修复了低噪声水平的预测。
Learning Clean Generative Processes from Noisy Measurements
We study how to learn a generative model of clean images using only noisy observations. Diffusion processes and their generalizations to non-Gaussian noise require posterior predictions at every noise level. We first show that it is possible to learn these predictions from independent noisy views using Noise2Noise regression, but only at or above the noise level of the training data. To learn the predictions below that level, needed to generate clean images, we impose consistency: a prediction should equal its expectation after continuing the sampling process. We derive conditions under which consistency uniquely determines the continuation to the clean image distribution and verify them for Poisson, binomial, Gamma, and negative-binomial measurements. Experiments on CIFAR-10, photon-counting microscopy, and synthetic aperture radar show that the required posterior predictions can be learned from noisy views alone and that the consistency relation repairs the continuation beyond the noise level of the data, which severely deteriorates without consistency.