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.

翻译：条件分布的推断是统计学中的一个基本问题，对于预测、不确定性量化和概率建模至关重要。针对这一任务已发展出多种方法学。本文回顾并比较了几种代表性的方法，涵盖经典的非参数方法和现代生成模型。我们从Hall和Yao（2005）的单指标方法开始，该方法通过降维指标及对所得一维累积条件分布函数进行非参数平滑来估计条件分布。接着，我们考察基展开方法，包括FlexCode（Izbicki和Lee，2017）与DeepCDE（Dalmasso等人，2020），这些方法将条件密度估计转化为一组非参数回归问题。此外，我们讨论了两种近期基于模拟的生成式方法，它们利用了现代深度生成架构：生成式条件分布采样器（Zhou等人，2023）和条件去噪扩散概率模型（Fu等人，2024；Yang等人，2025）。我们使用一个确保公平性和可复现性的统一评估框架，对这些方法进行了系统的数值比较。用于评估估计条件分布的性能指标包括条件均值和标准差均方误差，以及Wasserstein距离。我们还讨论了它们的灵活性和计算成本，并着重指出了每种方法独特的优势与局限性。