Yes, indeed it is jasminum nudiflorum.....I'm still pulling out sprouts of that...lol...
We inherited a huge old mound of that in a house that we bought years ago. Yes, it does root wherever it touches...and in my zone that means it goes wild. Somehow some of it moved down here to the back property with us and yep, it's still coming up. I might add that it was so large that in taking it all out, we found a very old grove mower that had been swallowed up by the plant....lol..