Quantum Diffusion Models: Score Reversal Is Not Free in Gaussian Dynamics

arXiv:2603.06488v1 Announce Type: cross
Abstract: Diffusion-based generative modeling suggests reversing a noising semigroup by adding a score drift. For continuous-variable Gaussian Markov dynamics, complete positivity couples drift and diffusion at the generator level. For a quantum-limited attenuator with thermal parameter $\nu$ and squeezing $r$, the fixed-diffusion Wigner-score (Bayes) reverse drift violates CP iff $\cosh(2r)>\nu$. Any Gaussian CP repair must inject extra diffusion, implying $-2\ln F\ge c_{\text{geom}}(\nu_{\min})I_{\mathrm{dec}}^{\mathrm{wc}}$.



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