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The recent introduction of Graph Neural Networks (GNNs) and their growingpopularity in the past few years has enabled the application of deep learningalgorithms to non-Euclidean, graph-structured data. GNNs have achievedstate-of-the-art results across an impressive array of graph-based machinelearning problems. Nevertheless, despite their rapid pace of development, muchof the work on GNNs has focused on graph classification and embeddingtechniques, largely ignoring regression tasks over graph data. In this paper,we develop a Graph Mixture Density Network (GraphMDN), which combines graphneural networks with mixture density network (MDN) outputs. By combining thesetechniques, GraphMDNs have the advantage of naturally being able to incorporategraph structured information into a neural architecture, as well as the abilityto model multi-modal regression targets. As such, GraphMDNs are designed toexcel on regression tasks wherein the data are graph structured, and targetstatistics are better represented by mixtures of densities rather than singularvalues (so-called ``inverse problems"). To demonstrate this, we extend anexisting GNN architecture known as Semantic GCN (SemGCN) to a GraphMDNstructure, and show results from the Human3.6M pose estimation task. Theextended model consistently outperforms both GCN and MDN architectures on theirown, with a comparable number of parameters.

GraphMDN: Leveraging graph structure and deep learning to solve inverse problems