  We developed an integer lattice gas method for the fluctuating diffusion
equation. Such a method is unconditionally stable and able to recover the
Poisson distribution for the microscopic densities. A key advance for integer
lattice gases introduced in this paper is a new sampling collision operator
that replaces particle collisions with sampling from an equilibrium
distribution. This can increase the efficiency of our integer lattice gas by
several orders of magnitude.

Fluid Dynamics;Soft Condensed Matter