# Counterfactual Identifiability via Dynamic Optimal Transport

arXiv: https://arxiv.org/abs/2510.08294 · HTML: https://mlsanity.com/paper/2510.08294/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 84 references that are in the map.
- First posted on arXiv 9 Oct 2025.

## Builds on (most cited first, 30 of 52)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [Causality matters in medical imaging](https://mlsanity.com/paper/1912.08142/) (2019)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [Causal Autoregressive Flows](https://mlsanity.com/paper/2011.02268/) (2020)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (2013)
- [Diffusion Causal Models for Counterfactual Estimation](https://mlsanity.com/paper/2202.10166/) (2022)
- [External Validity: From Do-Calculus to Transportability Across Populations](https://mlsanity.com/paper/1503.01603/) (2015)
- [Causal structure based root cause analysis of outliers](https://mlsanity.com/paper/1912.02724/) (2019)
- [Sample-Efficient Reinforcement Learning via Counterfactual-Based Data Augmentation](https://mlsanity.com/paper/2012.09092/) (2020)
- [Identifiability of latent-variable and structural-equation models: from linear to nonlinear](https://mlsanity.com/paper/2302.02672/) (2023)
- [Neural Causal Models for Counterfactual Identification and Estimation](https://mlsanity.com/paper/2210.00035/) (2022)
- [On the Identifiability and Estimation of Causal Location-Scale Noise Models](https://mlsanity.com/paper/2210.09054/) (2022)
- [High Fidelity Image Counterfactuals with Probabilistic Causal Models](https://mlsanity.com/paper/2306.15764/) (2023)
- [Causal normalizing flows: from theory to practice](https://mlsanity.com/paper/2306.05415/) (2023)
- [MoCoDA: Model-based Counterfactual Data Augmentation](https://mlsanity.com/paper/2210.11287/) (2022)

## Built on by (most cited first, 6 of 6)

- [Scaling Generative Foundation Models for Chest Radiography with Rectified Flow Transformers](https://mlsanity.com/paper/2606.19460/) (2026)
- [Pixel-level Counterfactual Contrastive Learning for Medical Image Segmentation](https://mlsanity.com/paper/2603.17110/) (2026)
- [Elucidating the Design Space of Flow Matching for Cellular Microscopy](https://mlsanity.com/paper/2603.26790/) (2026)
- [Generating Chest X-Ray Counterfactuals by Specialising Foundation Image Models](https://mlsanity.com/paper/2609.24879/) (2026)
- [Counterfactual Stress Testing for Image Classification Models](https://mlsanity.com/paper/2605.10894/) (2026)
- [Amortized Counterfactual Prediction with Graph Neural Networks](https://mlsanity.com/paper/2610.13724/) (2026)

## Abstract (arXiv)

We address the open question of counterfactual identification for high-dimensional multivariate outcomes from observational data. Pearl (2000) argues that counterfactuals must be identifiable (i.e., recoverable from the observed data distribution) to justify causal claims. A recent line of work on counterfactual inference shows promising results but lacks identification, undermining the causal validity of its estimates. To address this, we establish a foundation for multivariate counterfactual identification using continuous-time flows, including non-Markovian settings under standard criteria. We characterise the conditions under which flow matching yields a unique, monotone, and rank-preserving counterfactual transport map with tools from dynamic optimal transport, ensuring consistent inference. Building on this, we validate the theory in controlled scenarios with counterfactual ground-truth and demonstrate improvements in axiomatic counterfactual soundness on real images.