Geometry Adaptive Counterfactual Distribution Learning with Diffusion-Guided Smoothing

Generative models for counterfactual outcomes have great potential to support decision-making under complex interventions, but existing approaches are limited by unstable estimation, poor generalization across environments, and bias from nuisance model misspecification. We introduce ADIGen, a framework for automatic, debiased, and invariant counterfactual generation under general interventions, including high-dimensional interventions and outcomes. ADIGen combines Riesz regression to avoid unstable density-ratio estimation, causal invariance to improve generalization under distribution shift, and orthogonal statistical learning to obtain doubly robust guarantees against nuisance model misspecification. We provide excess-risk bounds showing that ADIGen controls counterfactual risk under general interventions, with a product-bias nuisance remainder and an invariant risk bound across environments.

Estimating counterfactual distributions under interventions is central to treatment risk assessment and counterfactual generation tasks. Existing approaches model the counterfactual distribution as a standalone generative target, without exploiting its relationship to the observational data. In this work, we show that under standard assumptions, observational and counterfactual outcome distributions are tightly linked: they have identical support and tail behavior, remain statistically close under weak confounding, and share any features of high-dimensional outcomes which are invariant to confounders. These properties motivate learning counterfactual distributions not from scratch, but via a deconfounding flow from the observational distribution. We formulate this problem via flow-matching and derive a semiparametrically efficient estimator based on a novel efficient influence function correction. We subsequently extend our estimator to target minimal-energy flows in high-dimensions, which we show can be especially simple targets between observational and counterfactual distributions. In experiments, deconfounding flows outperform existing debiased counterfactual distribution estimators, while also mitigating known failure modes of flow-based methods.

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.