  The well-known diffusion theory describes propagation of light and
electromagnetic waves in complex media. While diffusion theory is known to fail
both for predominant forward scattering or strong absorption, its precise range
of validity has never been established. Therefore we present precise, universal
limits on the scattering properties, beyond which diffusion theory yields
unphysical negative energy density and negative incident flux. When applying
diffusion theory to samples outside validity ranges to {\it infer} scattering
properties from transmission and reflection, the resulting transport parameters
deviate by up to an order of magnitude compared to the true ones. These
discrepancies are relevant to atmospheric and climate sciences, biophysics and
health sciences, white LEDs and lighting, and Anderson localization of waves.
