The 1/f (or any) noise spectrum represents only the *mean* amplitude in frequency domain. In reality, the amplitude at each frequency itself has an associated

The 1/f (or any) noise spectrum represents only the *mean* amplitude in frequency domain. In reality, the amplitude at each frequency itself has an associated distribution. Since frequency domain is complex the amplitude represents a radius in 2D space and if the underlying random walk is Gaussian then the amplitude is distributed according to Rayleigh. For generating artistic images, the artist may ignore this fact and generate only the random phases. Image to image, humans probably won't know the shortcut. But in fact, each image will have exactly the same amplitude spectra and that's not physical for real stochastic processes. Depending on the usage of the images, the shortcut could be fatal. Eg, if we train a neural net on these generated images we should not expect that NN to perform well on the real data which our generated images were meant to represent.