Mine only does it when cold, then it goes away on its own.
As to the OP, it may never go away completely. Its just a nature of the beast with a clutch type LSD.
2013 M3 Coupe-MR/BLK ZCP, ACM test pipes, BPM Stg2 dev. tune and Megan catback, more to come
Previous rides: 2011 M3 Coupe-MR/Blk
2007 Porsche 997C2S Speed Yellow/Blk sport seats
2004 BMW M3 Imola/Blk