Solving Inverse Problems with Ambient Diffusion

We provide the first framework to solve inverse problems with diffusion models learned from linearly corrupted data. Our method leverages a generative model trained on one type of corruption (e.g. highly inpainted images) to perform posterior sampling conditioned on measurements from a different forward process (e.g. blurred images). This fully unlocks the potential of ambient diffusion models that are essential in scientific applications where access to fully observed samples is impossible or undesirable. Our experimental evaluation shows that diffusion models trained on corrupted data can even outperform models trained on clean data for image restoration in both speed and performance.