Distributional causal inference requires estimating not only average treatment effects but also interventional outcome distributions, including quantiles, tail risks, and policy-dependent uncertainty. As a method for distributional causal inference, generative adversarial network (GAN)-based counterfactual methods are flexible tools for this task. However, these methods have several limitations. First, the objectives of certain techniques do not coincide with the statistical risk of the identifiable causal target, and therefore provide limited theoretical guarantees regarding estimable counterfactual distributions or optimality. Second, implementing target-design risks under observational sampling can require density-ratio estimation. In this paper, we propose GANICE (GAN for Interventional Conditional Estimation) with several advantages: it (i) specifies the conditional interventional distribution for each treatment--covariate state as the causal estimation target; (ii) estimates the conditional distribution such that its averaged Wasserstein risk is minimized; (iii) attains minimax optimality. GANICE achieves these advantages through the extended Wasserstein distance and cell-normalized estimation, with minimax bounds based on Wasserstein GAN oracle inequalities and an anisotropic Assouad construction; Besov theory characterizes the cellwise critics. Our experiments show that GANICE outperforms existing methods on most benchmarks.

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