Geometric Generative Modeling with Noise-Conditioned Graph Networks

TL;DR

This paper introduces Noise-Conditioned Graph Networks (NCGNs) that adapt their architecture based on noise levels, improving the generative modeling of spatial graphs across various domains.

Contribution

We propose NCGNs, a novel class of graph neural networks that dynamically adjust their structure according to noise levels, enhancing generative modeling capabilities.

Findings

DMP outperforms noise-independent models on multiple datasets

Graphs require more distant information as noise increases

Lower resolution representations are effective at higher noise levels

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 \textit{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.