doesn’t it follow that AI-generated CSAM can only be generated if the AI has been trained on CSAM?

Not quite, since the whole thing with image generators is that they're able to combine different concepts to create new images. That's why DALL-E 2 was able to create a images of an astronaut riding a horse on the moon, even though it never saw such images, and probably never even saw astronauts and horses in the same image. So in theory these models can combine the concept of porn and children even if they never actually saw any CSAM during training, though I'm not gonna thoroughly test this possibility myself.

Still, as the article says, since Stable Diffusion is publicly available someone can train it on CSAM images on their own computer specifically to make the model better at generating them. Based on my limited understanding of the litigations that Stability AI is currently dealing with (1, 2), whether they can be sued for how users employ their models will depend on how exactly these cases play out, and if the plaintiffs do win, whether their arguments can be applied outside of copyright law to include harmful content generated with SD.

My question is: why aren’t OpenAI, Google, Microsoft, Anthropic… sued for possession of CSAM? It’s clearly in their training datasets.

Well they don't own the LAION dataset, which is what their image generators are trained on. And to sue either LAION or the companies that use their datasets you'd probably have to clear a very high bar of proving that they have CSAM images downloaded, know that they are there and have not removed them. It's similar to how social media companies can't be held liable for users posting CSAM to their website if they can show that they're actually trying to remove these images. Some things will slip through the cracks, but if you show that you're actually trying to deal with the problem you won't get sued.

LAION actually doesn't even provide the images themselves, only linking to images on the internet, and they do a lot of screening to remove potentially illegal content. As they mention in this article there was a report showing that 3,226 suspected CSAM images were linked in the dataset, of which 1,008 were confirmed by the Canadian Centre for Child Protection to be known instances of CSAM, and others were potential matching images based on further analyses by the authors of the report. As they point out there are valid arguments to be made that this 3.2K number can either be an overestimation or an underestimation of the true number of CSAM images in the dataset.

The question then is if any image generators were trained on these CSAM images before they were taken down from the internet, or if there is unidentified CSAM in the datasets that these models are being trained on. The truth is that we'll likely never know for sure unless the aforementioned trials reveal some email where someone at Stability AI admitted that they didn't filter potentially unsafe images, knew about CSAM in the data and refused to remove it, though for obvious reasons that's unlikely to happen. Still, since the LAION dataset has billions of images, even if they are as thorough as possible in filtering CSAM chances are that at least something slipped through the cracks, so I wouldn't bet my money on them actually being able to infallibly remove 100% of CSAM. Whether some of these AI models were trained on these images then depends on how they filtered potentially harmful content, or if they filtered adult content in general.