## 1 Introduction  
Traffic prediction is an important part of the Intelligent Transportation System (ITS), which can reasonably allocate road resources, alleviate traffic congestion, and improve road traffic efficiency [1, 2]. Traffic prediction has always been extremely challenging because traffic in road networks changes dynamically over time. There is a complex, nonlinear and multimodal spatio-temporal dependency between historical traffic and predicted traffic. This temporal dependence relationship is expressed as the mutual influence of traffic at different times within the road network. The spatial dependence relationship is expressed as the mutual influence of the traffic between different roads within the road network, as shown in Figure 1.  
With the vigorous development of neural networks, deep learning has achieved success in obtaining complex nonlinear relationships [3]. Graph Convolutional Networks (GCNs) are good at processing nonlinear structural data and are widely used in traffic prediction [4, 5, 6, 7]. Most existing traffic prediction studies are aimed at short-term prediction (15 min) [8, 9, 10, 1]. DCRNN [8] uses the graph convolution operation to replace the original linear transformation in the recursive unit of the Recurrent Neural Network (RNN) for obtaining spatio-temporal information. To avoid the complex gating operation of RNN, STGCN [9] uses graph convolution and 1D convolution to obtain spatio-temporal information, reduce parameters, and achieve a good short-term prediction effect. GWnet [10] further uses graph convolution and block stacking of the Temporal Convolution Network(TCN) to achieve better short-term prediction. STSGCN [11] constructs a local spatio-temporal graph for convolution to obtain a better short-term prediction effect. [PERSON] [12] pointed out that the existing models pay more attention to short-term prediction and therefore spatio-temporal attention and an encoder-decoder mechanism were used to obtain better long-term predictions (1 h). However, this did not significantly help with short-term predictions. To be able to consider the combined effect of both short-term and long-term traffic prediction, we propose a new deep learning model Multi-Stage Spatio-Temporal Fusion Diffusion Graph Convolutional Network (MFDGCN). First, we propose a new spatio-temporal multi-association graph generation method, which obtains the static and dynamic representations of traffic flow in the spatial dimension based on spatial distance and spatial similarity. We then obtain the static and dynamic representation of the temporal dimension per the temporal connection relationship and temporal similarity. However, modeling based on a simple distance graph [8; 9; 10] will ignore the deep relationship between non-adjacent spatial and temporal dimensions. It will also be less able to capture the interaction of traffic between different roads. While using weather and POI (Point of Interest) as features to build models is possible [1; 13], these data are not easy to obtain. Second, we propose a multi-stage hybrid spatio-temporal fusion method that can capture longer-term spatio-temporal relationships. It uses basic fusion operations to capture early low-level spatio-temporal information, followed by the use of an adaptive gating mechanism to fuse high-level spatio-temporal information after convolution. It then finally captures deeper complex spatio-temporal information through a multi-head attention mechanism [14]. The spatial and temporal data in traffic prediction can be regarded as multimodal data with different dimensions. However, simple connection or addition operations are not sufficient to deeply mine for information from the mutual fusion of different models [8; 9; 10; 15]. For example, STGCN [9] and HetGAT [16] use separate modules to sequentially capture spatial and temporal relationships, thereby splitting the association between both dimensions.