# Conditional Diffusion Models Based Conditional Independence Testing

arXiv: https://arxiv.org/abs/2412.11744 · HTML: https://mlsanity.com/paper/2412.11744/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 3 of its 64 references that are in the map.
- First posted on arXiv 16 Dec 2024.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 3 of 3)

- [Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory](https://mlsanity.com/paper/2403.11968/) (2024)
- [Exchangeability, Conformal Prediction, and Rank Tests](https://mlsanity.com/paper/2005.06095/) (2020)
- [Gene Regulatory Network Inference in the Presence of Dropouts: a Causal View](https://mlsanity.com/paper/2403.15500/) (2024)

## Built on by (most cited first, 9 of 9)

- [On Conditional Stochastic Interpolation for Generative Nonlinear Sufficient Dimension Reduction](https://mlsanity.com/paper/2512.18971/) (2025)
- [From Conditional to Unconditional Independence: Testing Conditional Independence via Transport Maps](https://mlsanity.com/paper/2504.09567/) (2025)
- [Diffusion Models with Double Guidance: Generate with aggregated datasets](https://mlsanity.com/paper/2505.13213/) (2025)
- [Toward Scalable and Valid Conditional Independence Testing with Spectral Representations](https://mlsanity.com/paper/2512.19510/) (2025)
- [Generative and Nonparametric Approaches for Conditional Distribution Estimation: Methods, Perspectives, and Comparative Evaluations](https://mlsanity.com/paper/2601.22650/) (2026)
- [Fast Flow Matching based Conditional Independence Tests for Causal Discovery](https://mlsanity.com/paper/2602.08315/) (2026)
- [Causality-Encoded Diffusion Models for Interventional Sampling and Edge Inference](https://mlsanity.com/paper/2604.21843/) (2026)
- [Conditional Independence Tests for Constraint-Based Causal Discovery: A Survey](https://mlsanity.com/paper/2608.11156/) (2026)
- [seq2cause: One Autoregressive Backbone, Four Causal Discovery Tasks in Event Sequences](https://mlsanity.com/paper/2609.31801/) (2026)

## Abstract (arXiv)

Conditional independence (CI) testing is a fundamental task in modern statistics and machine learning. The conditional randomization test (CRT) was recently introduced to test whether two random variables, X and Y, are conditionally independent given a potentially high-dimensional set of random variables, Z. The CRT operates exceptionally well under the assumption that the conditional distribution X|Z is known. However, since this distribution is typically unknown in practice, accurately approximating it becomes crucial. In this paper, we propose using conditional diffusion models (CDMs) to learn the distribution of X|Z. Theoretically and empirically, it is shown that CDMs closely approximate the true conditional distribution. Furthermore, CDMs offer a more accurate approximation of X|Z compared to GANs, potentially leading to a CRT that performs better than those based on GANs. To accommodate complex dependency structures, we utilize a computationally efficient classifier-based conditional mutual information (CMI) estimator as our test statistic. The proposed testing procedure performs effectively without requiring assumptions about specific distribution forms or feature dependencies, and is capable of handling mixed-type conditioning sets that include both continuous and discrete variables. Theoretical analysis shows that our proposed test achieves a valid control of the type I error. A series of experiments on synthetic data demonstrates that our new test effectively controls both type-I and type-II errors, even in high dimensional scenarios.