I have got a diesel E53 too that seems to have this same issue. What i find is sometimes if u time the acceleration incorrectly it does not go as well. Me sales rep said that u need to ride the turbo. Let me try and explain what i think is happening with my E53.

Sometimes jump on the pedal, the computer will sometimes over-fuel the engine (especially with remaps), and then u hear the engine work very hard and there is not much of real acceleration. In that scenario if u do not have a particle filter like my older X5, u will see a lot of smoke in the back due to incomplete combustion. U guys on the E70 will not see any smoke coz of DPF but when u do that u are kinda choking ur engine and over fueling because the turbo has not spool up enough to provide enough air for the additional fuel ur pumping in. Next time u should try pushing in th petal gradually with the acceleration hence 'riding the turbo' or rolling the throttle as refer to this other post.

BMW 3-Series (E90 E92) Forum - View Single Post - 4 months with 330D - Likes & Dislikes

Maybe the new twin turbo is different but i hope this helps.