  GFlowNets is a novel flow-based method for learning a stochastic policy to
generate objects via a sequence of actions and with probability proportional to
a given positive reward. We contribute to relaxing hypotheses limiting the
application range of GFlowNets, in particular: acyclicity (or lack thereof). To
this end, we extend the theory of GFlowNets on measurable spaces which includes
continuous state spaces without cycle restrictions, and provide a
generalization of cycles in this generalized context. We show that losses used
so far push flows to get stuck into cycles and we define a family of losses
solving this issue. Experiments on graphs and continuous tasks validate those
principles.
