snypher: I have the same issue. GeForce GTX 680M. Not that new, but should meet the minimum spec I believe. I installed Nvidia's 5/18 driver that was intended for W3. Silent fail...
The game works ok for me with Geforce GTX 670M (on ASUS G75VW laptop running Windows 7/64bit). Also using the latest drivers that NVidia just released specifically for The Witcher 3.
If I recall right, 680M might be already different (newer) architecture (Kepler?) than 670M, but I'd presume it to be just as compatible with the game. So it could be something else?
Forgot to mention that I am running the non-Galaxy version (installed with the installer setup files).