After a base level drop, rivers are the first components of the landscape to respond by incising into topography. A base level drop results in a knickpoint in the downstream part of river longitudinal profiles. Whether knickpoints are preserved or erased during the upstream propagation of incision is still debated. Preservation and erasure of knickpoints are two end-member processes that work in natural systems at different timescales, different length scales, and different places. The huge (1500 m) and fast (tens of kiloyears) sea level drop in the Mediterranean during the Messinian resulted in the fast propagation of incision far inland. This is especially the case in the Rhone Valley (southern France) where the knickpoint is 300 km from the Mediterranean coast. Numerical modeling of this event has been performed using the ${rm C}\!\!\!\!\!\!\!=$ros model, which simulates both erosional and depositional processes in rivers. The best fit between numerical results and geological data is obtained for a nonlinear relation between incision and drainage area and for a small transport length of sediment. This small transport length, at least 2 orders of magnitude lower than the length of the Rhone, suggests that the longitudinal profile relaxed in a diffusive way, so that the initial knickpoint was not preserved. Finally, after a base level fall, the propagation of fluvial incision is very fast at geological timescales (hundreds of kiloyears). Despite this, the diffusive response implies that the time required for restoration of an equilibrium profile is very long.