Geometric Generative Modeling with Noise-Conditioned Graph Networks

2025-07-12

AI Summary

Existing flow-based graph generation models employ noise-level-agnostic GNN architectures, which fail to adapt to the dynamically varying noise characteristics throughout the generative process, thereby limiting representational capacity and generation quality. To address this, we propose the Noise-Conditional Graph Network (NCGN) coupled with a Dynamic Message Passing (DMP) mechanism—marking the first approach to jointly adapt GNN architecture parameters, message-passing scope, and spatial resolution in response to the current noise level. By conditioning the GNN on noise embeddings and integrating multi-scale representation learning, NCGN significantly enhances modeling fidelity for spatial-structural graph data—including 3D point clouds, spatiotemporal transcriptomics, and image graphs. Extensive evaluations across multiple benchmarks demonstrate consistent superiority over noise-agnostic baselines, with substantial improvements in generation quality. This work establishes a novel paradigm for conditional graph generation grounded in noise-aware architectural adaptation.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Natural Language Processing: Generation
• Computer Vision: Generative Adversarial Networks (GANs) for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

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 extit{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. Code is available at https://github.com/peterpaohuang/ncgn.

Problem

• Modeling graphs with spatial structure lacks noise-level adaptability
• Existing graph neural networks ignore noise level dependencies
• Need dynamic architecture adjusting to noise for better performance

Innovation

• Dynamic architecture adjusts to noise levels
• Dynamic Message Passing adapts range and resolution
• Noise-Conditioned Graph Networks outperform traditional models