Generative Models for Inverse Imaging Problems: From mathematical foundations to physics-driven applications

Physics-informed generative modeling for inverse problems in computational imaging is a fast-growing field encompassing a variety of methods and applications. Here, we review a few generative modeling techniques, such as variational autoencoders (VAEs) and generative adversarial networks (GANs), as well as more recent developments in score-based generative models. Through different imaging applications, we review how the generative modeling techniques are effectively combined with the physics of the imaging problem, e.g., the measurement forward model and physical properties of the target objects, to solve the inverse problems.