While preparing a lab on heat diffusion, I thought it would be interesting to compute the diffusion of topographic relief using the same forward Euler finite difference in 2D (explicit method with central difference in space and forward in time, see here).
I downloaded a dem of largest topographic reflief on the planet, the Himalayas and roughly converted the lat/long into meters before applying the finite difference method. As expected, diffusion acts on the small scale features first, and especially those with large gradients… So the board topography remains but the details are progressively vanishing. Although it is incorrect for a landscape simulation, it is valuable to show the characteristics of diffusion.
In the second figure you can see the difference between the start and end stages and a few zoom-ins showing how material is diffused from the small (sic!), steep peaks to fill in the valleys.