In cyclic discrete environments, GFlowNet flows are expected visit counts, and training a non-acyclic GFlowNet with the smallest expected trajectory length is equivalent to minimizing total flow.
A theory of non-acyclic generative flow networks
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Revisiting Non-Acyclic GFlowNets in Discrete Environments
In cyclic discrete environments, GFlowNet flows are expected visit counts, and training a non-acyclic GFlowNet with the smallest expected trajectory length is equivalent to minimizing total flow.