We calculate how correlations in a Bose lattice gas grow during a finite-speed ramp from the Mott to the superfluid regime. We use an interacting doublon-holon model, applying a mean-field approach for implementing hard-core constraints between these degrees of freedom. Our solutions are valid in any dimension and agree with experimental results and with density matrix renormalization group calculations in one dimension. We find that the final energy density of the system drops quickly with increased ramp time for ramps shorter than one hopping time, Jτramp1. For longer ramps, the final energy density depends only weakly on ramp speed. We calculate the effects of inelastic light scattering during such ramps. © 2016 American Physical Society.