Graph Guided Diffusion: Unified Guidance for Conditional Graph Generation

TL;DR

This paper introduces GGDiff, a unified guidance framework for conditional graph generation using diffusion models, capable of handling both differentiable and non-differentiable reward signals through a stochastic control approach.

Contribution

It proposes a novel, versatile guidance method for diffusion-based graph generation that unifies multiple strategies and enables zero-shot conditioning with diverse reward functions.

Findings

Effective guidance under various reward types

Superior reward alignment and diversity in generated graphs

Applicable to tasks like motif constraints, fairness, and link prediction

Abstract

Diffusion models have emerged as powerful generative models for graph generation, yet their use for conditional graph generation remains a fundamental challenge. In particular, guiding diffusion models on graphs under arbitrary reward signals is difficult: gradient-based methods, while powerful, are often unsuitable due to the discrete and combinatorial nature of graphs, and non-differentiable rewards further complicate gradient-based guidance. We propose Graph Guided Diffusion (GGDiff), a novel guidance framework that interprets conditional diffusion on graphs as a stochastic control problem to address this challenge. GGDiff unifies multiple guidance strategies, including gradient-based guidance (for differentiable rewards), control-based guidance (using control signals from forward reward evaluations), and zero-order approximations (bridging gradient-based and gradient-free optimization). This comprehensive, plug-and-play framework enables zero-shot guidance of pre-trained diffusion models under both differentiable and non-differentiable reward functions, adapting well-established guidance techniques to graph generation--a direction largely unexplored. Our formulation balances computational efficiency, reward alignment, and sample quality, enabling practical conditional generation across diverse reward types. We demonstrate the efficacy of GGDiff in various tasks, including constraints on graph motifs, fairness, and link prediction, achieving superior alignment with target rewards while maintaining diversity and fidelity.