A Lagrangian method has been developed to solve heterogeneous diffusion. The time domain on which the method rests allows for the coupling with a Gauss-Newton inversion in which the sensitivity to parameters is derived analytically. This tool has proved very rapid and efficient, even for large computation grids as those extracted from autoradiographs of rock samples. It offers a more comprehensive view of transport by diffusion for many applications, one of them being for instance, the safety of underground repository sites.