The mesh-free method of smoothed particle hydrodynamics (SPH) is interpreted atomistically to treat the local density of nodes as representing solute concentration, instead of interpolating a concentration field between function values at the nodes. We exploit the conceptual simplicity of tracking little packets (representing supermolecular aggregates) of solute, as in Brownian dynamics simulations, but replace the stochastic generation of diffusive spreading over statistically, independent realizations with a purely, deterministic summation for extracting the local diffusion velocity, using only, the instantaneous locations of nearby, nodes. Four test problems demonstrate the versatility and accuracy of the atomistic SPH,method (ASPH) for mass transfer. Finally, by comparing ASPH with a new Stokeslet-swarm technique for simulating drop flows (Nitsche and Schaflinger, 2001), a fundamental analogy between diffusion and interfacial tension is exposed.