There are both similarities and differences between instabilities of planar laminar flame fronts and ablation fronts in inertial-confinement fusion (ICF). The mathematical formulation of the problem in ICF is the same as for flames propagating upward; the differences stem from the different order of magnitude of the Froude number and thermal conductivity variations. When the thermal conductivity varies strongly, as in ICF, a wide range of characteristic diffusive lengths occurs across the wave structure. For disturbances with intermediate wavelengths, there is then a universal diffusive relaxation rate of thermal waves that is independent of the thermal conductivity. A kinematic relation for the ablation front is discussed here that includes this thermal relaxation. The resulting formulation facilitates comparison of the two types of fronts.