# Counterfactual Generative Modeling with Variational Causal Inference

arXiv: https://arxiv.org/abs/2410.12730 · HTML: https://mlsanity.com/paper/2410.12730/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 57 references that are in the map.
- First posted on arXiv 16 Oct 2024.

## Builds on (most cited first, 30 of 36)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Images](https://mlsanity.com/paper/2011.10650/) (2020)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA](https://mlsanity.com/paper/2107.10098/) (2021)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Weakly supervised causal representation learning](https://mlsanity.com/paper/2203.16437/) (2022)
- [Counterfactual Generative Networks](https://mlsanity.com/paper/2101.06046/) (2021)
- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [Independent mechanism analysis, a new concept?](https://mlsanity.com/paper/2106.05200/) (2021)
- [Diffusion Causal Models for Counterfactual Estimation](https://mlsanity.com/paper/2202.10166/) (2022)
- [Weakly Supervised Disentanglement with Guarantees](https://mlsanity.com/paper/1910.09772/) (2019)
- [Weakly Supervised Disentangled Generative Causal Representation Learning](https://mlsanity.com/paper/2010.02637/) (2020)
- [Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICA](https://mlsanity.com/paper/2106.09620/) (2021)
- [Morpho-MNIST: Quantitative Assessment and Diagnostics for Representation Learning](https://mlsanity.com/paper/1809.10780/) (2018)
- [Evaluating and Mitigating Bias in Image Classifiers: A Causal Perspective Using Counterfactuals](https://mlsanity.com/paper/2009.08270/) (2020)
- [High Fidelity Image Counterfactuals with Probabilistic Causal Models](https://mlsanity.com/paper/2306.15764/) (2023)
- [Counterfactual Fairness with Disentangled Causal Effect Variational Autoencoder](https://mlsanity.com/paper/2011.11878/) (2020)
- [Deep Generative Stochastic Networks Trainable by Backprop](https://mlsanity.com/paper/1306.1091/) (2013)
- [Measuring axiomatic soundness of counterfactual image models](https://mlsanity.com/paper/2303.01274/) (2023)
- [Benchmarking Counterfactual Image Generation](https://mlsanity.com/paper/2403.20287/) (2024)

## Built on by (most cited first, 11 of 11)

- [Diffusion Counterfactual Generation with Semantic Abduction](https://mlsanity.com/paper/2506.07883/) (2025)
- [Counterfactual Identifiability via Dynamic Optimal Transport](https://mlsanity.com/paper/2510.08294/) (2025)
- [Causal-Adapter: Taming Text-to-Image Diffusion for Faithful Counterfactual Generation](https://mlsanity.com/paper/2509.24798/) (2025)
- [TimeSqueeze: Dynamic Patching for Efficient Time Series Forecasting](https://mlsanity.com/paper/2603.11352/) (2026)
- [Cross-World Assumption and Refining Prediction Intervals for Individual Treatment Effects](https://mlsanity.com/paper/2507.12581/) (2025)
- [Synthesising Counterfactual Explanations via Label-Conditional Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/2510.04855/) (2025)
- [Cyclic Counterfactuals under Shift-Scale Interventions](https://mlsanity.com/paper/2510.25005/) (2025)
- [Are Good Generators Good Decision-Makers? Policy Learning for General Interventions via Retargeted Counterfactual Generation](https://mlsanity.com/paper/2606.07399/) (2026)
- [Semi-Supervised Conditional Diffusion via Label Augmentation](https://mlsanity.com/paper/2607.16685/) (2026)
- [CAFE: Counterfactual Prediction via Fast Posterior Estimation](https://mlsanity.com/paper/2609.32167/) (2026)
- [Amortized Counterfactual Prediction with Graph Neural Networks](https://mlsanity.com/paper/2610.13724/) (2026)

## Abstract (arXiv)

Estimating an individual's counterfactual outcomes under interventions is a challenging task for traditional causal inference and supervised learning approaches when the outcome is high-dimensional (e.g. gene expressions, facial images) and covariates are relatively limited. In this case, to predict one's outcomes under counterfactual treatments, it is crucial to leverage individual information contained in the observed outcome in addition to the covariates. Prior works using variational inference in counterfactual generative modeling have been focusing on neural adaptations and model variants within the conditional variational autoencoder formulation, which we argue is fundamentally ill-suited to the notion of counterfactual in causal inference. In this work, we present a novel variational Bayesian causal inference framework and its theoretical backings to properly handle counterfactual generative modeling tasks, through which we are able to conduct counterfactual supervision end-to-end during training without any counterfactual samples, and encourage disentangled exogenous noise abduction that aids the correct identification of causal effect in counterfactual generations. In experiments, we demonstrate the advantage of our framework compared to state-of-the-art models in counterfactual generative modeling on multiple benchmarks.