# Neural Generative Distributional Regression

arXiv: https://arxiv.org/abs/2605.02062 · HTML: https://mlsanity.com/paper/2605.02062/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 May 2026.

## Built on by (most cited first, 2 of 2)

- [Error Analysis of Neural-Network-Based Engression](https://mlsanity.com/paper/2607.27723/) (2026)
- [Belted Engression: Sufficient Dimension Reduction for Generative Distributional Regression](https://mlsanity.com/paper/2609.23789/) (2026)

## Abstract (arXiv)

Any continuous conditional distribution of Y given X can be generated from a transform of a known noise distribution U such as the uniform or normal distribution via Y = g(X, U). This paper provides an estimator of such a generative transformation g by minimizing the empirical energy distance between distributions of Y and g(X, U), and implements it via neural networks. The estimated distribution can then be readily applied to downstream tasks such as conditional moment estimation, predictive interval construction, and conditional density estimation. By leveraging the representation power of neural networks, the estimator can adaptively exploit low-dimensional structures in a purely algorithmic manner. Theoretically, we establish an oracle inequality attaining the adaptive optimal nonparametric rates. Numerical simulations and real data analysis further demonstrate the practical effectiveness of the proposed method.