  I show that a usual propagator cannot be defined for the pseudo-diffusion
equation of the Q-functions. Instead, a forward-backward propagator is defined,
which motivated a generalization of Cahill-Glauber interpolating operator. Our
generalized operator ${\bf Q}(p,q;\sigma_p^{-1},\sigma_q)$ depends on two
squeezing parameters $\sigma_p$ and $\sigma_q$, and is shown to obey a
generalized pseudo-diffusion equation or a diffusion equation, depending on the
curve $(\sigma_p(\mu),\sigma_q(\mu))$ along which one moves in the
$(\sigma_p,\sigma_q)$ plane. An algorithm is also given for squeezing Q
functions directly, using one-dimensional diffusion propagators.
