For good visibility lidar return signals may be analyzed using the classical lidar equation which describes the single scattering contribution only. Here the range, from which a contribution to the return signal comes, is proportional to the time difference between emission and reception. For dense cloud sensing with a ground-based lidar or for a spaceborne lidar system, the return signal contains also essential contributions from higher orders of multiple scattering. In this case the physical range or the distance along the emitted beam, from which the contribution comes, is no longer proportional to the time elapsed since emission. The elapsed time is only proportional to the photon path-length. Thus making the analysis of the return signal much more difficult. Which part of the return signal comes from what range and, hence, from which type of scatterers? The diffusion process of multiple scattering of light in the atmosphere is non-isotropic and extremely complicated. The key to the solution of the problem is the simulation of multiple scattering lidar returns where the separate orders of scattering are tracked. Such information about the diffusion of the laser beam is needed to give a better understanding of the extend of contribution from the type of scatterers to the return signal. In this paper, we offer such a non-trivial analysis of the diffusion of the laser beam in the cloud modeled by two kinds of atmospheric particles, i.e., aerosols and ice crystals, by using a multi-dimensional contribution distribution for different orders of scattering. This is done by conditioning the probability of return e.g. by the time elapsed, the order of scattering, the distance from the axis of the direction of emission, and the distance of the projection of the point of contribution on this axis to the emitter. This gives a fairly complete information about the diffusion process as it is seen from the receiver.