We study counterfactual distribution learning for high-dimensional outcomes whose counterfactual law may concentrate near lower-dimensional structure. Standard isotropic smoothing treats all ambient directions equally, leading to unfavorable scaling and unstable local inference. We propose two diffusion-guided estimators based on semiparametric debiasing: diffusion-informed smoothing for counterfactual densities and diffusion-informed score smoothing for counterfactual scores. The estimators combine causal nuisance adjustment with geometry-adaptive localization driven by diffusion score information, removing first-order nuisance bias while aligning smoothing with local outcome geometry. We establish asymptotic expansions, risk bounds, and inference procedures for smoothed density and score-based targets, with ambient density inference obtained under additional approximation conditions. Under structural geometry conditions, the leading stochastic error is governed by an effective dimension induced by the diffusion-guided kernel, rather than by the ambient dimension. Semi-synthetic experiments based on CelebA show steeper error decay for geometry-adaptive methods, supporting the proposed effective-dimension theory.

翻译：我们研究了高维结果的反事实分布学习问题，其中反事实分布可能集中在低维结构附近。标准的各向同性平滑对所有环境方向一视同仁，导致不利的缩放和不稳定的局部推断。我们提出了两种基于半参数去偏的扩散引导估计量：用于反事实密度的扩散信息平滑和用于反事实得分的扩散信息得分平滑。这些估计量将因果干扰调整与扩散得分信息驱动的几何自适应定位相结合，在消除一阶干扰偏差的同时使平滑与局部结果几何对齐。我们建立了平滑密度和基于得分目标的渐近展开、风险界限和推断程序，并在额外近似条件下得到了环境密度推断。在结构几何条件下，主要随机误差由扩散引导核诱导的有效维度控制，而非环境维度。基于CelebA的半合成实验表明，几何自适应方法的误差衰减更陡峭，支持了所提出的有效维度理论。