sounds to me like the top end, if it were crank related all the sounds I've heard had a "deeper" thud to it. Oil level is good? Oil was changed recently? Those round discs atop the valves below the cams are free and move about? ........................... I'm thinking get a good engine flush, (Amsoil sells one called:
Engine and Transmission Flush
Product Code: FLSHCN-EA
And sell it for about $10 retail. I'm no employee of Amsoil but I've had good results using their and another manufacturer by the name of BG products)
Long story even longer, try it, replace with a good quality synthetic, (Like Mobil 1 0W40 or Amsoil 5W40, again, not affiliated with either company), and hopefully that dieseling sound will go away. If it does not you can always attack the VANOS issue after. I'm of the same mind set of a M5 Guru poster who has as a conclusion to any of his posts: Keep it simple, if not simpler. Try the easy stuff first and then dig into it slowly if it doesn't get any better
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This post makes the most sense. For me, a car that has four cams and 32 valves, trying to distinguish between the two, IMO, would be a challenge, at best. In my experience, valve train noise is usually associated with the valves, worn seals, seats, damaged valve stems, etc. A cam, when it wears down enough, can really affect performance/power, but doesn't normally make noise. Unless the cam bearings are shot and those are making noise, but it doesn't sound like that to me.
It's already been said, but replacing a worn VANOS, seals, etc., would be the cheapest and is the most likely culprit from the audio you attached.
I can only truly tell the difference in sounds between the valve-train, piston slap and the bottom-end; the crank and it's parts. You probably can too. If it gets louder and more of a deep knock at the bottom of the motor, then you know it's not in the valve-train, but in the crank, rod and main bearings.
I may have said this to you already. Take it to a BMW Dealership and get the ear of a Service Advisor, if you want to try and diagnose purely by sound. Worst thing that could happen, they may say there's no way we can tell without a complete inspection.
At least price a pair of complete heads out, so you know if it's worth it to you to fix it, in case it's not the VANOS. You could probably replace complete heads yourself. I dread these types of serious issues.
Best of luck.