  The diffusion model is used to calculate the time-averaged flow of particles
in stochastic media and the propagation of waves averaged over ensembles of
disordered static configurations. For classical waves exciting static
disordered samples, such as a layer of paint or a tissue sample, the flux
transmitted through the sample may be dramatically enhanced or suppressed
relative to predictions of diffusion theory when the sample is excited by a
waveform corresponding to a transmission eigenchannel. Even so, it is widely
acknowledged that the velocity of waves is irretrievably randomized in
scattering media. Here we demonstrate in microwave measurements and numerical
simulations that the statistics of velocity of different transmission
eigenchannels remain distinct on all length scales and are identical on the
incident and output surfaces. The interplay between eigenchannel velocities and
transmission eigenvalues determines the energy density within the medium, the
diffusion coefficient, and the dynamics of propagation. the diffusion
coefficient and all scatter9ng parameters, including the scattering mean free
path, oscillate with width of the sample as the number and shape of the
propagating channels in the medium change.
