On Divergence Measures for Training GFlowNets

Generative Flow Networks (GFlowNets) are amortized samplers of unnormalized distributions over compositional objects with applications to causal discovery, NLP, and drug design. Recently, it was shown that GFlowNets can be framed as a hierarchical variational inference (HVI) method for discrete distributions. Despite this equivalence, attempts to train GFlowNets using traditional divergence measures as learning objectives were unsuccessful. Instead, current approaches for training these models rely on minimizing the log-squared difference between a proposal (forward policy) and a target (backward policy) distributions. In this work, we first formally extend the relationship between GFlowNets and HVI to distributions on arbitrary measurable topological spaces. Then, we empirically show that the ineffectiveness of divergence-based learning of GFlowNets is due to large gradient variance of the corresponding stochastic objectives. To address this issue, we devise a collection of provably variance-reducing control variates for gradient estimation based on the REINFORCE leave-one-out estimator. Our experimental results suggest that the resulting algorithms often accelerate training convergence when compared against previous approaches. All in all, our work contributes by narrowing the gap between GFlowNet training and HVI, paving the way for algorithmic advancements inspired by the divergence minimization viewpoint.