  We present an ab initio computational approach for the calculation of
resonant Raman intensities, including both excitonic and non-adiabatic effects.
Our diagrammatic approach, which we apply to two prototype, semiconducting
layered materials, allows a detailed analysis of the impact of phonon-mediated
exciton-exciton scattering on the intensities. In the case of bulk hexagonal
boron nitride, this scattering leads to strong quantum interference between
different excitonic resonances, strongly redistributing oscillator strength
with respect to optical absorption spectra. In the case of MoS$_2$, we observe
that quantum interference effects are suppressed by the spin-orbit splitting of
the excitons.
