Wave-enhanced interfacial transport by small-amplitude waves at low flow rates has been previously explained as distortion of the diffusion boundary layer by the normal disturbance velocity. We improve these earlier small wave theories by including a time-oscillatory Taylor dispersion mechanism due to coupling between tangential diffusion and normal convection. The combined mechanism produces a small(< 10%) enhancement for falling film absorption processes which scales as (1 + 9/16h(2)alpha(2)[1 + R-2/200])(1/2) where ct is the wavenumber, fi is the interfacial disturbance height and R is the Reynolds number. For higher laminar flows at the most practical flow rates (10 < R < 300), the enhanced interfacial transport is shown here to be due to sustained diffusion boundary layers under the crests of large stationary solitary waves with large-amplitude recirculations. The corresponding enhancement is now large (several factors) and scales as root c ln(Pe)/lambda where Pe = h(N)c'/D, h(N) is the Nusselt film thickness, c is the wave speed c' scaled by the Nusselt velocity U-N, D is the diffusivity, and lambda. is the equilibrium wavelength between successive solitary waves normalized with respect to h(N) Data for both types of waves are available from our earlier statistical theory for wave dynamics. These new scalings allow us to correlate literature data on interfacial transport and explain the existence of an optimal flow rate at R similar to 40 (for water) for maximum Aux, beyond which the enhancement decays as R-1/2.