Don't know if this helps...
My e46 did something very similar to this. It could be unmetered air getting into your motor and your ecu adding and pulling fuel to try and balance out your afr's. mind you an engine code should present itself. I would check any piping on your intake as well as soft plastic boots that could be cracked. As I said I doubt this is it on a newer car, but the symptoms sound earily similar.