The fast quenching of CaF2 crystals preheated up to 1000 degrees C allows to stabilize the high-temperature disordering of anion sublattice typical for the superionic state of the crystal. Such procedure results in the formation of structured ultraviolet to vacuum ultraviolet (UV-VUV) absorption with a lengthy long-wavelength tail stretching into the visible spectral range. Such absorption in the quenched crystals cannot be related to any local center and testifies to the presence of nano-sized complexes of displaced anions, the electron structure of which is drastically changed as compared with a regular lattice. Possibly, these clusters are frozen dynamic clusters that were discovered earlier in the superionic state with quasi-elastic diffuse neutron-scattering technique. Four luminescence bands in near UV and visible spectral range correspond to four low-energy absorption bands. Unlike absorption bands that are of zone nature, the luminescence occurs from the localized state that arises due to strong electron-vibration coupling in the clusters. Absorption and luminescence states are divided by a potential barrier that is responsible for the spacing between corresponding excitation and emission bands as well as the temperature quenching of luminescence. The luminescence study reveals the features of the electronic structure of clusters within preheated/quenched CaF2 crystals. The quenching method allows to study the high-temperature superionic state of crystals with fluorite structure using a wide set of experimental techniques.