# Generative and Nonparametric Approaches for Conditional Distribution Estimation: Methods, Perspectives, and Comparative Evaluations

arXiv: https://arxiv.org/abs/2601.22650 · HTML: https://mlsanity.com/paper/2601.22650/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 28 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Builds on (most cited first, 10 of 10)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [CARD: Classification and Regression Diffusion Models](https://mlsanity.com/paper/2206.07275/) (2022)
- [Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory](https://mlsanity.com/paper/2403.11968/) (2024)
- [Converting High-Dimensional Regression to High-Dimensional Conditional Density Estimation](https://mlsanity.com/paper/1704.08095/) (2017)
- [Conditional Density Estimation Tools in Python and R with Applications to Photometric Redshifts and Likelihood-Free Cosmological Inference](https://mlsanity.com/paper/1908.11523/) (2019)
- [Conditional Diffusion Models Based Conditional Independence Testing](https://mlsanity.com/paper/2412.11744/) (2024)
- [Distributional (Single) Index Models](https://mlsanity.com/paper/2006.09219/) (2020)

## Built on by (most cited first, 1 of 1)

- [Parallel gradient boosting for flexible estimation of conditional distributions](https://mlsanity.com/paper/2607.13550/) (2026)

## Abstract (arXiv)

The inference of conditional distributions is a fundamental problem in statistics, essential for prediction, uncertainty quantification, and probabilistic modeling. A wide range of methodologies have been developed for this task. This article reviews and compares several representative approaches spanning classical nonparametric methods and modern generative models. We begin with the single-index method of Hall and Yao (2005), which estimates the conditional distribution through a dimension-reducing index and nonparametric smoothing of the resulting one-dimensional cumulative conditional distribution function. We then examine the basis-expansion approaches, including FlexCode (Izbicki and Lee, 2017) and DeepCDE (Dalmasso et al., 2020), which convert conditional density estimation into a set of nonparametric regression problems. In addition, we discuss two recent generative simulation-based methods that leverage modern deep generative architectures: the generative conditional distribution sampler (Zhou et al., 2023) and the conditional denoising diffusion probabilistic model (Fu et al., 2024; Yang et al., 2025). A systematic numerical comparison of these approaches is provided using a unified evaluation framework that ensures fairness and reproducibility. The performance metrics used for the estimated conditional distribution include the mean-squared errors of conditional mean and standard deviation, as well as the Wasserstein distance. We also discuss their flexibility and computational costs, highlighting the distinct advantages and limitations of each approach.