Classical macroscopic models of metal–hydride (MH) hydrogen storage rely on empirical Arrhenius laws that neglect quantum phenomena such as tunneling, zero-point motion, and hydrogen–lattice interactions. As a result, their predictive and control performance degrade across wide temperature ranges, particularly in cryogenic regimes where quantum transport remains active. This paper presents a unified \emph{quantum-informed diffusion and control framework} that bridges microscopic hydrogen–lattice physics with macroscopic predictive control. A temperature-dependent quantum correction operator is incorporated into the classical diffusion law, yielding an analytically tractable yet physically enriched model. Parameters are identified through weighted robust regression with bootstrap-based uncertainty quantification and integrated into a model predictive control (MPC) scheme that adapts to temperature-dependent dynamics. Simulation results show that tunneling-enhanced diffusion improves low-temperature response and reduces steady-state error and control effort by up to 50\% compared with classical Arrhenius-based control. While the present study focuses on numerical validation, the proposed architecture establishes a transferable foundation for \emph{digital-twin development}—linking microscopic quantum transport and system-level predictive control for next-generation hydrogen storage technologies.