  Graph neural networks (GNNs), especially dynamic GNNs, have become a research
hotspot in spatio-temporal forecasting problems. While many dynamic graph
construction methods have been developed, relatively few of them explore the
causal relationship between neighbour nodes. Thus, the resulting models lack
strong explainability for the causal relationship between the neighbour nodes
of the dynamically generated graphs, which can easily lead to a risk in
subsequent decisions. Moreover, few of them consider the uncertainty and noise
of dynamic graphs based on the time series datasets, which are ubiquitous in
real-world graph structure networks. In this paper, we propose a novel Dynamic
Diffusion-Variational Graph Neural Network (DVGNN) for spatio-temporal
forecasting. For dynamic graph construction, an unsupervised generative model
is devised. Two layers of graph convolutional network (GCN) are applied to
calculate the posterior distribution of the latent node embeddings in the
encoder stage. Then, a diffusion model is used to infer the dynamic link
probability and reconstruct causal graphs in the decoder stage adaptively. The
new loss function is derived theoretically, and the reparameterization trick is
adopted in estimating the probability distribution of the dynamic graphs by
Evidence Lower Bound during the backpropagation period. After obtaining the
generated graphs, dynamic GCN and temporal attention are applied to predict
future states. Experiments are conducted on four real-world datasets of
different graph structures in different domains. The results demonstrate that
the proposed DVGNN model outperforms state-of-the-art approaches and achieves
outstanding Root Mean Squared Error result while exhibiting higher robustness.
Also, by F1-score and probability distribution analysis, we demonstrate that
DVGNN better reflects the causal relationship and uncertainty of dynamic
graphs.
