Negative sampling determines whether a knowledge graph embedding (KGE) model learns from informative counterexamples or wastes updates on implausible corruptions. Uniform negatives are diverse but easy, whereas hard-negative miners concentrate on few entities and collide more with held-out positives.

We introduce FlowNeg, a context-conditioned hierarchical generative flow network that amortizes reward-proportional sampling without normalizing a composite reward over the entity set: given a positive triple and corruption side, it selects a type, then an entity. Its terminal reward combines bounded model-based hardness with a training-only structural score for held-out-positive collision, over a relation-specific type-compatible support.

We derive the reward, specialize standard trajectory balance, and bound multiplicatively how residual imbalance perturbs terminal and mode probability. Across a descriptive five-seed grid of five architectures and five benchmarks, FlowNeg has higher mean MRR than EMU and than IF-NS in 24 of 25 cells ($+0.0172$ and $+0.0160$ on average).

A separate 15-seed FB15k-237/RotatE control fixing negative count, diagnostic budget, and compute gives FlowNeg $0.359\pm0.001$ MRR against $0.346\pm0.002$ for EMU, with near-uniform fixed-partition diversity, high gradient informativeness, and low collision. The evidence supports mode-covering negative generation without treating structural similarity as an open-world truth oracle.