The 1D diffusion equation for the dynamics of the coastline is revisited. It is found that the classical evaluation of the diffusivity coefficient over-predicts it by a factor ranging from 1.25 up to infinity since the diffusivity may become zero while the classical prediction is always positive. The over-prediction depends on wave steepness and wave incidence angle. It is larger for swell than for sea waves and it increases with increasing angle. For moderate angles it can easily be about a factor 10. Negative diffusivity occurs in case of large angles, consistent with the large angle morphodynamic instability.