What is the intuition behind the following entanglement distillation protocol for continuous variable systems?

The protocol is:
We start with a supply
of identically prepared bipartite non-Gaussian states. The overall protocol then amounts to an iteration of the following
basic steps.

1. The states will be mixed pairwise locally at 50:50
   beam splitters.
2. On one of the outputs of each beam splitter, a photon
   detector distinguishes between the absence and presence of
   photons. It should be noted that we do not require photon
   counters that can discriminate between different photon
   numbers.
3. In case of absence of photons at both detectors for a
   particular pair, one keeps the remaining modes as an input
   for the next iteration, otherwise the state is discarded.
   This is one iteration of the protocol which we will continue
   until we finally end up with a small number of states
   that closely resemble Gaussian states.
   

This protocol is presented in the paper: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.67.062320

Specifically, what I am trying to understand is: why does vacuum detection at both outputs lead to distillation? What is the motivation for this step?