Abstract This study on the diffusion equation was performed to gain new insight into the adequacy of the analytically solvable linear diffusion equation which is used as an approximation to Saint-Venant's equations for flood routing in open channels. The derivation of the diffusion equation was approached assuming a variable trapezoidal channel cross-section, variable channel slope, constant lateral inflow, a generalized velocity—depth relationship and the diffusion approximation to the full Saint-Venant's momentum equation. A new modified diffusion equation was obtained which theoretically accounts for channel and wave variations resulting in new non-linear expressions for the wave celerity and diffusion coefficients. Numerical testing on a linearized version of the modified diffusion equation shows that the assumption of constant values for the parameters of the diffusion approximation yields inadequate flood routing results. Since the assumption of constant wave celerity and constant diffusion coefficient in the diffusion equation amounts to the linearization of the equation, the numerical results of this paper show that the linear form of the diffusion equation is inadequate for flood routing. Therefore it is necessary to consider the non-linear form of the diffusion approximation to Saint-Venant's equations as an approximate model for flood routing.