  Generative models have gained popularity for their potential applications in
imaging science, such as image reconstruction, posterior sampling and data
sharing. Flow-based generative models are particularly attractive due to their
ability to tractably provide exact density estimates along with fast,
inexpensive and diverse samples. Training such models, however, requires a
large, high quality dataset of objects. In applications such as computed
imaging, it is often difficult to acquire such data due to requirements such as
long acquisition time or high radiation dose, while acquiring noisy or
partially observed measurements of these objects is more feasible. In this
work, we propose AmbientFlow, a framework for learning flow-based generative
models directly from noisy and incomplete data. Using variational Bayesian
methods, a novel framework for establishing flow-based generative models from
noisy, incomplete data is proposed. Extensive numerical studies demonstrate the
effectiveness of AmbientFlow in learning the object distribution. The utility
of AmbientFlow in a downstream inference task of image reconstruction is
demonstrated.
