I think this has more to do with probability, the sum of all random variables approaches a gaussian distribution. We can prove it using Central limit theorem. So what that really means is that the noise can map all sorts of information. Also when you add noise consistently, at one point you reach the normal distribution however, the noise pattern at hand is unique. Think of it as this way, 0,0 have a mean of 0 while -1,1 also have a mean of 0. The unique noise pattern actually contains useful information where as if you were to create a blank canvas, your generator would have no idea about what to generate from it for it is a many to one mapping. The additive noise process is a unique mapping