Diffusion-Based Solver for CNF Placement on the Cloud-Continuum

TL;DR

This work addresses the NP-hard problem of placing Cloud-Native Network Functions (CNFs) and routing Service Function Chains (SFCs) across the Cloud-Continuum under strict resource, bandwidth, and latency constraints. It introduces a diffusion-based solver that casts placement as a generative graph-to-assignment task, leveraging a Graph Neural Network (GNN) denoiser within a Denoising Diffusion Probabilistic Model (DDPM) to learn feasible CNF-to-cloud mappings while directly incorporating constraint losses. The approach encodes the network and CNFs as a heterogeneous graph, trains with forward diffusion to predict noise, and performs constrained reverse diffusion at inference to generate multiple candidate deployments, selecting the best feasible one. Empirical results on diverse topologies show the method achieves high feasibility (around 94%), substantially faster inference than a classical MINLP solver, and competitive suboptimal cost, including in scenarios where exact solvers fail due to time limits. This diffusion-based, topology-aware framework offers a scalable, flexible solution for practical orchestration of distributed CNFs in next-generation networks.

Abstract

The placement of Cloud-Native Network Functions (CNFs) across the Cloud-Continuum represents a core challenge in the orchestration of current 5G and future 6G networks. The process involves the placement of interdependent computing tasks, structured as Service Function Chains, over distributed cloud infrastructures. This is achieved while satisfying strict resource, bandwidth and latency constraints. It is acknowledged that classical approaches, including mixed-integer nonlinear programming, heuristics and reinforcement learning are limited in terms of scalability, constraint handling and generalisation capacity. In the present study, a novel theoretical framework is proposed, which is based on Denoising Diffusion Probabilistic Models (DDPM) for CNF placement. The present approach proposes a reconceptualisation of placement as a generative graph to assignment task, where the placement problem is encoded as a heterogeneous graph, and a Graph Neural Network denoiser is trained to iteratively refine noisy CNF-to-cloud assignment matrices. The model incorporates constraint-specific losses directly into the loss function, thereby allowing it to learn feasible solution spaces. The integration of the DDPM formulation with structured combinatorial constraints is achieved through a rigorous and systematic approach. Extensive evaluations across diverse topologies have been conducted, which have confirmed that the model consistently produces feasible solutions with orders of magnitude faster inference than MINLP solvers. The results obtained demonstrate the potential of diffusion-based generative modelling for constrained network embedding problems, making an impact towards the practical, scalable orchestration of distributed Cloud-Native Network Functions.

Figures (7)

• Figure 1: Network model of the problem
• Figure 2: Example of CNFs and SFCs
• Figure 3: CNF placement problem on the Cloud-Continuum
• Figure 4: Diffusion-based CNF placement framework architecture
• Figure 5: Comparison between MINLP and diffusion solver