# Testing Conditional Distribution Equality Using Generative Models

arXiv: https://arxiv.org/abs/2610.20447 · HTML: https://mlsanity.com/paper/2610.20447/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 38 references that are in the map.
- First posted on arXiv 14 Oct 2026.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Age Progression/Regression by Conditional Adversarial Autoencoder](https://mlsanity.com/paper/1702.08423/) (2017)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [Training generative neural networks via Maximum Mean Discrepancy optimization](https://mlsanity.com/paper/1505.03906/) (2015)
- [Engression: Extrapolation through the Lens of Distributional Regression](https://mlsanity.com/paper/2307.00835/) (2023)
- [Deep Knockoffs](https://mlsanity.com/paper/1811.06687/) (2018)
- [Diagnostics for Conditional Density Models and Bayesian Inference Algorithms](https://mlsanity.com/paper/2102.10473/) (2021)
- [Double Generative Adversarial Networks for Conditional Independence Testing](https://mlsanity.com/paper/2006.02615/) (2020)
- [Statistical Inference for Fairness Auditing](https://mlsanity.com/paper/2305.03712/) (2023)
- [A Two-Sample Conditional Distribution Test Using Conformal Prediction and Weighted Rank Sum](https://mlsanity.com/paper/2010.07147/) (2020)
- [Deep Dimension Reduction for Supervised Representation Learning](https://mlsanity.com/paper/2006.05865/) (2020)
- [Evaluating Aleatoric Uncertainty via Conditional Generative Models](https://mlsanity.com/paper/2206.04287/) (2022)
- [Distance and Kernel-Based Measures for Global and Local Two-Sample Conditional Distribution Testing](https://mlsanity.com/paper/2210.08149/) (2022)
- [A Kernel-Based Conditional Two-Sample Test Using Nearest Neighbors (with Applications to Calibration, Regression Curves, and Simulation-Based Inference)](https://mlsanity.com/paper/2407.16550/) (2024)
- [Doubly Robust Conditional Independence Testing with Generative Neural Networks](https://mlsanity.com/paper/2407.17694/) (2024)
- [Distance-based and RKHS-based Dependence Metrics in High Dimension](https://mlsanity.com/paper/1902.03291/) (2019)
- [Enhancing Causal Effect Estimation with Diffusion-Generated Data](https://mlsanity.com/paper/2504.03630/) (2025)
- [Conditional Feature Importance with Generative Modeling Using Adversarial Random Forests](https://mlsanity.com/paper/2501.11178/) (2025)
- [From Conditional to Unconditional Independence: Testing Conditional Independence via Transport Maps](https://mlsanity.com/paper/2504.09567/) (2025)
- [Testing Equality of Conditional Distributions via Generative Models](https://mlsanity.com/paper/2606.06930/) (2026)
- [Measuring Differences between Conditional Distributions using Kernel Embeddings](https://mlsanity.com/paper/2605.02260/) (2026)

## Abstract (arXiv)

Conditional distribution equality testing is a core problem with applications in causal inference, model diagnostics, and transfer learning. Existing methods often lose power when the conditioning variable is high-dimensional. We propose a new test that leverages generative models to compare conditional distributions using both observed data and synthetic samples. A sample-splitting and studentization scheme is introduced to control estimation error. Under the null, the test statistic is asymptotically normal, and we establish local power against contiguous alternatives. Our theory under the null and fixed alternative requires only consistency of the learned conditional distribution, allowing for a broad class of generative models. Empirical results demonstrate accurate size control and strong power in high-dimensional settings compared to representative kernel-based conditional and joint two-sample tests.