I think when you switch to a cleaner diet it will start to clean your body out of all the garbage that has built up in it over time. And it can cause detox symptoms in the process, and breaking out can be one of those symptoms. Of course that's just one possible cause.
This girl talks about how she cleared up her skin:
https://www.youtube.com/watch?v=dX-fuHBs33s&t=599s