It is shown that some variational methods of quantum mechanics can be re-formulated for application to the problem of the diffusion of marked particles in a fluid in random motion. As an example, a variational derivation of the Wiener-Hermite approximation procedure is given. The simplest such approxi- mation is examined and it is made plausible that it gives the exact form for both the one- and two-particle distribution functions in a certain limiting situation.