I will admit to knowing the overall underlying technology better than the details of what specific implementations consist of. My understanding is, though, that "Stable Diffusion" is both a specific refinement (or set of refinements) of the same ML techniques that created DALL-E, Midjourney, and other ML art generators, and the trained model that the group working on it created to go with it.

So while it would be possible to create a "Public Diffusion" that took the Stable Diffusion refinements of the ML techniques and created a model built solely out of public-domain art, as it stands, "Stable Diffusion" includes by definition the model that is built from the copyrighted works in question.