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

Published 6 Mar 2026 in quant-ph, cs.LG, and math-ph | (2603.06488v1)

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 $ν$ and squeezing $r$, the fixed-diffusion Wigner-score (Bayes) reverse drift violates CP iff $\cosh(2r)>ν$. Any Gaussian CP repair must inject extra diffusion, implying $-2\ln F\ge c_{\text{geom}}(ν{\min})I{\mathrm{dec}}^{{\mathrm{wc}}$.}