  Normalizing flow-based sampling methods have been successful in tackling
computational challenges traditionally associated with simulating lattice
quantum field theories. Further works have incorporated gauge and translational
invariance of the action integral in the underlying neural networks, which have
led to efficient training and inference in those models. In this paper, we
incorporate locality of the action integral which leads to simplifications to
the input domain of conditional normalizing flows that sample constant time
sub-lattices in an autoregressive process, dubbed local-Autoregressive
Conditional Normalizing Flow (l-ACNF). We find that the autocorrelation times
of l-ACNF models outperform an equivalent normalizing flow model on the full
lattice by orders of magnitude when sampling $\phi^{4}$ theory on a 2
dimensional lattice.
