in which generating something with AI can be reasonably called "stealing"
Basically never. But since stealing sounds worse than plagiarism, people arguing against it, are using the worse sounding offense. Also, the stealing argument is usually used for the training data and not the output. Some models were trained with data that was not quite meant for public access. Plus the whole debate about giving consent for machines to learn from your work. All these are not stealing as such. That word has lost a lot of meaning over the years. If I steal something from you, you no longer have it.
There is no "training"
I am not sure how you mean that. Your hypderdimensional math is using matrix multiplication or something like that, is it not? How are the values in those matrixes filled? To calculate probabilities, you need data to derive the chances. And you need a mapping from natural language to whatever the system uses internally. Guess that's tokens.
But maybe you were very specific for this movie transformation thing. Maybe it does not even count as "ai" in the sense it is so often used these days. And that is "generative ai" and means using a large language model or something related to it. Whatever is under the hood there, those things are trained to have a "model" which would be the map to navigate your hyperspace.
There is no "output", only the input transformed.
i * m = o
There is an m. You need a model to transform your input into an output. And you are right in the way that if you keep record of your random seed and your exact parameters and the model, you will reproduce the exact same output. So in a way, it's just like "there is no 21", only a transformed 7.