Graph neural networks (GNNs), especially dynamic GNNs, have become a research hotspot in spatiotemporal forecasting problems. While many dynamic graph construction methods have been developed, relatively few of them explore the causal relationship between neighbor nodes. Thus, the resulting models lack strong explainability for the causal relationship between the neighbor 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 article, we propose a novel dynamic diffusion-variational GNN (DVGNN) for spatiotemporal 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 (CGs) 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 (ELBO) 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 square error (RMSE) results 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. The website of the code is https://github.com/gorgen2020/DVGNN.