The identifiability of excited-state processes in the presence of transient effects is studied. The Smoluchowski and Collins-Kimball models of diffusion-mediated association are considered. The kinetic parameters of single-species quenching and related kinetic schemes (double-species quenching without excited-state interchange, and irreversible association with separated excited-species spectra) can be uniquely recovered from the same or a smaller number of decay traces than are necessary within classical kinetics where time-invariant rate constants are used. For single-species quenching in low dimensions, 1D and 2D, the system parameters can be uniquely recovered from a single decay trace at one nonzero quencher concentration. In three dimensions, decays traces measured at two concentrations are necessary and sufficient to recover the parameters. For double-species quenching without interchange of the excited states, decay traces at two wavelengths collected in the absence and presence of quencher guarantee local identifiability of the model in each dimension with or without transient effects. Irreversible association with separate excited-species spectra is identifiable in each dimension, given decay traces at two quencher concentrations and two wavelengths.