PO-Flow: Flow-based Generative Models for Sampling Potential Outcomes and Counterfactuals

We propose PO-Flow, a novel continuous normalizing flow (CNF) framework for causal inference that jointly models potential outcomes and counterfactuals. Trained via flow matching, PO-Flow provides a unified framework for individualized potential outcome prediction, counterfactual predictions, and uncertainty-aware density learning. Among generative models, it is the first to enable density learning of potential outcomes without requiring explicit distributional assumptions (e.g., Gaussian mixtures), while also supporting counterfactual prediction conditioned on factual outcomes in general observational datasets. On benchmarks such as ACIC, IHDP, and IBM, it consistently outperforms prior methods across a range of causal inference tasks. Beyond that, PO-Flow succeeds in high-dimensional settings, including counterfactual image generation, demonstrating its broad applicability.