  We study the perturbative response of a complex quantum system on time
changes of an external parameter $X$. The driven dynamics is treated in
adiabatic basis of the system's Hamiltonian $\hat{H}[X]$. Within a random
matrix approach we obtained non--Markovian Fokker--Planck equation for the
occupancy of given adiabatic state. We observed normal diffusion regime of the
driven quantum dynamics at quite small values of the memory time defined by the
time scales of the $X$--correlations and energy--distribution of the coupling
matrix elements $(\partial \hat{H}/\partial X)_{nm}$. Here the normal energy
diffusion was found to drop out with the width of the matrix elements'
energy--distribution and the diffusion may be significantly suppressed with the
decrease of the correlations between the matrix elements. In the opposite limit
of relatively large memory times we obtained ballistic regime of the dynamics.
