GDR-learners: Orthogonal Learning of Generative Models for Potential Outcomes

Various deep generative models have been proposed to estimate potential outcomes distributions from observational data. However, none of them have the favorable theoretical property of general Neyman-orthogonality and, associated with it, quasioracle efficiency and double robustness. In this paper, we introduce a general suite of generative Neyman-orthogonal (doubly-robust) learners that estimate the conditional distributions of potential outcomes. Our proposed generative doubly-robust learners (GDR-learners) are flexible and can be instantiated with many state-ofthe-art deep generative models. In particular, we develop GDR-learners based on (a) conditional normalizing flows (which we call GDR-CNFs), (b) conditional generative adversarial networks (GDR-CGANs), (c) conditional variational autoencoders (GDR-CVAEs), and (d) conditional diffusion models (GDR-CDMs). Unlike the existing methods, our GDR-learners possess the properties of quasi-oracle efficiency and rate double robustness, and are thus asymptotically optimal. In a series of (semi-)synthetic experiments, we demonstrate that our GDR-learners are very effective and outperform the existing methods in estimating the conditional distributions of potential outcomes. INTRODUCTION Causal machine learning (ML) is widely used to predict potential outcomes (POs), namely, the outcome after an intervention. In medicine, for example, an accurate prediction of POs can guide the choice of the optimal treatment from several available treatment options (Feuerriegel et al., 2024) ). The POs have a central role in the causal ML as they define various causal quantities, such as treatment effects (Curth & van der Schaar, 2021) or a policy value (Qian & Murphy, 2011; Frauen et al., 2025b). Recently, many works have suggested departing from estimating simple conditional averages of the POs (CAPOs) and rather aim at the whole conditional distributions (