Capacity-Aware Sampling for Frozen Generative Flow Networks

GFlowNets are trained so that the terminal distribution is proportional to reward, yet scientific discovery deployments draw only a finite pool of samples from a frozen GFlowNet. We show that reward-proportional i.i.d. deployment is generally misaligned with finite-budget coverage and cannot adapt local flow to capacity as the sample pool grows. We first derive the finite-pool coverage target, which is generally not reward-proportional. To approximate this target, we propose Capacity-Aware Sampling (CaS), a local reweight-and-renormalize rule applied to the frozen policy. The penalty combines two deployment-time signals: a soft threshold on low-probability actions, and capacity-relative congestion of intermediate resources under the current sample history. CaS requires no retraining, no extra reward calls, and does not delete valid actions. Across five frozen GFlowNet benchmarks, a single default CaS setting improves finite-budget mode discovery over standard i.i.d. sampling on every task and achieves the best or near-best final-budget performance against tuned history-blind inference baselines. At $N=2000$, CaS increases discovered modes from $51.8$ to $252.8$ on QM9Str and from $4.4$ to $131.8$ on sEHStr.