Phenotype-driven approaches identify disease-counteracting compounds by analysing the phenotypic signatures that distinguish diseased from healthy states. Here we introduce PDGrapher, a causally inspired graph neural network model that predicts combinatorial perturbagens (sets of therapeutic targets) capable of reversing disease phenotypes. Unlike methods that learn how perturbations alter phenotypes, PDGrapher solves the inverse problem and predicts the perturbagens needed to achieve a desired response by embedding disease cell states into networks, learning a latent representation of these states, and identifying optimal combinatorial perturbations. In experiments in nine cell lines with chemical perturbations, PDGrapher identifies effective perturbagens in more testing samples than competing methods. It also shows competitive performance on ten genetic perturbation datasets. An advantage of PDGrapher is its direct prediction, in contrast to the indirect and computationally intensive approach common in phenotype-driven models. It trains up to 25× faster than existing methods, providing a fast approach for identifying therapeutic perturbations and advancing phenotype-driven drug discovery.