Stable GFlowNets with TV Monitoring and Probabilistic Guarantees

Generative Flow Networks (GFlowNets) sample diverse structured objects in proportion to reward and have been applied to molecular discovery and biological-sequence design, where finding multiple high-quality candidates is more useful than returning a single optimum. Despite their theoretical promise, practical training is often unstable, exhibiting severe loss spikes and mode collapse. To address this, we first assess the sensitivity of GFlowNet objectives, demonstrating that a small Total Variation (TV) distance between the learned and target distributions does not preclude an unbounded training loss. Motivated by this mismatch, we establish converse guarantees by deriving loss-to-TV bounds that certify global fidelity from bounded trajectory balance losses. Lastly, we propose Stable GFlowNets, which leverages our theory to stabilize training via adaptive reference flow and improves the trade-off among mode coverage, robustness, and certifiability.