I assumed Rain meant the named versions of the thug sort. Most of those are nowhere near as rampagingly invasive as the standard blue or white wild violet.
Do you realise just HOW invasive they are Trixiebelle? They are slowly, but surely killing everything in part of my rock garden by choking the other plants out and even the lawn is not sacrosanct. The seeds are explosively projectile and germinate in their thousands with a deep tap root. Weedkiller has little effect on them and handweeding is difficult without killing the plant you are trying to protect from them. They are our third most loathesome pest after bindweed and ground elder.