Rooted Absorbed Prefix Trajectory Balance with Submodular Replay for GFlowNet Training

Abstract: Generative Flow Networks (GFlowNets) enable fine-tuning LLMs to approximate reward-proportional posteriors, but they remain prone to mode collapse, manifesting as prefix collapse and length bias. We attribute this to two factors: (i) weak credit assignment to early prefixes, and (ii) biased replay that induces a shifted, non-representative training flow distribution. We propose Rooted absorbed prefix Trajectory Balance RapTB, an objective that anchors subtrajectory supervision at the root and propagates terminal rewards to intermediate prefixes via absorbed suffix-based backups, providing dense prefix-level learning signals. To mitigate replay-induced distribution shift, we further introduce SubM, a submodular replay refresh strategy that promotes both high reward and diversity. Empirically, on tasks such as molecule generation with LLM using SMILES strings, RapTB combined with SubM consistently improves optimization performance and molecular diversity while preserving high validity.