Traditional neural solvers for vehicle routing problems (VRPs) often suffer from limited solution diversity, which has driven interest toward Generative Flow Network (GFlowNet) based models. GFlowNet learns a probability distribution over solutions by constructing a flow in the solution space, yet its flow expansion in high‑reward regions is usually insufficient, making it hard to allocate probability to promising routes.
Diffusion models, by contrast, provide stronger structural guidance for exploration: they inject stochastic noise and then denoise, enabling systematic search over a broader space. The two paradigms are naturally complementary—GFlowNet can supply edge‑level signals for diffusion, while diffusion can steer global exploration.
Motivated by this synergy, we propose Diffusion‑Enhanced GFlowNet (DEG). DEG first leverages GFlowNet's inherent diversity to generate backward signals for each edge, perturbs these signals according to the stochastic noise schedule of a diffusion model, and finally denoises them within the GFlowNet framework. This process enriches flow expansion toward high‑reward regions, yielding higher‑quality routing solutions.
To improve scalability, DEG introduces a specialized decoder that dynamically adapts its architecture to the problem size, preserving computational efficiency across varied instance scales.
Extensive experiments on synthetic and real‑world datasets, including instances with up to 10,000 nodes, demonstrate that DEG consistently outperforms baseline methods, confirming its effectiveness on large‑scale VRPs.
Review: DEG combines the local diversity of GFlowNet with the global exploration capability of diffusion models, offering a practical route to high‑quality solutions in massive VRP settings. Future work may explore adaptive noise schedules and integration with reinforcement learning techniques.