  We report experimental and theoretical investigations on photon diffusion in
a second-order nonlinear disordered medium under conditions of strong
nonlinearity. Experimentally, photons at the fundamental wavelength
($\lambda=1064$ nm) are launched into the structure in the form of a
cylindrical pellet, and the second-harmonic ($\lambda=532$ nm) photons are
temporally analyzed in transmission. For comparison, separate experiments are
carried out with incident green light at $\lambda=532$ nm. We observe that the
second harmonic light peaks earlier compared to the incident green photons.
Next, the sideways spatial scattering of the fundamental as well as
second-harmonic photons is recorded. The spatial diffusion profiles of
second-harmonic photons are seen to peak deeper inside the medium in comparison
to both the fundamental and incident green photons. In order to give more
physical insights into the experimental results, a theoretical model is derived
from first principles. It is based on the coupling of transport equations.
Solved numerically using a Monte Carlo algorithm and experimentally estimated
transport parameters at both wavelengths, it gives excellent semi-quantitative
agreement with the experiments for both fundamental and second-harmonic light.
