In order to objectively assess new medical imaging technologies via computer-simulations, it is important to account for all sources of variability that contribute to image data. One important source of variability that can significantly limit observer performance is associated with the variability in the ensemble of objects to-be-imaged. This source of variability can be described by stochastic object models (SOMs), which are generative models that can be employed to sample from a distribution of to-be-virtually-imaged objects. It is generally desirable to establish SOMs from experimental imaging measurements acquired by use of a well-characterized imaging system, but this task has remained challenging. Deep generative neural networks, such as generative adversarial networks (GANs) hold potential for such tasks. To establish SOMs from imaging measurements, an AmbientGAN has been proposed that augments a GAN with a measurement operator. However, the original AmbientGAN could not immediately benefit from modern training procedures and GAN architectures, which limited its ability to be applied to realistically sized medical image data. To circumvent this, in this work, a modified AmbientGAN training strategy is proposed that is suitable for modern progressive or multi-resolution training approaches such as employed in the Progressive Growing of GANs and Style-based GANs. AmbientGANs established by use of the proposed training procedure are systematically validated in a controlled way by use of computer-simulated measurement data corresponding to a stylized imaging system. Finally, emulated single-coil experimental magnetic resonance imaging data are employed to demonstrate the methods under less stylized conditions.