We provide a framework for solving inverse problems with diffusion models learned from linearly corrupted data. Our method, Ambient Diffusion Posterior Sampling (A-DPS), leverages a generative model pre-trained on one type of corruption (e.g. image inpainting) to perform posterior sampling conditioned on measurements from a potentially different forward process (e.g. image blurring). We test the efficacy of our approach on standard natural image datasets (CelebA, FFHQ, and AFHQ) and we show that A-DPS can sometimes outperform models trained on clean data for several image restoration tasks in both speed and performance. We further extend the Ambient Diffusion framework to train MRI models with access only to Fourier subsampled multi-coil MRI measurements at various acceleration factors (R=2, 4, 6, 8). We again observe that models trained on highly subsampled data are better priors for solving inverse problems in the high acceleration regime than models trained on fully sampled data. We open-source our code and the trained Ambient Diffusion MRI models: https://github.com/utcsilab/ambient-diffusion-mri .

我们提供了一个用于解决扩散模型的反问题的框架，该框架可以从线性损坏的数据中学习。我们的方法是环境扩散后验采样（A-DPS），利用在一种类型的损坏上进行预训练的生成模型，在来自可能不同的前向过程的测量条件下进行后验采样。我们在标准的自然图像数据集上测试了我们的方法（CelebA、FFHQ和AFHQ），并且我们表明A-DPS在速度和性能上有时可以超过在干净数据上训练的模型进行几项图像修复任务。我们进一步扩展了环境扩散框架，用访问仅限于傅里叶子采样的多线圈MRI测量，加速因子为2、4、6、8来训练MRI模型。我们再次观察到，在高加速度区间内，与在完全采样数据上训练的模型相比，训练在高度子采样数据上的模型更适用于解决反问题。我们开源了我们的代码和训练的环境扩散MRI模型。

环境扩散后验采样：使用在损坏数据上训练的扩散模型解决逆问题