# Discrete flow matching

Discrete flow matching (DFM) decouples graph-generation training from sampling, but existing graph DFM samplers often rely on task-specific heuristics and need sampling budgets comparable to diffusion, so the speedup potential is only partly realized. H-GLow decomposes the continuous-time Markov chain generator into hazards and conditional jump distributions, then uses both to plan graph edits and adjust sampling time to graph activity. Adaptable to pretrained graph DFM models, it reports better generation quality with substantially fewer sampling steps on molecular and synthetic graph benchmarks; a companion graph DFM model predicts hazards and conditional jumps directly, with a training objective that decomposes exactly into hazard matching and hazard-weighted jump prediction.

Discrete flow matching (DFM) decouples graph-generation training from sampling, but existing graph DFM samplers often rely on task-specific heuristics and need sampling budgets comparable to diffusion, so the speedup potential is only partly realized. H-GLow decomposes the continuous-time Markov chain generator into hazards and conditional jump distributions, then uses both to plan graph edits and adjust sampling time to graph activity. Adaptable to pretrained graph DFM models, it reports better generation quality with substantially fewer sampling steps on molecular and synthetic graph benchmarks; a companion graph DFM model predicts hazards and conditional jumps directly, with a training objective that decomposes exactly into hazard matching and hazard-weighted jump prediction.