Wide area networking infrastructures (WANs), particularly science and research WANs, are the backbone for moving large volumes of scientific data between experimental facilities and data centers. With demands growing at exponential rates, these networks are struggling to cope with large data volumes, real-time responses, and overall network performance. Network operators are increasingly looking for innovative ways to manage the limited underlying network resources. Forecasting network traffic is a critical capability for proactive resource management, congestion mitigation, and dedicated transfer provisioning. To this end, we propose a nonautoregressive graph-based neural network for multistep network traffic forecasting. Specifically, we develop a dynamic variant of diffusion convolutional recurrent neural networks to forecast traffic in research WANs. We evaluate the efficacy of our approach on real traffic from ESnet, the U.S. Department of Energy's dedicated science network. Our results show that compared to classical forecasting methods, our approach explicitly learns the dynamic nature of spatiotemporal traffic patterns, showing significant improvements in forecasting accuracy. Our technique can surpass existing statistical and deep learning approaches by achieving approximately 20% mean absolute percentage error for multiple hours of forecasts despite dynamic network traffic settings.