AmbientFlow: Invertible generative models from incomplete, noisy imaging measurements

Generative models, including normalizing flows, are gaining popularity in imaging science for tasks such as image reconstruction, posterior sampling, and data sharing. However, training them requires a high-quality dataset of objects, which can be challenging to obtain in fields such as tomographic imaging. This work proposes AmbientFlow, a framework for training flow-based generative models directly from noisy and incomplete data using variational Bayesian methods. The effectiveness of AmbientFlow in learning invertible generative models of objects from noisy, incomplete stylized imaging measurements is demonstrated via numerical studies.