Instrumental variable (IV) and control function (CF) methods are powerful tools for causal effect estimation in the presence of unmeasured confounding, yet most existing approaches target only mean effects and/or demand substantial fitting and tuning effort. In this paper, we introduce a simple method, TabCF, for control function regression using tabular foundation models, which enables accurate, fast, identification-transparent, and tuning-light causal estimation of distributional quantities, such as interventional means and quantiles; we also propose a copula-based approximation for multivariate outcomes. TabCF performs favorably against representative methods across a broad range of small- to medium-sized synthetic and real data scenarios. The central message is two-fold: for practitioners, it highlights that TabCF is an effective tool for distributional causal inference; for researchers, it suggests that the proposed approach could be considered a strong baseline for future method development. Code is available at https://github.com/GepingChen/TabCF.
We develop exponential family synthetic controls (EFSC), a distributional version of synthetic controls for a panel of datasets. Each cell of the panel corresponds to a dataset drawn from an exponential family whose natural parameters factorize probabilistically across units and times. We estimate the latent factors using black-box variational inference. This replaces the usual weighted-average view of synthetic controls with a flexible probabilistic model that operates on full distributions. We propose causal estimands based on divergences between pre- and post-intervention distributions induced by the posterior of the natural parameters, together with distributional placebo tests to support causal inference and assess the significance of the estimated effects. We validate the proposed framework on synthetic and real data. Across a variety of exponential-family distributions, EFSC accurately recovers causal effects induced by exponential tilts, together with the corresponding divergences between treated and counterfactual distributions. The framework also captures effects induced by structural perturbations of the latent factors and by heavy-tailed noise contamination. Finally, we apply EFSC to study the expansion of Medicaid under the Affordable Care Act (ACA) and its impact on the distribution of health insurance coverage across U.S. states. Code is available at https://github.com/blei-lab/efsc.
Causal inference guides operational and managerial decisions but remains challenging in high-dimensional panel or tensor settings, where decisions may depend on the joint conditional distribution of missing control outcomes. We develop \emph{Counterfactual Tucker Diffusion} (\CFTDiff), which integrates the treatment mask and latent Tucker structure into conditional diffusion to recover this distribution given observed control outcomes through efficient nonlinear score learning in a low-dimensional core. The masked Tucker score preserves dependence across tensor modes while reducing the dimension of nonlinear score learning from the product of mode dimensions to the much smaller product of Tucker ranks. We establish high-probability error bounds for conditional score estimation that depend on the Tucker ranks, largest mode dimension, and the factor-strength-adjusted number of missing outcomes, and show how these bounds translate into recovery guaranties for the conditional distribution of the missing control outcomes. Across missing rates, simulations show more accurate point recovery than common causal panel and matrix/tensor completion methods; comparisons with nested diffusion specifications further demonstrate the gains from masked conditioning and Tucker dimension reduction. In Norway's iFlex experiment, \CFTDiff recovers missing outcomes more accurately than competing methods; when applied to causal analysis, its estimated conditional distributions yield counterfactual prediction intervals and target-attainment probabilities, allowing pricing interventions to be evaluated by demand-reduction magnitude and reliability.
Estimating causal effects from observational data has become increasingly critical in diverse fields including healthcare, economics, and social policy. The fundamental challenge in causal inference arises from the missing counterfactuals and the selection bias. Existing methods are largely limited to point estimates and lack the capacity for distribution modeling. In this work, we propose RepFlow, a novel framework that formulates causal effect estimation as a joint optimization problem integrating representation learning with Conditional Flow Matching (CFM). RepFlow mitigates selection bias by minimizing the entropically regularized Wasserstein distance between treated and control representations. To enhance numerical stability, we further introduce an L2 normalization constraint on latent representations. This balanced representation enables the flow model to accurately capture the distribution of potential outcomes. Extensive experiments across a wide range of benchmarks demonstrate that RepFlow consistently outperforms existing methods in both point and distributional causal effect estimation.