The concept of the adjoint neutron density is extended to a time-dependent field. The importance of neutrons and precursors is defined as the contribution of each to some final arbitrarily selected detectable process. An axiom is given which expresses the consistency requirement for such a definition. From this axiom, the equations and boundary conditions for the importance in the diffusion approximation are derived. The nature of the solutions to these equations is considered with particular regard to the time-dependent behavior of the importance. Several normalizations or final boundary conditions are proposed which include as special cases the conventional interpretations of the adjoint function in a just critical reactor. In particular, for a noncritical reactor, the equivalence is introduced as the number of neutrons and precursors distributed in the persisting solution that would replace one neutron or precursor with equivalent asymptotic results.