DiffSG: A Generative Solver for Network Optimization with Diffusion Model

TL;DR

This work addresses the challenge of solving complex, non-differentiable network optimization problems by reframing them as distribution-learning tasks. It introduces DiffSG, a diffusion-model-based solver that learns a high-quality solution distribution p_theta(y|x) and samples high-probability solutions conditioned on network state x, enabling robust performance across MINLP, convex, and hierarchical non-convex problems. The approach leverages DDPM/DDIM with classifier-free guidance and demonstrates superior in-domain and out-of-domain generalization compared to GD, MTFNN, and PPO on computation offloading, multi-channel sum-rate, and UAV-enabled NOMA tasks. These findings indicate that generative diffusion models can effectively serve as direct optimization solvers in dynamic networking environments, offering strong generalization and practical efficiency. The work opens promising directions for scalable, distributed, and guided diffusion-based optimization in communications."

Abstract

Generative diffusion models, famous for their performance in image generation, are popular in various cross-domain applications. However, their use in the communication community has been mostly limited to auxiliary tasks like data modeling and feature extraction. These models hold greater promise for fundamental problems in network optimization compared to traditional machine learning methods. Discriminative deep learning often falls short due to its single-step input-output mapping and lack of global awareness of the solution space, especially given the complexity of network optimization's objective functions. In contrast, generative diffusion models can consider a broader range of solutions and exhibit stronger generalization by learning parameters that describe the distribution of the underlying solution space, with higher probabilities assigned to better solutions. We propose a new framework Diffusion Model-based Solution Generation (DiffSG), which leverages the intrinsic distribution learning capabilities of generative diffusion models to learn high-quality solution distributions based on given inputs. The optimal solution within this distribution is highly probable, allowing it to be effectively reached through repeated sampling. We validate the performance of DiffSG on several typical network optimization problems, including mixed-integer non-linear programming, convex optimization, and hierarchical non-convex optimization. Our results demonstrate that DiffSG outperforms existing baseline methods not only on in-domain inputs but also on out-of-domain inputs. In summary, we demonstrate the potential of generative diffusion models in tackling complex network optimization problems and outline a promising path for their broader application in the communication community. Our code is available at https://github.com/qiyu3816/DiffSG.

Figures (5)

• Figure 1: Advantages of generative output over discriminative output.
• Figure 2: The proposed DIFFSG framework.
• Figure 3: The training and generation process for the computation offloading problem (CO), including the current solution and the optimal solution within the solution space determined by a given $\mathbf{x}$.
• Figure 4: The training and generation process for maximizing the sum rate of multiple channels (MSR), including the current solution and the optimal solution within the solution space determined by a given $\mathbf{x}$.
• Figure 5: The training and generation process for maximizing the sum rate of multiple channels in the NOMA-UAV system (NU), including the current solution and the optimal solution within the solution space determined by a given $\mathbf{x}$. The two optimization variables, the UAV's 2D coordinates and the channel power allocation for the three users, are displayed using a 2D heatmap and a 3D heatmap, respectively. The 2D heatmap at step $t$ is determined by the channel power allocation of $\mathbf{y}_t$, while the 3D heatmap is determined by the UAV's coordinates of $\mathbf{y}_t$.