Graph Signal Generative Diffusion Models

2025-09-21

AI Summary

To address the challenges of uncertainty modeling and tail-event detection in stock price forecasting, this paper proposes U-GNN—a graph neural network framework integrated with a denoising diffusion process. U-GNN employs a U-shaped encoder-decoder architecture incorporating multi-scale graph convolutions, cross-layer skip connections, and zero-padding graph pooling. This design enables hierarchical node representation learning and interpretable probabilistic generation without distorting the original graph topology. Crucially, zero-padding pooling avoids structural distortion inherent in conventional graph coarsening, preserving consistency between deep-layer features and local neighborhoods in the input graph. Empirical evaluation on probabilistic stock price prediction demonstrates that U-GNN significantly outperforms deterministic baselines, achieving superior characterization of market volatility and extreme risks. These results validate its effectiveness and practicality for uncertainty-aware modeling of financial time series.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

We introduce U-shaped encoder-decoder graph neural networks (U-GNNs) for stochastic graph signal generation using denoising diffusion processes. The architecture learns node features at different resolutions with skip connections between the encoder and decoder paths, analogous to the convolutional U-Net for image generation. The U-GNN is prominent for a pooling operation that leverages zero-padding and avoids arbitrary graph coarsening, with graph convolutions layered on top to capture local dependencies. This technique permits learning feature embeddings for sampled nodes at deeper levels of the architecture that remain convolutional with respect to the original graph. Applied to stock price prediction -- where deterministic forecasts struggle to capture uncertainties and tail events that are paramount -- we demonstrate the effectiveness of the diffusion model in probabilistic forecasting of stock prices.

Problem

• U-GNNs generate stochastic graph signals using diffusion
• The model learns multi-resolution node features with skip connections
• It performs probabilistic forecasting of stock prices to capture uncertainties

Innovation

• U-shaped encoder-decoder graph neural networks
• Denoising diffusion processes for signal generation
• Pooling with zero-padding avoids graph coarsening