# Learning Structural Causal Models from Ordering: Identifiable Flow Models

arXiv: https://arxiv.org/abs/2412.09843 · HTML: https://mlsanity.com/paper/2412.09843/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 42 references that are in the map.
- First posted on arXiv 13 Dec 2024.

## Builds on (most cited first, 7 of 7)

- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [Relating Graph Neural Networks to Structural Causal Models](https://mlsanity.com/paper/2109.04173/) (2021)
- [Neural Structure Learning with Stochastic Differential Equations](https://mlsanity.com/paper/2311.03309/) (2023)
- [A Fixed-Point Approach for Causal Generative Modeling](https://mlsanity.com/paper/2404.06969/) (2024)
- [From Ordinary Differential Equations to Structural Causal Models: the deterministic case](https://mlsanity.com/paper/1304.7920/) (2013)

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

- [Amortized Counterfactual Prediction with Graph Neural Networks](https://mlsanity.com/paper/2610.13724/) (2026)

## Abstract (arXiv)

In this study, we address causal inference when only observational data and a valid causal ordering from the causal graph are available. We introduce a set of flow models that can recover component-wise, invertible transformation of exogenous variables. Our flow-based methods offer flexible model design while maintaining causal consistency regardless of the number of discretization steps. We propose design improvements that enable simultaneous learning of all causal mechanisms and reduce abduction and prediction complexity to linear O(n) relative to the number of layers, independent of the number of causal variables. Empirically, we demonstrate that our method outperforms previous state-of-the-art approaches and delivers consistent performance across a wide range of structural causal models in answering observational, interventional, and counterfactual questions. Additionally, our method achieves a significant reduction in computational time compared to existing diffusion-based techniques, making it practical for large structural causal models.