AI Generated Images

I assume all online platforms, even payed ones have censorship.

No, as there are services that are specifically aimed at generating porn, and I'm sure that they won't censor. Well...hmm, okay, maybe they'll censor child porn, as there may be legal obligations there, depending upon the specifics of the content and the jurisdiction in which they're doing business. But they won't have filtering in the sense that Microsoft or whatever will.

That being said, in general, I agree that if censorship is a concern, and buying hardware isn't an issue, the best way to avoid it is to run things locally, else one is always going to have to be dealing with whatever restrictions generative AI services put in place, and that will depend on whatever the current laws that affect them in jurisdictions where they do business, and that may depend on political upset in areas somewhere else in the world.

Stable Diffusion's (current) default model does aim to censor specifically pornographic images by eliding images from the training corpus that could be used to generate porn. It's not that the software blocks it, per se, but that the default model just doesn't know much about pornography. However, people have promptly gone out and trained new, NSFW-capable models derived from Stable Diffusion's default model on porn and put those on civitai.com -- I've another comment discussing this in more detail elsewhere in the thread -- so that's really only one extra step.

https://civitai.com/tag/nsfw

I don't think that Stable Diffusion's default model tries to censor urine/bodily functions or anything like that, though I'll concede that I haven't gone experimenting to try to find out.