A tokamak equilibrium reconstruction can benefit much from internal measurements of the current distribution. If lacking robust internal measurements, the reconstruction will be ill posed in the plasma core, not allowing for a sensible estimation of the current distribution. Such deficiencies can be compensated for by modeling the current distribution evolution by employing the current diffusion equation between successive equilibria. A scheme for the coupling of the predictive current diffusion equation with the equilibrium reconstruction from an inverse Grad-Shafranov equilibrium solver minimizing a least-squares criterion on measured and modeled data is proposed. The scheme is intended for routine equilibrium analysis shortly after the discharge where all diagnostic data are available. Results from the implementation at ASDEX Upgrade are shown, applied to a reversed-shear plasma with counter-current electron cyclotron current drive and to the start-up phase of the plasma. Results are compared to TRANSP calculations.