We introduce a new class of auto-encoders for directed graphs, motivated by a direct extension of Weisfeiler-Leman algorithm to pairs of node labels. This model learns pairs of interpretable latent representations for the nodes of directed graphs. It uses parameterized graph convolutional network (GCN) layers for its encoder and an asymmetric inner product decoder. Parameters in the encoder control the weighting of representations exchanged between neighboring nodes. We demonstrate the ability of the proposed model to learn meaningful latent embeddings on a suite of directed link prediction tasks and on several popular citation network datasets.