Latent Structural Causal Modeling for High-Dimensional Counterfactual Generation

High-dimensional counterfactual generation must bridge the dimensional gap between causal variables and complex observations while preserving unit-specific variation. We introduce a manifold-guided factorization that maps causal nodes into a shared low-dimensional latent space. An additive structural causal model performs abduction, intervention, and prediction while preserving semantic exogenous residuals, and a conditional flow-matching generator models observation-level noise and renders the terminal state. On Morpho-MNIST, our method recovers causal mechanisms and produces graph-consistent counterfactuals; on OASIS brain MRI, it generates subject-preserving, anatomically ordered images under demographic, anatomical, and dementia-severity interventions within a working graph. Together, these results establish low-dimensional structural propagation as a practical approach to counterfactual generation for high-dimensional observations.