Minimizing moment-matching losses on classical computers doesn't guarantee quantum generative models will generalize well—the field needs to rethink training objectives or architectures for the "train classical, deploy quantum" paradigm to work reliably.
This paper challenges a popular strategy for quantum machine learning where models are trained classically using moment-matching losses (like MMD²) and then deployed on quantum hardware. The authors show that models trained this way generalize poorly to new data, despite achieving low training loss.