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Generative models can only rely on efficient local denoising up to the exact moment they commit to global semantics, after which both phenomena collapse into a single sharp phase transition as system size grows.
Diffusion models' reliance on global information isn't just a quirk – it's fundamentally linked to the moment they commit to a specific semantic outcome.
Quantum generative models get a boost: mixed states prepared by shallow channel circuits can be efficiently learned from measurement data, even without knowing the original preparation circuit.
