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.

翻译：我们探讨了从观测数据中识别高维多元结果反事实这一开放性问题。Pearl（2000）指出，反事实必须具有可辨识性（即能够从观测数据分布中恢复）才能为因果论断提供依据。近期关于反事实推断的研究取得了有前景的结果，但缺乏可辨识性保障，这削弱了其估计的因果有效性。为解决这一问题，我们利用连续时间流为多元反事实的可辨识性奠定了理论基础，涵盖了标准准则下的非马尔可夫情形。我们通过动态最优传输工具，刻画了流匹配生成唯一、单调且保序的反事实传输图所需的条件，从而确保了推断的一致性。在此基础上，我们在具有反事实真值的受控场景中验证了该理论，并在真实图像上展示了反事实公理可靠性的改进。