An improved approximation to the time-dependent Schrodinger equation is developed by correcting the time-dependent self-consistent field ansatz with a Jastrow prefactor defined via a set of variationally determined time-dependent parameters and a linearly independent set of prespecified spatial functions. The method is applicable in any number of dimensions, conserves norm and energy, is without parametric singularities, possesses an internal estimate of the accuracy, and has computational costs that scale algebraically with the number of degrees of freedom. The new formalism is applied to a two-dimensional double well potential to demonstrate the improved accuracy of the method. An extension of the method to electronically nonadiabatic problems is also presented.