We propose a method for efficient storage and recall of arbitrary nonstationary light fields, such as, for instance, single photon time-bin qubits or intense fields, in optically dense atomic ensembles. Our approach to quantum memory is based on controlled, reversible, inhomogeneous broadening and relies on a hidden time-reversal symmetry of the optical Bloch equations describing the propagation of the light field. We briefly discuss experimental realizations of our proposal.