For the relationship, you have to read most of the way through:
What I find most interesting is that the problem of generating noise in the time domain has been recast into shaping and denoising a spectrum in the frequency domain. It starts as white noise, and gets turned into a pre-designed picture. You do so by swapping pixels in the other domain. The state for this process is kept in the phase channel, which is not directly relevant to the problem, but drifts into alignment over time.
Hence I called it Stable Fiddusion. If you swap the two domains, you're turning noise into a picture by swapping frequency bands without changing their values. It would result in a complex-valued picture, whose magnitude is the target, and whose phase encodes the progress of the convergence process.
This is approximately what you get when you add a hidden layer to a diffusion model.
It seems obvious to me that blue noise generation wouldn't require anything novel from recent advances in ML generation. Further the name is silly.
Also, your "clarifying" (about generating 3d blue noise for rendering) description is just a rewording of the title. Is your comment also trying to mislead people then?
It's about generating 3D blue noise for rendering, it's very interesting on its own but the title is misleading.