  We discuss a connection (and a proper place in this framework) of the
unforced and deterministically forced Burgers equation for local velocity
fields of certain flows, with probabilistic solutions of the so-called
Schr\"{o}dinger interpolation problem. The latter allows to reconstruct the
microscopic dynamics of the system from the available probability density data,
or the input-output statistics in the phenomenological situations. An issue of
deducing the most likely dynamics (and matter transport) scenario from the
given initial and terminal probability density data, appropriate e.g. for
studying chaos in terms of densities, is here exemplified in conjunction with
Born's statistical interpretation postulate in quantum theory, that yields
stochastic processes which are compatible with the Schr\"{o}dinger picture free
quantum evolution.
