To be honest, I don't know how "fast"/"good-quality" these are (I don't have a machine I can test this on) but from a small and simple perspective the likes of chained AES or SHA instructions should provide a good sequence from a single instruction. The result could provide multiple random values per iteration and can then be normalised/rebased accordingly. Something along these lines..may need some tweaking.

Yes, thanks, I'm going to look into aesenc and others just for fun even if I don't end up using them (I guess they aren't so fast). Because I'm not really in the loop with all the new instructions so it's good exercise.