H-GLow: Accelerating Graph Generation via Hazard-Guided Discrete Flow Matching
Abstract Overview
H-Glow is a hazard-guided framework for accelerating graph generation in discrete flow matching by decomposing continuous-time Markov chain generators into componentwise hazards and conditional jump distributions. The sampler uses these quantities to prioritize node and edge edits, adapt the sampling clock to predicted graph activity, and stop early when activity becomes low, rather than relying on fixed discretizations or task-specific heuristics. The method can be applied to pretrained graph DFM models as a drop-in sampler, and the paper also introduces a graph DFM model that directly predicts hazards and conditional jumps under a decomposed generator-matching objective. Experiments on molecular and synthetic graph benchmarks indicate that this structure improves sample quality while reducing the number of sampling steps and function evaluations.
Novelty
The paper’s main novelty is to use the hazard-jump decomposition of CTMC graph generators as a unified basis for both sampling and model design. This yields a hazard-guided sampler that can accelerate pretrained graph DFM models without retraining, and a new graph DFM parameterization whose training objective decomposes exactly into hazard matching and hazard-weighted jump prediction.
Results
On QM9, H-Glow with a 50-step budget achieves FCD 0.10 with 22.4±2.3 mean NFE and 99.1% validity, outperforming the listed 50-step and 500-step baselines on FCD. On MOSES and GuacaMol, the 100-step model reports the best FCD in Table 2 (0.96 on MOSES and 77.7 on GuacaMol), surpassing 500-step baselines, while synthetic graph experiments reach 95.0%/93.5% V.U.N. at 20 steps and 100%/100% at 200 steps on Planar/Tree. The sampler also accelerates pretrained DeFoG models, matching or exceeding 500-step Euler sampling with 100 steps and approaching the 500-step guided configuration at 200 steps.
Key Points
- H-Glow selects graph edits and allocates sampling time using predicted hazards and conditional jump distributions, with an early-stopping rule based on low graph activity.
- The paper introduces a graph DFM model that directly predicts node and edge hazards together with conditional jump distributions, and derives an exact decomposition of the generator-matching loss.
- Empirical results across QM9, MOSES, GuacaMol, and synthetic graph benchmarks show improved or competitive quality with substantially fewer sampling steps and function evaluations, including as a drop-in accelerator for pretrained models.