  We prove a factorization formula for the point-to-point partition function
associated with a model of directed polymers on the space-time lattice
$\mathbb{Z}^{d+1}$, subject to an i.i.d. random potential and in the regime of
weak disorder. In particular, we show that the error term in the factorization
formula is uniformly small for starting and end points $x, y$ in the
sub-ballistic regime $\| x - y \| \leq t^{\sigma}$, where $\sigma < 1$ can be
arbitrarily close to $1$. This extends a result of Sinai. We also derive
asymptotics for spatial and temporal correlations of the field of limiting
partition functions.
