We propose a framework for causal inference with panel data in the presence of network interference and unobserved confounding. Key to our approach is a novel latent factor model that takes into account network interference and generalizes the factor models typically used in panel data settings. We propose an estimator–the Network Synthetic Interventions estimator—and show that it consistently estimates the counterfactual outcomes for a unit under an arbitrary set of treatments, if certain observation patterns hold in the data. We corroborate our theoretical findings with simulations. In doing so, our framework extends the Synthetic Control and Synthetic Interventions methods to incorporate network interference.