Graph neural network (GNN) is a robust model for processing non-Euclidean data, such as graphs, by extracting structural information and learning high-level representations. GNN has achieved state-of-the-art recommendation performance on collaborative filtering (CF) for accuracy. Nevertheless, the diversity of the recommendations has not received good attention. Existing work using GNN for recommendation suffers from the accuracy-diversity dilemma, where slightly increases diversity while accuracy drops significantly. Furthermore, GNN-based recommendation models lack the flexibility to adapt to different scenarios' demands concerning the accuracy-diversity ratio of their recommendation lists. In this work, we endeavor to address the above problems from the perspective of aggregate diversity, which modifies the propagation rule and develops a new sampling strategy. We propose graph spreading network (GSN), a novel model that leverages only neighborhood aggregation for CF. Specifically, GSN learns user and item embeddings by propagating them over the graph structure, utilizing both diversity-oriented and accuracy-oriented aggregations. The final representations are obtained by taking the weighted sum of the embeddings learned at all layers. We also present a new sampling strategy that selects potentially accurate and diverse items as negative samples to assist model training. GSN effectively addresses the accuracy-diversity dilemma and achieves improved diversity while maintaining accuracy with the help of a selective sampler. Moreover, a hyper-parameter in GSN allows for adjustment of the accuracy-diversity ratio of recommendation lists to satisfy the diverse demands. Compared to the state-of-the-art model, GSN improved R @20 by 1.62% , N @20 by 0.67% , G @20 by 3.59% , and E @20 by 4.15% on average over three real-world datasets, verifying the effectiveness of our proposed model in diversifying overall collaborative recommendations.