We propose a quantum approach to nonequilibrium dynamics which combines the successful aspects of classical-statistical simulations on a lattice with the ability to take into account quantum corrections. It is based on the 2PI effective action for inhomogeneous fields and a volume average. This procedure does not involve any double counting which could appear in sampling prescriptions for inhomogeneous quantum evolutions. As an example, we study nonequilibrium dynamics of defect formation in 1+1 dimensional relativistic scalar field theory and compare to insufficient descriptions based on homogeneous quantum fields. The latter are analyzed in detail by coupling the field to an external source, such that the emerging influence of defects can be studied by lowering the source to zero.