  We prove that the density of the law of any finite dimensional projection of
solutions of the Navier--Stokes equations with noise in dimension $3$ is
H\"older continuous in time with values in the natural space $L^1$. When
considered with values in Besov spaces, H\"older continuity still holds. The
H\"older exponents correspond, up to arbitrarily small corrections, to the
expected diffusive scaling.
