  In order to understand how the chemical and isotopic compositions of dust
grains in a gaseous turbulent protoplanetary disk are altered during their
journey in the disk, it is important to determine their individual
trajectories. We study here the dust-diffusive transport using lagrangian
numerical simulations using the the popular "turbulent diffusion" formalism.
However it is naturally expressed in an Eulerian form, which does not allow the
trajectories of individual particles to be studied. We present a simple
stochastic and physically justified procedure for modeling turbulent diffusion
in a Lagrangian form that overcomes these difficulties. We show that a net
diffusive flux F of the dust appears and that it is proportional to the gas
density ({\rho}) gradient and the dust diffusion coefficient Dd:
(F=Dd/{\rho}\timesgrad({\rho})). It induces an inward transport of dust in the
disk's midplane, while favoring outward transport in the disk's upper layers.
We present tests and applications comparing dust diffusion in the midplane and
upper layers as well as sample trajectories of particles with different sizes.
We also discuss potential applications for cosmochemistry and SPH codes.
