Quantum Diffusion Models: Score Reversal Is Not Free in Gaussian Dynamics
This work identifies a fundamental constraint in reversing Gaussian dynamics for quantum generative models, impacting the design of quantum diffusion models.
This paper investigates the reversal of noising semigroups in continuous-variable Gaussian Markov dynamics for quantum diffusion models. It finds that for a quantum-limited attenuator, the fixed-diffusion Wigner-score reverse drift violates complete positivity (CP) if the squeezing parameter exceeds the thermal parameter, and any CP repair requires injecting extra diffusion.
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 $-2\ln F\ge c_{\text{geom}}(ν_{\min})I_{\mathrm{dec}}^{\mathrm{wc}}$.