  We solve an inverse problem for fluid particle pair-statistics: we show that
a time sequence of probability density functions (PDF's) of separations can be
exactly reproduced by solving the diffusion equation with a suitable
time-dependent diffusivity. The diffusivity tensor is given by a time-integral
of a conditional Lagrangian velocity structure-function, weighted by a ratio of
PDF's. Physical hypotheses for hydrodynamic turbulence (sweeping, short memory,
mean-field) yield simpler integral formulas, including one of Kraichnan and
Lundgren. We evaluate the latter using a spacetime database from a numerical
Navier-Stokes solution for driven turbulence. This diffusion theory reproduces
PDF's well at rms separations, but growth rate of mean-square dispersion is
overpredicted due to neglect of memory effects. More general applications of
our approach are sketched.
