Older discussions here talk about it.

For text... It was Llama at first, but then, because money, it was downgraded to DeepSeek. After that, because money, it was downgraded to Gemini/Gemma, which is the actual state. And within Gemini/Gemma, also probably because money, it also suffer some downgrades some times.

As for image, it was Stable Diffusion at first. But because money, it was downgraded to Flux, and that's the actual state. And within Flux, also probably because money, it also suffer some downgrades some times.

As for being open source or not...

Perchance is a platform that allow users to create their own generators, and it offers such AIs through "plugins" and alike. You can view and edit the code of practically any generator on perchance, but the AI itself is on server's side. They do use Open Source AIs, but if you want to mess with them, will will probably need to get them from other sources, since you obviously can't mess with Perchance's servers.

At least, that was what I got from the time I've been here.