Stochastic Path Integral Formalism of Causal Field Theory

Virtual tissue models aim to predict the effect of localized interventions in a spatial context. Yet current generative counterfactual models focus largely on global metadata or image-level semantic attributes. Biological interventions, like targeted therapy or targeted radiation, perturb stochastic tissue dynamics in space and time, requiring a field-theoretic perspective rather than just high-dimensional variable sets. Modalities like spatial transcriptomics and serial H&E imaging provide only partial snapshots of the stochastic evolution. Such settings require path-level causal questions: what trajectory follows from a localized treatment, and what would have happened in the same patient under a different region, dose, or timing? We give a causal path-integral formulation for It\^o stochastic PDEs with additive Gaussian noise by interpreting the Martin-Siggia-Rose-Janssen-de Dominicis and related Onsager-Machlup construction as a structural causal model on trajectories. The noise path is the exogenous variable, drift deformations are interventions, and doubled same-noise path integrals implement Pearl-style twin-world counterfactuals. We show that we recover Causal Field Theory in the tree-level linear response limit. The construction translates field-theoretic tools into estimators for nonlinear treatment effects, fluctuation-induced feedback, and counterfactual path sampling. We evaluate the framework on known-mechanism systems and demonstrate finite interventions, same-noise counterfactuals, rare events, and higher-order treatment interactions. The resulting dictionary provides a path-space route to evaluate counterfactuals in spatiotemporal systems where sequential abduction-action-prediction estimators are unstable.