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Generative Flow Networks (GFlowNets) are recently proposed models forlearning stochastic policies that generate compositional objects by sequencesof actions with the probability proportional to a given reward function. Thecentral problem of GFlowNets is to improve their exploration andgeneralization. In this work, we propose a novel path regularization methodbased on optimal transport theory that places prior constraints on theunderlying structure of the GFlowNets. The prior is designed to help theGFlowNets better discover the latent structure of the target distribution orenhance its ability to explore the environment in the context of activelearning. The path regularization controls the flow in GFlowNets to generatemore diverse and novel candidates via maximizing the optimal transportdistances between two forward policies or to improve the generalization viaminimizing the optimal transport distances. In addition, we derive an efficientimplementation of the regularization by finding its closed form solutions inspecific cases and a meaningful upper bound that can be used as anapproximation to minimize the regularization term. We empirically demonstratethe advantage of our path regularization on a wide range of tasks, includingsynthetic hypergrid environment modeling, discrete probabilistic modeling, andbiological sequence design.

Improving Generative Flow Networks with Path Regularization