After one research it seems like only one variant of Paulownia is "invasive" - as in super aggressively spreading, but it does make me wonder if have acres and acres filled with them will result in some mutant offspring developing the super aggressive spread that the species is clearly capable of. Very much like what happened with that invasive pear [1]

[1] I dug up the article https://www.washingtonpost.com/lifestyle/magazine/how-we-tur...