There are ongoing concerns around copyright infringement in the use of some content in the generative AI training process.
In early 2024 Time sued Microsoft and OpenAI for copyright infringement, alleging that they used millions of Time's copyrighted work in their training data.
This follows from the authors guild threatening to sue leading AI companies with copyright lawsuits.
In contrast, Stephen King has noted that he doesn't mind if his work is used to train generative AI models.
This has parallels in art, but the response from artists seems to have been different.
And there are also questions about how owns the output of language models. In most cases, these are documented in the terms of service. For example, Athropics ToS in relation to Claude states that users "...retain ownership rights over any outputs you generate through your use of our services."