Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high Reynolds numbers. A numerical method is here introduced for simulating the dynamics of diffusive heavy inertial particles in turbulent flows. The approach is based on the position/velocity phase–space particle distribution. The discretization of velocities is inspired from lattice Boltzmann methods and is chosen to match discrete displacements between two time steps. For each spatial position, the time evolution of particles momentum is approximated by a finite-volume approach. The proposed method is tested for particles experiencing a Stokes viscous drag with a prescribed fluid velocity field in one dimension using a random flow, and in two dimensions with the solution to the forced incompressible Navier–Stokes equations. Results show good agreements between Lagrangian and Eulerian dynamics for both spatial clustering and the dispersion in particle velocities. In particular, the proposed method, in contrast to hydrodynamical Eulerian descriptions of the dispersed phase, is able to reproduce fine particle kinetic phenomena, such as caustic formation or trajectory crossings. This indicates the suitability of this approach at large Stokes numbers for situations where details of collision processes are important.