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Stable GFlowNets with Probabilistic Guarantees

NeurIPS 2026 · Probabilistic and scientific modeling › Variational and generative sampling · approach: Flow matching and flow sampling

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Shows that small TV error does not bound GFlowNet training loss, derives loss-to-TV and probabilistic TV certificates from trajectory sampling, and proposes Stable GFlowNets using adaptive reference flow.

Problem

GFlowNet training is unstable (loss spikes, mode collapse), and the relation between non-zero training losses and global sampling fidelity (TV error) is unclear.

Approach

Shows small TV error can coexist with unbounded local losses, derives converse loss-to-TV bounds for TB, and uses an adaptive reference flow added to flow conservation constraints to cap loss magnitude, with backward-sampled trajectories enabling probabilistic TV certificates.

Key results

• On sEH, Stable discovers 14142.6 scaffolds versus 8680.2 for TB with backward sampling (a 63% improvement).
• On Hypergrid D=4 H=32, Stable reaches empirical L1 of 0.713, matching TB with backward sampling and beating TB (1.875) and DB (0.944).
• M_TV correlates with true TV at 0.915 to 0.999 on Regular Tree and 0.930 to 0.997 on other environments except L14-RNA1 (0.930) .

Surprising findings

• Small TV error does not imply bounded training loss: a near-correct distribution can still yield loss scaling as (log epsilon)^2.
• On L14-RNA1, TB with backward sampling attains a slightly higher test mode count than Stable (670.4 vs 649.6).

Limitations

• Guarantees rely on backward sampling, which may be difficult in continuous settings.
• Probabilistic certificate B_TV is conservative and can be vacuous on larger Hypergrid and L14-RNA1.

Experimental setup

Datasets: Regular Tree Hypergrid L14-RNA1 sEH

Benchmarks: Hypergrid L14-RNA1 sEH Regular Tree

Metrics: empirical total L1 error number of modes number of scaffolds true TV correlation with true TV RMSE

Baselines: TB DB FM SubTB WDB Adaptive Teacher TB + backward sampling

Builds on: trajectory balance detailed balance flow matching subtrajectory balance adaptive teacher

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