Phenotype-driven approaches identify disease-counteracting compounds by analyzing the phenotypic signatures that distinguish diseased from healthy states. These approaches can guide the discovery of targeted perturbations, including small-molecule drugs and genetic interventions, that modulate disease phenotypes toward healthier states. Here, we introduce PDGrapher, a causally inspired graph neural network (GNN) designed to predict combinatorial perturbagens (sets of therapeutic targets) capable of reversing disease phenotypes. Unlike methods that learn how perturbations alter phenotypes, PDGrapher solves the inverse problem of directly predicting the perturbagens needed to achieve a desired response. PDGrapher is a GNN that embeds disease cell states into gene regulatory or protein-protein interaction networks, learns a latent representation of these states, and identifies the optimal combinatorial perturbations that most effectively shift the diseased state toward the desired treated state within that latent space. In experiments in nine cell lines with chemical perturbations, PDGrapher identified effective per-turbagens in up to 13.33% more test samples than competing methods and achieved a normalized discounted cumulative gain of up to 0.12 higher to classify therapeutic targets. It also demonstrated competitive performance on ten genetic perturbation datasets. A key advantage of PDGrapher is its direct prediction paradigm, in contrast to the indirect and computationally intensive models traditionally employed in phenotype-driven research. This approach accelerates training by up to 25 times compared to existing methods. PDGrapher provides a fast approach for identifying therapeutic perturbations and advancing phenotype-driven drug discovery.