In the mission Institutionalized on the part Meet the Division Leaders, I've talked to everyone it asked me to, but the quest marker is still hovering over Madison Li. I've tried all of the dialogue options and none of them progress the quest further and she only tells me she is leaving to go to the BoS. As far as I can tell, there is no way out of the Institute without finishing this quest or killing Li and all of my save files are during this quest.