Solving inverse problems using normalizing flow prior: Application to optical spectra

We introduce a machine learning approach for solving ill-posed inverse problems, specifically addressing the Fredholm integral equation of the first kind. Harnessing the powerful capabilities of normalizing flows to approximate data distributions, combined with a robust probabilistic framework, our approach stands out by delivering robust solutions capable of handling high-level noises and out-of-distribution data and providing uncertainty estimation. A distinct feature lies in the unsupervised learning framework inherent in deep generative models, providing our approach with unparalleled flexibility across diverse experimental setups. This flexibility is exemplified through the successful application of our method to measured optical spectra.