Recommender Systems assist the user by suggesting items to be consumed based on the user's history. The topic of diversity in recommendation gained momentum in recent years as additional criterion besides recommendation accuracy, to improve user satisfaction. Accuracy and diversity in recommender systems coexist in a delicate trade-off due to the complexity in capturing user tastes through a limited amount of interactions. Graphs have been employed for recommendation, given their ability to efficiently represent user-item interactions. Graph convolutions, as learning over graphs tools, have reached state-of-the-art accuracy on recommender system benchmarks. However, the potential of graph convolutions to improve the accuracy-diversity trade-off is unexplored. Here, we develop a model that learns from a nearest neighbor and a furthest neighbor graph via a joint convolutional model to establish a novel accuracy-diversity trade-off for recommender systems. In detail, the nearest neighbor graph connects entities (users or items) based on their similarities and is responsible for improving accuracy, while the furthest neighbor graph connects entities based on their dissimilarities and is responsible for diversifying recommendations. The information between the two convolutional modules is balanced already in the training phase through a regularizer inspired by multi-kernel learning. Numerical experiments on three benchmark datasets showed the joint convolutional model can improve substantially the catalog coverage or the diversity among recommended items; or boost both by a lesser amount. We compared our model against state-of-the-art accuracy-oriented algorithms, showing diversity gains up to seven times by trading as little as 1\% in accuracy. We also compared the joint model against algorithms proposing a different accuracy-diversity trade-off, evidencing our model achieves better accuracy while preserving a wide diversity range. Our findings highlight that the joint convolutional model offers a balance in each setting that is difficult to be achieved with a single model.