# Does a pilot-wave theory need to be stochastic in a discrete space-time?

I have found an article about Bohmian mechanics on a lattice with discrete space and time, the link of which is given below:

https://arxiv.org/abs/1606.02883

Here the motion of quantum particles is described by a $$|\Psi|^2$$ - distributed Markov chain. It is discussed that "the discreteness is by itself responsible for the randomness of the motion on the basic level", and

The transformation of a discrete distribution $$|\Psi(t_0)|^2$$, e.g. at the slits, into the discrete distribution $$|\Psi(t)|^2$$, e.g. far from the slits, cannot be made in a non-stochastic manner, as it would require transitions from every (initial or intermediate) state into a single subsequent state.

What do the quoted sentences exactly mean? Pilot-wave theory is deterministic in a continuous space-time. Can someone explain to me why a pilot-wave theory needs to be non-deterministic in a discrete space-time? Is this stochasticity necessary for it to be able to reproduce the predictions of Quantum mechanics?