Abstract: Consider the problem to infer the input data X given outcome labels Y, where both X and Y are defined on each node on a graph. The problem can be viewed as reversing the node prediction problem on a graph, and since the mapping from Y to X is one-to-many, it can be formulated as a conditional generative task. We propose a model of invertible graph neural networks to address the problem, where an invertible normalizing flow network is used to construct a one-to-one mapping from X to an intermediate feature H, and then a classification network is used to map H to Y. The expressiveness of graph convolution layers is analyzed in the context of the problem and supported by experiments. In computation, we introduce Wasserstein-2 regularization in the training of the flow network. We will also discuss new designs of the invertible flow network based on Wasserstein gradient flow. Joint work with Chen Xu and Yao Xie.