(from a conversation w/ KZ)
tldr: The huge amount of randomness that is involved in a generative model's generation process could be argued to greatly overshadow the human input, making most direct output of AI models non-copyrightable. Repeated prompt iteration using a fixed seed value could likely be used to support a copyright claim.
Existing copyright law (I speak only of US/Canada, which I know of somewhat) only applies to creative works by human beings. The result of a math formula is not copyrightable. Data from nature is not copyrightable. A photo taken by a monkey is not copyrightable. Photography of nature is copyrightable (it is argued that the photographer has enough knobs to choose when taking a photo that they are making significant creative choices). Creative post-processing of non-copyrightable content does create copyrightable work. Curating has some copyright protection (ex. selecting 10 public domain images out of millions to showcase together, ie. anthologies).
Suno is an AI model that generates music. For copyright, we are concerned with the human input involved. Let's look at the potential inputs to the Suno system:  - data used to train the model  - the algorithm of the model  - the prompt  - random numbers used during the model ("temperature")
It is TBD whether using copyrighted works as input to a model is (a) copyright infringement, and (b) whether it means all resultant works are derivative works (and thus the original owners have some copyright claim - a given work can be encumbered by multiple simultaneous claimants).Â
The choice of what data goes in vs what doesn't is "curation", but has weak standing for being creative work (...in general, but one can imagine someone arguing that they painstakingly fine-tuned a model on certain inputs for creative purpose.)
Specific code is copyrightable, but algorithms aren't ("it's just math") and AI architectures are also probably not copyrightable. (The abstract rules to Catan are not copyrightable, but a specific set of words that were used in the rulebook to describe the rules ARE copyrightable.). Creating an AI model does involve a lot of work, but, only the code artefact itself is copyrightable. If the codebase of Suno were leaked, the company could sue anyone distributing it. If the model was leaked, they may be able to claim copyright (but I could see this going either way). In terms of the outputs of these models, the models themselves are like kaleidoscope. The device itself might be copyrightable (and/or patentable), but the output is separate question.
That leaves us with the prompt. That is a legitimate creative input to the model. BUT, copyright doesn't apply to trite content (ex. if I tweet: "I went to the store today.", I can't claim that anyone that says the same thing in the future is infringing upon my copyright). For a prompt to be copyrightable, it would have to be creative / unique.
The same prompt can be re-run and have billions of different incarnations (due to randomness being a big input to generative models). In practice, the output of a model cannot be "reverse engineered" back to the input prompt (because of the randomness involved), making for a tenuous connection between prompt and output work. The output of the model is likely not considered a derivative work of the prompt.
So far in this argument, the output of a generative model seems to have little copyright-ability (it's feeding some seed data into a fancy algorithm that also makes use of tons of randomness).
I think photography will be used as the primary precedent for future generative AI copyright-ability (unless specific laws are written). The generative model is "math / the real world". The prompt is "knobs on your camera, choice of angle, etc.". But, the randomness involved in AI models is likely to challenge the "prompt is creative, therefore the work is creative" argument.
Post-processing a generative artwork (with, say, Photoshop) though, unambiguously results in a creative work. (Although, someone else could take the original output of the model and post-process it themselves in their own way, and not infringe your copyright). The extent of the copyright depends on the creative input. (If I take a picture of the Mona Lisa and draw a black stripe across her eyes - yes, my work is copyrightable, but, can I stop someone from distributing a picture of the Mona Lisa with a red stripe? Civil law involves proving damages, and thus, defers to the market to determine the creative value of a work. If the owner of the original was making a lot of money, or the creator of the alleged-infringement is making a lot of money, it bolsters the claim that there was creative effort involved.)
Iterative prompting gets interesting. It could still be argued that it's just a longer prompt. But, it can also be argued as a form of post-processing (using the generative model as a tool). I think it will come down to how deterministic a given model is (high determinism - more copyright claim to the prompter; low determinism - low claim). Using a fixed seed value and iterating on a prompt gives the human more agency, and a basis to argue that their creative input was meaningful.
With copyright law, the onus is usually on the claimant to prove their work was sufficiently creative/unique to be copyrightable (and that there were damages), and (probably, going forward), that they had significant agency in creating the work.