Domain-Adapted Diffusion Models for Conditional Independence Testing
Abstract
Conditional independence (CI) is a fundamental concept in statistics and machine learning. Recent advances in conditional generative modeling provide flexible tools for generative-model-based CI tests, which rely on an estimated conditional distribution to generate randomized samples. However, errors in estimating this distribution accumulate in existing Type I error bounds, and consistency of the generative estimator alone does not guarantee asymptotic Type I error control. To address this limitation, we formulate conditional generative modeling as a domain adaptation problem and leverage auxiliary data from multiple source domains to improve estimation in the target CI testing domain. We propose Domain-Adapted Diffusion (DA-Diff), a multi-source domain adaptation framework for conditional diffusion models based on weighted empirical risk minimization over both target and source domains. We establish the convergence rate of DA-Diff and show how transferable source data can improve target-domain estimation through an increased effective sample size while controlling transfer bias. Building on DA-Diff, we further propose Domain-Adapted Conditional Independence Testing (DA-CIT) and show that its Type I error satisfies P(p ≤ α) ≤ α+ o(1). Experiments demonstrate that DA-Diff improved conditional generation quality compared with transfer-learning diffusion baselines, while DA-CIT provides strong Type I error control and competitive power.
Related
- Sequential Conditional Independence Testing with Machine Learning Models
- Graph-Based Testing of Conditional Mean Independence with Applications to Large Language Model Evaluation
- Conditional independence testing through marginal permutation
- Embedding-Bias in Conditional Independence Testing
- Conditional Independence Testing in Time Series
BibTeX
@misc{yang2026domainadapted,
title = {{Domain-Adapted Diffusion Models for Conditional Independence Testing}},
author = {Yanfeng Yang and Junda Zhao and Yijie Gao and Jiaqi Yang and Xinyu Shi and Ziqi Chen and Shunyu Zhao and Shuai Li and Wei Huang and Eshant English and Kenji Fukumizu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33490},
eprint = {2609.33490},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33490},
}
RIS
TY - UNPB
TI - Domain-Adapted Diffusion Models for Conditional Independence Testing
AU - Yanfeng Yang
AU - Junda Zhao
AU - Yijie Gao
AU - Jiaqi Yang
AU - Xinyu Shi
AU - Ziqi Chen
AU - Shunyu Zhao
AU - Shuai Li
AU - Wei Huang
AU - Eshant English
AU - Kenji Fukumizu
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33490
UR - https://arxiv.org/abs/2609.33490
AB - Conditional independence (CI) is a fundamental concept in statistics and machine learning. Recent advances in conditional generative modeling provide flexible tools for generative-model-based CI tests, which rely on an estimated conditional distribution to generate randomized samples. However, errors in estimating this distribution accumulate in existing Type I error bounds, and consistency of the generative estimator alone does not guarantee asymptotic Type I error control. To address this limitation, we formulate conditional generative modeling as a domain adaptation problem and leverage auxiliary data from multiple source domains to improve estimation in the target CI testing domain. We propose Domain-Adapted Diffusion (DA-Diff), a multi-source domain adaptation framework for conditional diffusion models based on weighted empirical risk minimization over both target and source domains. We establish the convergence rate of DA-Diff and show how transferable source data can improve target-domain estimation through an increased effective sample size while controlling transfer bias. Building on DA-Diff, we further propose Domain-Adapted Conditional Independence Testing (DA-CIT) and show that its Type I error satisfies P(p ≤ α) ≤ α+ o(1). Experiments demonstrate that DA-Diff improved conditional generation quality compared with transfer-learning diffusion baselines, while DA-CIT provides strong Type I error control and competitive power.
ER -