  We analyze circumstances under which the microscopic dynamics of particles
which are driven by a forced, gradient-type flow can be consistently
interpreted as a Markovian diffusion process. Special attention is paid to
discriminating between forces that are presumed to act selectively upon
diffusing particles, while leaving the random medium statistically at rest
(Smoluchowski diffusion processes), and those perturbing the random medium
itself and thus creating the nontrivial flows. We focus on the deterministic
"stirring" scenarios.
