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Single-cell transcriptomics, in conjunction with genetic and compound perturbations, offers a robust approach for exploring cellular behaviors in diverse contexts. Such experiments allow uncovering cell-state-specific responses to perturbations and unraveling the intricate molecular mechanisms governing cellular behavior. However, prevailing computational methods predominantly focus on predicting average cellular responses, disregarding inherent response heterogeneity associated with cell state diversity and model explainability. In this study, we present CellCap, a deep generative model designed for the end-to-end analysis of single-cell perturbation experiments. CellCap employs sparse dictionary learning in a latent space to deconstruct cell-state-specific perturbation responses into a set of transcriptional response programs and utilizes an attention mechanism to capture correspondence between cell state and perturbation response. We thoroughly evaluate CellCap's interpretability using multiple simulated scenarios as well as two real single-cell perturbation datasets. Our results demonstrate that CellCap successfully uncovers the relationship between cell state and perturbation response, unveiling insights overlooked in previous analyses.