  We consider the stochastic continuity equation associated to an It\^{o}
diffusion with irregular drift and diffusion coefficients. We give regularity
conditions under which weak solutions are renormalized in the sense of
DiPerna/Lions, and prove well-posedness in $L^p$. As an application, we give a
new proof of renormalizability (hence uniqueness) of weak solutions to the
stochastic continuity equation when the diffusion matrix is constant and the
drift only belongs to $L^q_tL^p$, where $\frac{2}{q} + \frac{n}{p} <1$, without
resorting to the regularity of the stochastic flow or a duality method.
