Classical causal inference typically targets low-dimensional estimands such as the average treatment effect. A richer understanding, however, requires characterizing the entire outcome distribution under different treatments. Recent advances in distributional learning provide a principled framework for this broader goal. In this talk, we build on engression—a distributional learning approach—to develop methods for estimating distributional causal effects and simulating data from causal models. We first introduce a distributional estimation method for the instrumental variable setting with unobserved confounders, which enables the estimation of full interventional distributions from which conventional causal estimands arise as functionals. Beyond estimation, the approach is generative: it allows simulation from learned causal models, offering a powerful tool for counterfactual and interventional analysis. Furthermore, we extend the approach to jointly model the observed data distribution around marginal causal effects of interest, yielding a flexible framework for both estimation and simulation under user-specified interventions.
