We present a semi-empirical model for the evolving far-infrared to ultraviolet diffuse background produced by stars in galaxies . The model is designed to reproduce the results of deep galaxy surveys , and therefore may be considered as a cosmology-independent lower limit to the extragalactic background light . Using this model and recent HEGRA data , we infer the intrinsic spectrum at multi-TeV gamma-ray energies for Mkn 501 and find that it is consistent with a power law of spectral index 2.49 \pm 0.04 . In turn , this finding renders it rather unlikely that the present-day infrared background has an intensity as high as claimed by Finkbeiner et al . [ ? ] . Future 10 GeV to TeV observations could be used to either constrain the ultraviolet-to-infrared background model at high redshifts or cosmological parameters .