My 320i sounds like a diesel at idle and all the other ones I have listened to sound the same. Worried me at first but now convinced it is normal. Just doesn't sound like a BMW should. Believe it has to do with the valvetronics setup, quietens down with a few more revs and worse when the engine is warm.
M-Sport Pack | BMW Individual Paint - Moonstone | BMW 193 18" Wheels | BMW Individual Interior Trim - Anthracite Maple