Geometry Adaptive Counterfactual Distribution Learning with Diffusion-Guided Smoothing

• URL: http://arxiv.org/abs/2605.25811v1
• Date: Mon, 25 May 2026 13:02:56 GMT
• Title: Geometry Adaptive Counterfactual Distribution Learning with Diffusion-Guided Smoothing
• Abstract summary: Standard isotropic smoothing treats all ambient directions equally, leading to unfavorable scaling and unstable local inference.<n>We propose two diffusion-guided estimators based on semi-parametric debiasing: diffusion-informed smoothing for counterfactual densities and diffusion-informed score smoothing for counterfactual scores.
• Score: 4.727838288363022
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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