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

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 $-2\ln F\ge c_{\text{geom}}(ν_{\min})I_{\mathrm{dec}}^{\mathrm{wc}}$.

Source: arXiv:2603.06488v1 - http://arxiv.org/abs/2603.06488v1 PDF: https://arxiv.org/pdf/2603.06488v1 Original Link: http://arxiv.org/abs/2603.06488v1