They do seed around. People who grow it have it everywhere around here.

I haven't grown it myself, but it is invasive enough that it is mentioned in the "My Stupidest Gardening Mistake", "Chinese Lanterns *WARNING*", and "Plants I Wish I had Never Planted" threads. I would stay away.

Worst thing I ever put in the ground. Spread all into the lawn with long white roots that took days to dig out and even then they just kept coming. Even mowing the lawn wouldn't stop the spread!

Hmmmmm.Maybe I'll keep them in pots, and just bury that in the ground. But I'm getting the feeling that I should just throwout any seeds I have left. Same with the seedlings.

Give them as a gift to someone you don't much like. Ha!

Someone gave me one last year; I almost ripped her head off! But, I decided to keep it potted up on the deck...

Well, I'm glad you posted this question! I have some Chinese Lantern seeds sprouting right now. I'll be sure to keep them in a container.
Also, the seed packet seems to say that they won't flower this year. MsB