  We establish circumstances under which the dispersion of passive contaminants
in a forced, deterministic or random, flow can be consistently interpreted as a
Markovian diffusion process. In case of conservative forcing the repulsive case
only, $\vec{F}=\vec{\nabla }V$ with $V(\vec{x},t)$ bounded from below, is
unquestionably admitted by the compatibility conditions. A class of diffusion
processes is exemplified, such that the attractive forcing is allowed as well,
due to an appropriate compensation coming from the "pressure" term. The
compressible Euler flows form their subclass, when regarded as stochastic
processes. We establish circumstances under which the dispersion of passive
contaminants in a forced, deterministic or random, flow can be consistently
interpreted as a Markovian diffusion process. In case of conservative forcing
the repulsive case only, $\vec{F}=\vec{\nabla }V$ with $V(\vec{x},t)$ bounded
from below, is unquestionably admitted by the compatibility conditions. A class
of diffusion processes is exemplified, such that the attractive forcing is
allowed as well, due to an appropriate compensation coming from the "pressure"
term. The compressible Euler flows form their subclass, when regarded as
stochastic processes.
