Heterogeneous Coupled Diffusion for Graph Generation with $α$-Stable Node Feature Noise

Chengyu Tang, Ercan Engin Kuruoglu
Proceedings of The 1st Symposium on Probabilistic Machine Learning, PMLR 327:314-345, 2026.

Abstract

Graph generation requires jointly modeling node semantics and graph structure. Existing coupled graph diffusion models mostly use light-tailed perturbations throughout the graph state, which may be too conservative for node features that encode rare semantic roles or long-tailed attribute patterns. We propose a heterogeneous coupled graph diffusion model that applies discrete-time symmetric $\alpha$-stable noise to node features and Gaussian DDPM noise to adjacency, while keeping reverse denoising joint over the full graph state. Using a Gaussian scale-mixture representation, we derive an exact augmented variational objective for the stable feature branch and a same-marginal coupled deterministic sampler. On a controlled benchmark, stable feature diffusion improves rare-role recall and joint generation quality, while Gaussian adjacency provides the more reliable structural bias. On molecular and generic graph benchmarks, keeping adjacency Gaussian and varying only the feature tail index often improves over both a GDSS baseline retrained under our setup and a Gaussian-limit variant, though the best tail index remains dataset-dependent. These results support stable diffusion on features in coupled graph diffusion, while the case for Gaussian adjacency is primarily established by the controlled probe.

Cite this Paper

BibTeX
@InProceedings{pmlr-v327-tang26a, title = {Heterogeneous Coupled Diffusion for Graph Generation with $α$-Stable Node Feature Noise}, author = {Tang, Chengyu and Kuruoglu, Ercan Engin}, booktitle = {Proceedings of The 1st Symposium on Probabilistic Machine Learning}, pages = {314--345}, year = {2026}, editor = {Swaroop, Siddharth and Rügamer, David and Kristiadi, Agustinus}, volume = {327}, series = {Proceedings of Machine Learning Research}, month = {05 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v327/main/assets/tang26a/tang26a.pdf}, url = {https://proceedings.mlr.press/v327/tang26a.html}, abstract = { Graph generation requires jointly modeling node semantics and graph structure. Existing coupled graph diffusion models mostly use light-tailed perturbations throughout the graph state, which may be too conservative for node features that encode rare semantic roles or long-tailed attribute patterns. We propose a heterogeneous coupled graph diffusion model that applies discrete-time symmetric $\alpha$-stable noise to node features and Gaussian DDPM noise to adjacency, while keeping reverse denoising joint over the full graph state. Using a Gaussian scale-mixture representation, we derive an exact augmented variational objective for the stable feature branch and a same-marginal coupled deterministic sampler. On a controlled benchmark, stable feature diffusion improves rare-role recall and joint generation quality, while Gaussian adjacency provides the more reliable structural bias. On molecular and generic graph benchmarks, keeping adjacency Gaussian and varying only the feature tail index often improves over both a GDSS baseline retrained under our setup and a Gaussian-limit variant, though the best tail index remains dataset-dependent. These results support stable diffusion on features in coupled graph diffusion, while the case for Gaussian adjacency is primarily established by the controlled probe. } }
Endnote
%0 Conference Paper %T Heterogeneous Coupled Diffusion for Graph Generation with $α$-Stable Node Feature Noise %A Chengyu Tang %A Ercan Engin Kuruoglu %B Proceedings of The 1st Symposium on Probabilistic Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Siddharth Swaroop %E David Rügamer %E Agustinus Kristiadi %F pmlr-v327-tang26a %I PMLR %P 314--345 %U https://proceedings.mlr.press/v327/tang26a.html %V 327 %X Graph generation requires jointly modeling node semantics and graph structure. Existing coupled graph diffusion models mostly use light-tailed perturbations throughout the graph state, which may be too conservative for node features that encode rare semantic roles or long-tailed attribute patterns. We propose a heterogeneous coupled graph diffusion model that applies discrete-time symmetric $\alpha$-stable noise to node features and Gaussian DDPM noise to adjacency, while keeping reverse denoising joint over the full graph state. Using a Gaussian scale-mixture representation, we derive an exact augmented variational objective for the stable feature branch and a same-marginal coupled deterministic sampler. On a controlled benchmark, stable feature diffusion improves rare-role recall and joint generation quality, while Gaussian adjacency provides the more reliable structural bias. On molecular and generic graph benchmarks, keeping adjacency Gaussian and varying only the feature tail index often improves over both a GDSS baseline retrained under our setup and a Gaussian-limit variant, though the best tail index remains dataset-dependent. These results support stable diffusion on features in coupled graph diffusion, while the case for Gaussian adjacency is primarily established by the controlled probe.
APA
Tang, C. & Kuruoglu, E.E.. (2026). Heterogeneous Coupled Diffusion for Graph Generation with $α$-Stable Node Feature Noise. Proceedings of The 1st Symposium on Probabilistic Machine Learning, in Proceedings of Machine Learning Research 327:314-345 Available from https://proceedings.mlr.press/v327/tang26a.html.

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