  Resonant inelastic x-ray scattering (RIXS) is a widely used spectroscopic
technique, providing access to the electronic structure and dynamics of atoms,
molecules, and solids. However, RIXS requires a narrow bandwidth x-ray probe to
achieve high spectral resolution. The challenges in delivering an energetic
monochromated beam from an x-ray free electron laser (XFEL) thus limit its use
in few-shot experiments, including for the study of high energy density
systems. Here we demonstrate that by correlating the measurements of the
self-amplified spontaneous emission (SASE) spectrum of an XFEL with the RIXS
signal, using a dynamic kernel deconvolution with a neural surrogate, we can
achieve electronic structure resolutions substantially higher than those
normally afforded by the bandwidth of the incoming x-ray beam. We further show
how this technique allows us to discriminate between the valence structures of
Fe and Fe$_2$O$_3$, and provides access to temperature measurements as well as
M-shell binding energies estimates in warm-dense Fe compounds.
