Recent deep learning models that predict the Hi-C contact map from DNA sequence achieve promising accuracy but cannot generalize to new cell types and or even capture differences among training cell types. We propose Epiphany, a neural network to predict cell-type-specific Hi-C contact maps from widely available epigenomic tracks. Epiphany uses bidirectional long short-term memory layers to capture long-range dependencies and optionally a generative adversarial network architecture to encourage contact map realism. Epiphany shows excellent generalization to held-out chromosomes within and across cell types, yields accurate TAD and interaction calls, and predicts structural changes caused by perturbations of epigenomic signals.Supplementary InformationThe online version contains supplementary material available at 10.1186/s13059-023-02934-9.