Geometric Generative Modeling with Noise-Conditioned Graph Networks

Peter Pao-Huang, Mitchell Black, Xiaojie Qiu
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:47879-47901, 2025.

Abstract

Generative modeling of graphs with spatial structure is essential across many applications from computer graphics to spatial genomics. Recent flow-based generative models have achieved impressive results by gradually adding and then learning to remove noise from these graphs. Existing models, however, use graph neural network architectures that are independent of the noise level, limiting their expressiveness. To address this issue, we introduce Noise-Conditioned Graph Networks (NCGNs), a class of graph neural networks that dynamically modify their architecture according to the noise level during generation. Our theoretical and empirical analysis reveals that as noise increases, (1) graphs require information from increasingly distant neighbors and (2) graphs can be effectively represented at lower resolutions. Based on these insights, we develop Dynamic Message Passing (DMP), a specific instantiation of NCGNs that adapts both the range and resolution of message passing to the noise level. DMP consistently outperforms noise independent architectures on a variety of domains including $3$D point clouds, spatiotemporal transcriptomics, and images.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-pao-huang25a, title = {Geometric Generative Modeling with Noise-Conditioned Graph Networks}, author = {Pao-Huang, Peter and Black, Mitchell and Qiu, Xiaojie}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {47879--47901}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/pao-huang25a/pao-huang25a.pdf}, url = {https://proceedings.mlr.press/v267/pao-huang25a.html}, abstract = {Generative modeling of graphs with spatial structure is essential across many applications from computer graphics to spatial genomics. Recent flow-based generative models have achieved impressive results by gradually adding and then learning to remove noise from these graphs. Existing models, however, use graph neural network architectures that are independent of the noise level, limiting their expressiveness. To address this issue, we introduce Noise-Conditioned Graph Networks (NCGNs), a class of graph neural networks that dynamically modify their architecture according to the noise level during generation. Our theoretical and empirical analysis reveals that as noise increases, (1) graphs require information from increasingly distant neighbors and (2) graphs can be effectively represented at lower resolutions. Based on these insights, we develop Dynamic Message Passing (DMP), a specific instantiation of NCGNs that adapts both the range and resolution of message passing to the noise level. DMP consistently outperforms noise independent architectures on a variety of domains including $3$D point clouds, spatiotemporal transcriptomics, and images.} }
Endnote
%0 Conference Paper %T Geometric Generative Modeling with Noise-Conditioned Graph Networks %A Peter Pao-Huang %A Mitchell Black %A Xiaojie Qiu %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-pao-huang25a %I PMLR %P 47879--47901 %U https://proceedings.mlr.press/v267/pao-huang25a.html %V 267 %X Generative modeling of graphs with spatial structure is essential across many applications from computer graphics to spatial genomics. Recent flow-based generative models have achieved impressive results by gradually adding and then learning to remove noise from these graphs. Existing models, however, use graph neural network architectures that are independent of the noise level, limiting their expressiveness. To address this issue, we introduce Noise-Conditioned Graph Networks (NCGNs), a class of graph neural networks that dynamically modify their architecture according to the noise level during generation. Our theoretical and empirical analysis reveals that as noise increases, (1) graphs require information from increasingly distant neighbors and (2) graphs can be effectively represented at lower resolutions. Based on these insights, we develop Dynamic Message Passing (DMP), a specific instantiation of NCGNs that adapts both the range and resolution of message passing to the noise level. DMP consistently outperforms noise independent architectures on a variety of domains including $3$D point clouds, spatiotemporal transcriptomics, and images.
APA
Pao-Huang, P., Black, M. & Qiu, X.. (2025). Geometric Generative Modeling with Noise-Conditioned Graph Networks. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:47879-47901 Available from https://proceedings.mlr.press/v267/pao-huang25a.html.

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