Causal reasoning and “what if” analysis allow us to predict the outcomes of hypothetical changes and are fundamental to decision support in high stakes domains such as healthcare, economics, and robotics. Traditional causal discovery methods can find cause and effect graphs under simple assumptions but struggle with large, complex datasets and cannot predict what might happen after a hypothetical change. Algorithms like PC, FCI, and NOTEARS reliably infer directed acyclic graphs (DAGs) under linear or simple nonlinear assumptions but fail to scale to high dimensional data and lack mechanisms for counterfactual simulation. Conversely, deep generative models learn to reproduce complex data patterns but do not capture cause and effect relationships, so they cannot answer “what if” questions. We propose Interventional Structural Deep Generative Models (IS DGM), a unified framework that embeds a learnable DAG into the latent space of a variational autoencoder. We prove that, under realistic conditions, our approach can uniquely recover the true causal structure and generate reliable counterfactual predictions. IS DGM enforces acyclicity via a continuous matrix exponential penalty, encourages sparsity through regularization, and introduces a latent space intervention operator to clamp selected factors and propagate effects through the graph. Under mild exponential family priors and with diverse interventional data, IS DGM recovers the true DAG up to element wise reparameterization. Empirically, on synthetic benchmarks (latent dimensions up to 100), IS DGM reduces structural Hamming distance by 30–55% and achieves over 50% lower counterfactual RMSE than state of the art baselines. On real clinical data (MIMIC III), it halves prediction error of treatment response simulations relative to identifiable VAEs and NOTEARS. Ablation studies confirm the necessity of each loss component, and scalability analyses quantify runtime and memory trade offs. IS DGM thus offers a principled, scalable solution for joint causal discovery and counterfactual inference in complex, high dimensional settings.