  We present a theoretical and experimental study of light transport in
disordered media with strongly heterogeneous distribution of scatterers formed
via non-scattering regions. Step correlations induced by quenched disorder are
found to prevent diffusivity from diverging with increasing heterogeneity
scale, contrary to expectations from annealed models. Spectral diffusivity is
measured for a porous ceramic where nanopores act as scatterers and macropores
render their distribution heterogeneous. Results agree well with Monte Carlo
simulations and a proposed analytical model.
