there are some local genai music models, although I don’t know how good they are yet as I haven’t tried any myself (stable audio is one, but I’m sure there are others)
also minor linguistic nitpick but LLM stands for ‘language model’ (you could maybe get away with it for pixart and sd3 as they use t5 for prompt encoding, which is an llm, i’m sure some audio models with lyrics use them too), the term you’re looking for is probably ‘generative’