Geometry Adaptive Counterfactual Distribution Learning with Diffusion-Guided Smoothing
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910255158394880 |
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| author | Kim, Kwangho |
| author_facet | Kim, Kwangho |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25811 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometry Adaptive Counterfactual Distribution Learning with Diffusion-Guided Smoothing Kim, Kwangho Methodology Machine Learning 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. |
| title | Geometry Adaptive Counterfactual Distribution Learning with Diffusion-Guided Smoothing |
| topic | Methodology Machine Learning |
| url | https://arxiv.org/abs/2605.25811 |