Geometric Generative Modeling with Noise-Conditioned Graph Networks
This work addresses the limitation of existing graph neural networks in generative modeling for applications such as computer graphics and spatial genomics, offering an incremental improvement by adapting to noise levels.
The paper tackled the problem of generative modeling for graphs with spatial structure by introducing Noise-Conditioned Graph Networks (NCGNs), which dynamically adapt architecture to noise levels, resulting in consistent outperformance over noise-independent methods across domains like 3D point clouds and spatiotemporal transcriptomics.
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.