The fact that the white smoke disperses quickly would suggest that its caused by water/antifreeze. Smoke caused by oil would linger in the air (eventually causing a smoke screen).
Another good indication is what the smoke smells like. Antifreeze will have a sweet smell – well – like antifreeze(!), which is 100% different to a burning oil smell.
If it is a smell of antifreeze, the most likely place for it to enter an engine is via the head/head gasket (although it could also be via a crack in the block). You say that the head gasket was replaced. Was the head checked for cracks/warping when it was off?

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'02 X5 3.0d, Auto, Topaz Blue