# GDR-learners: Orthogonal Learning of Generative Models for Potential Outcomes

arXiv: https://arxiv.org/abs/2509.22953 · HTML: https://mlsanity.com/paper/2509.22953/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 62 of its 100 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 30 of 62)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Counterfactual Generative Networks](https://mlsanity.com/paper/2101.06046/) (2021)
- [Automated versus do-it-yourself methods for causal inference: Lessons learned from a data analysis competition](https://mlsanity.com/paper/1707.02641/) (2017)
- [Diffusion Causal Models for Counterfactual Estimation](https://mlsanity.com/paper/2202.10166/) (2022)
- [Causal machine learning for predicting treatment outcomes](https://mlsanity.com/paper/2410.08770/) (2024)
- [Generalization Bounds and Representation Learning for Estimation of Potential Outcomes and Causal Effects](https://mlsanity.com/paper/2001.07426/) (2020)
- [Treatment effect estimation with disentangled latent factors](https://mlsanity.com/paper/2001.10652/) (2020)
- [Conditional Density Estimation with Bayesian Normalising Flows](https://mlsanity.com/paper/1802.04908/) (2018)
- [High Fidelity Image Counterfactuals with Probabilistic Causal Models](https://mlsanity.com/paper/2306.15764/) (2023)
- [Quantifying Ignorance in Individual-Level Causal-Effect Estimates under Hidden Confounding](https://mlsanity.com/paper/2103.04850/) (2021)
- [Counterfactual Representation Learning with Balancing Weights](https://mlsanity.com/paper/2010.12618/) (2020)

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

- [ORTHOBO: Orthogonal Bayesian Hyperparameter Optimization](https://mlsanity.com/paper/2605.06454/) (2026)

## Abstract (arXiv)

Various deep generative models have been proposed to estimate potential outcomes distributions from observational data. However, none of them have the favorable theoretical property of general Neyman-orthogonality and, associated with it, quasi-oracle efficiency and double robustness. In this paper, we introduce a general suite of generative Neyman-orthogonal (doubly-robust) learners that estimate the conditional distributions of potential outcomes. Our proposed generative doubly-robust learners (GDR-learners) are flexible and can be instantiated with many state-of-the-art deep generative models. In particular, we develop GDR-learners based on (a) conditional normalizing flows (which we call GDR-CNFs), (b) conditional generative adversarial networks (GDR-CGANs), (c) conditional variational autoencoders (GDR-CVAEs), and (d) conditional diffusion models (GDR-CDMs). Unlike the existing methods, our GDR-learners possess the properties of quasi-oracle efficiency and rate double robustness, and are thus asymptotically optimal. In a series of (semi-)synthetic experiments, we demonstrate that our GDR-learners are very effective and outperform the existing methods in estimating the conditional distributions of potential outcomes.