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arXiv · 2510.08294

Counterfactual Identifiability via Dynamic Optimal Transport

Fabio De Sousa Ribeiro·Ainkaran Santhirasekaram·Ben Glocker
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Abstract

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.

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Fabio De Sousa Ribeiro, Ainkaran Santhirasekaram, Ben Glocker. 2025-10-09. Counterfactual Identifiability via Dynamic Optimal Transport. https://arxiv.org/abs/2510.08294

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