It is known that recursive training from generative models can lead to the so called `collapse' of the simulated probability distribution. This note shows that one in fact gets two different asymptotic behaviours depending on whether an external source, howsoever minor, is also contributing samples.
@article{arxiv.2506.09401,
title = {A theoretical basis for model collapse in recursive training},
author = {Vivek Shripad Borkar},
journal= {arXiv preprint arXiv:2506.09401},
year = {2025}
}