  While Markov chain Monte Carlo methods (MCMC) provide a general framework to
sample from a probability distribution defined up to normalization, they often
suffer from slow convergence to the target distribution when the latter is
highly multi-modal. Recently, Generative Flow Networks (GFlowNets) have been
proposed as an alternative framework to mitigate this issue when samples have a
clear compositional structure, by treating sampling as a sequential decision
making problem. Although they were initially introduced from the perspective of
flow networks, the recent advances of GFlowNets draw more and more inspiration
from the Markov chain literature, bypassing completely the need for flows. In
this paper, we formalize this connection and offer a new perspective for
GFlowNets using Markov chains, showing a unifying view for GFlowNets regardless
of the nature of the state space as recurrent Markov chains. Positioning
GFlowNets under the same theoretical framework as MCMC methods also allows us
to identify the similarities between both frameworks, and most importantly to
highlight their
