In this Forum piece, we address several common misunderstandings of the generative L2A framework that are current in the wider L2A literature. Many of these misunderstandings stem from proposals that, although tested and eventually discarded, are still cited as though they were still accepted and in active use. We hope that by addressing four of the most persistent myths, we can persuade the wider L2A field to let them go and move on. By highlighting what generative researchers have in common with the proponents of other frameworks, we want to pave the way for increased collaboration between frameworks.