  We study a class of discrete models in which a collection of particles
evolves in time following the gradient flow of an energy depending on the cell
areas of an associated Laguerre (i.e. a weighted Voronoi) tessellation. We
consider the high number of cell limit of such systems and, using a modulated
energy argument, we prove convergence towards smooth solutions of nonlinear
diffusion PDEs of porous medium type.
