Abstract Recent advances in multiplexed single-cell transcriptomics experiments are facilitating the high-throughput study of drug and genetic perturbations. However, an exhaustive exploration of the combinatorial perturbation space is experimentally unfeasible, so computational methods are needed to predict, interpret, and prioritize perturbations. Here, we present the compositional perturbation autoencoder (CPA), which combines the interpretability of linear models with the flexibility of deep-learning approaches for single-cell response modeling. CPA encodes and learns transcriptional drug responses across different cell type, dose, and drug combinations. The model produces easy-to-interpret embeddings for drugs and cell types, which enables drug similarity analysis and predictions for unseen dosage and drug combinations. We show that CPA accurately models single-cell perturbations across compounds, doses, species, and time. We further demonstrate that CPA predicts combinatorial genetic interactions of several types, implying that it captures features that distinguish different interaction programs. Finally, we demonstrate that CPA can generate in-silico 5,329 missing genetic combination perturbations (97.6% of all possibilities) with diverse genetic interactions. We envision our model will facilitate efficient experimental design and hypothesis generation by enabling in-silico response prediction at the single-cell level, and thus accelerate therapeutic applications using single-cell technologies.