  We apply the diabatic framework, a QCD-based formalism for the unified study
of quarkoniumlike systems in terms of heavy quark-antiquark and open-flavor
meson-meson components, to the description of coupled-channel meson-meson
scattering. For this purpose, we first introduce a numerical scheme to find the
solutions of the diabatic Schr\"odinger equation for energies in the continuum,
then we derive a general formula for calculating the meson-meson scattering
amplitudes from these solutions. We thus obtain a completely nonperturbative
procedure for the calculation of open-flavor meson-meson scattering cross
sections from the diabatic potential, which is directly connected to lattice
QCD calculations. A comprehensive analysis of various elastic cross sections
for open-charm and open-bottom meson-meson pairs is performed in a wide range
of the center-of-mass energies. The relevant structures are identified, showing
a spectrum of quasi-conventional and unconventional quarkoniumlike states. In
addition to the customary Breit-Wigner peaks we obtain nontrivial structures
such as threshold cusps and minimums. Finally, our results are compared with
existing data and with results from our previous bound-state--based analysis,
finding full compatibility with both.
