Information-Calibrated Quantum Diffusion: Linking Forward Information Loss to Reverse Recoverability

Quantum diffusion models generate distributions over quantum states by learning to reverse a prescribed sequence of noisy quantum channels. Existing methods typically organize the forward process by a scalar noise strength, such as the depolarizing strength, rather than by the information actually lost from the state ensemble. As a result, this noise parameter does not directly indicate how difficult the corresponding reverse step should be. We introduce the classical–quantum information decrement ${\Delta }_t=I(X:Q_{t-1})-I(X:Q_t)$ for depolarizing channels to directly connect forward scheduling with reverse recovery. We prove that the same decrement sets an attainable common-channel recovery budget and, at fixed dimension and ensemble size, vanishes exactly when the optimal common-channel recovery error vanishes; equalizing these decrements minimizes the largest one-step information loss. We further show that local recovery alone leaves the generated distribution underdetermined, while distribution matching supplies the missing distribution-level constraint. Together, these results recast quantum diffusion as a sequence of information-controlled inverse problems, where the forward schedule determines how reverse difficulty is allocated rather than merely how noise is applied. Rather than prescribing a noise schedule and learning its inverse afterward, information calibration makes the recovery burden induced by the forward process explicit: it allocates information loss across timesteps, assigns each step an attainable common-channel recovery reference, and motivates the joint design of forward scheduling, reverse recovery, and distribution-level generation.