Threshold-Guided Composition of GFlowNets for Multi-Objective Generation

Generating candidates that satisfy multiple property requirements is a central challenge in multi-objective generation. Optimizing an aggregate reward can improve some properties while leaving others below their required levels. We introduce $\mu$GFN, which composes independently trained GFlowNets through threshold-guided sampling. Each objective model provides a flow ratio, $\mu$, that estimates the expected terminal reward under its own policy. The sampler uses these estimates to penalize objective-wise threshold shortfalls, with no penalty once an estimate meets its threshold. This focuses guidance on predicted deficits while allowing the same models to serve different objective subsets and thresholds without retraining. Hypergrid diagnostics illustrate how objective-specific thresholds redirect sampling. Molecular experiments on three tasks with two to four objectives show competitive performance on the two-objective task and higher mean yields of distinct feasible molecules than preference-conditioned baselines on the three-objective task. On the four-objective task, achieves the highest mean objective-space coverage and top-candidate quality in the main comparison, although jointly feasible molecules remain rare. Ablations show that guidance improves mean unique success over unguided flow composition.