  In this article we combine a recently proposed method for factorisation-aware
matrix element surrogates with an unbiased unweighting algorithm. We show that
employing a sophisticated neural network emulation of QCD multijet matrix
elements based on dipole factorisation can lead to a drastic acceleration of
unweighted event generation. We train neural networks for a selection of
partonic channels contributing at the tree-level to $Z+4,5$ jets and
$t\bar{t}+3,4$ jets production at the LHC which necessitates a generalisation
of the dipole emulation model to include initial state partons as well as
massive final state quarks. We also present first steps towards the emulation
of colour-sampled amplitudes. We incorporate these emulations as fast and
accurate surrogates in a two-stage rejection sampling algorithm within the
Sherpa Monte Carlo that yields unbiased unweighted events suitable for
phenomenological analyses and post-processing in experimental workflows, e.g.
as input to a time-consuming detector simulation. For the computational cost of
unweighted events we achieve a reduction by factors between $16$ and $350$ for
the considered channels.
