Exploring Multiple High-Scoring Subspaces in Generative Flow Networks

Generative Flow Networks (GFlowNets) construct combinatorial objects through sequences of elementary actions, but exploration in large spaces can spend much of a finite sampling budget on low-reward regions. We propose CBFlowNet, an adaptive subspace exploration framework that periodically selects subsets of action types to guide trajectory collection. Its controller learns a set-level reward predictor from the mean terminal rewards collected under selected subsets. Policy-conditioned arm statistics, obtained from unrestricted evaluation, serve as auxiliary features rather than sufficient descriptions of subspace value. A Deep Sets scorer combines these features with action identities to model interactions, while bandit-inspired exploration encourages alternative selections as the GFlowNet evolves. Our analysis establishes trajectory-support and zero-loss target-consistency properties and decomposes the errors affecting current-policy set selection. Experiments on molecular, RNA, and bit-sequence design demonstrate improvements in high-reward candidate discovery. Implementations are available at https://anonymous.4open.science/r/ICLR-41377.