CoPHo: Classifier-guided Conditional Topology Generation with Persistent Homology

TL;DR

CoPHo introduces a novel classifier-guided diffusion method leveraging persistent homology to generate synthetic graphs with targeted topological features, improving control and performance over existing approaches.

Contribution

It presents a new discrete reverse diffusion approach guided by a pre-trained classifier and persistent homology, enabling real-time, condition-specific graph generation without retraining.

Findings

Outperforms existing methods in matching target metrics

Demonstrates transferability on molecular datasets

Effectively guides topology-aware graph generation

Abstract

The structure of topology underpins much of the research on performance and robustness, yet available topology data are typically scarce, necessitating the generation of synthetic graphs with desired properties for testing or release. Prior diffusion-based approaches either embed conditions into the diffusion model, requiring retraining for each attribute and hindering real-time applicability, or use classifier-based guidance post-training, which does not account for topology scale and practical constraints. In this paper, we show from a discrete perspective that gradients from a pre-trained graph-level classifier can be incorporated into the discrete reverse diffusion posterior to steer generation toward specified structural properties. Based on this insight, we propose Classifier-guided Conditional Topology Generation with Persistent Homology (CoPHo), which builds a persistent homology filtration over intermediate graphs and interprets features as guidance signals that steer generation toward the desired properties at each denoising step. Experiments on four generic/network datasets demonstrate that CoPHo outperforms existing methods at matching target metrics, and we further validate its transferability on the QM9 molecular dataset.