Anecdotical (10+ years running experience). I've found that jogging at slow speeds (~6 MPH) has a similar effect creatively on me as walking does (2-4 MPH). Running at medium speeds (~8 MPH), I still notice an increase in creativity as long as I have enough energy in me, but it's a bit reduced than jogging. Running at high speeds (10+ MPH), things are so intense that my mind can only focus on breathing, running, and mind tricks to keep going, so creative thinking goes right out the door.
It would be interesting to see a scientific study done on it.
I wonder how this plays out in terms of long-term benefits. There's an established association between exercise and increased BDNF, but I don't think there's been any investigation as to if that effect is modulated by exercise intensity or longer than average duration.
I'd like to get a (passive) treadmill desk at some point for these reasons. I don't think I've ever found myself to be particularly creative on runs. I think I treat it too seriously, and when I'm not too serious, then I'm trying to be meditative with it or listening to nature. Interesting to hear other people's experiences.
I often have coding breakthroughs while on a run. Other reply is right though, I have these during my easy runs. I do not have coding breakthroughs during intervals or insane fast runs.
It would be interesting to see a scientific study done on it.