# Nonparametric estimation of conditional probability distributions using a generative approach based on conditional push-forward neural networks

arXiv: https://arxiv.org/abs/2511.14455 · HTML: https://mlsanity.com/paper/2511.14455/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 59 references that are in the map.
- First posted on arXiv 18 Nov 2025.

## Builds on (most cited first, 18 of 18)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [The gap between theory and practice in function approximation with deep neural networks](https://mlsanity.com/paper/2001.07523/) (2020)
- [Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks](https://mlsanity.com/paper/1903.00954/) (2019)
- [Probabilistic Forecasting with Generative Networks via Scoring Rule Minimization](https://mlsanity.com/paper/2112.08217/) (2021)
- [Noise Regularization for Conditional Density Estimation](https://mlsanity.com/paper/1907.08982/) (2019)
- [Deep Conditional Transformation Models](https://mlsanity.com/paper/2010.07860/) (2020)
- [Probabilistic neural operators for functional uncertainty quantification](https://mlsanity.com/paper/2502.12902/) (2025)
- [LinCDE: Conditional Density Estimation via Lindsey's Method](https://mlsanity.com/paper/2107.12713/) (2021)
- [Wasserstein Generative Regression](https://mlsanity.com/paper/2306.15163/) (2023)
- [RFCDE: Random Forests for Conditional Density Estimation](https://mlsanity.com/paper/1804.05753/) (2018)
- [Generative Quantile Regression with Variability Penalty](https://mlsanity.com/paper/2301.03661/) (2023)
- [A Likelihood Based Approach to Distribution Regression Using Conditional Deep Generative Models](https://mlsanity.com/paper/2410.02025/) (2024)
- [Conditional Density Estimation with Histogram Trees](https://mlsanity.com/paper/2410.11449/) (2024)

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

- [Optimal Transport Dropout for Structured Predictive Uncertainty](https://mlsanity.com/paper/2609.33377/) (2026)

## Abstract (arXiv)

We introduce conditional push-forward neural networks (CPFN), a generative framework for conditional distribution estimation. Instead of directly modeling the conditional density fY|X, CPFN learns a stochastic map varphi=varphi(x,u) such that varphi(x,U) and Y|X=x follow approximately the same law, with U a suitable random vector of pre-defined latent variables. This enables efficient conditional sampling and straightforward estimation of conditional statistics through Monte Carlo methods. The model is trained via an objective function derived from a Kullback-Leibler formulation, without requiring invertibility or adversarial training. We establish a near-asymptotic consistency result and demonstrate experimentally that CPFN can achieve performance competitive with, or even superior to, state-of-the-art methods, including kernel estimators, tree-based algorithms, and popular deep learning techniques, all while remaining lightweight and easy to train.