# Causally Consistent Normalizing Flow

arXiv: https://arxiv.org/abs/2412.12401 · HTML: https://mlsanity.com/paper/2412.12401/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 19 references that are in the map.
- First posted on arXiv 16 Dec 2024.

## Builds on (most cited first, 12 of 12)

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Causal Autoregressive Flows](https://mlsanity.com/paper/2011.02268/) (2020)
- [Diffusion Causal Models for Counterfactual Estimation](https://mlsanity.com/paper/2202.10166/) (2022)
- [Directed Acyclic Graph Neural Networks](https://mlsanity.com/paper/2101.07965/) (2021)
- [Neural Causal Models for Counterfactual Identification and Estimation](https://mlsanity.com/paper/2210.00035/) (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)
- [Indeterminacy in Generative Models: Characterization and Strong Identifiability](https://mlsanity.com/paper/2206.00801/) (2022)
- [From Identifiable Causal Representations to Controllable Counterfactual Generation: A Survey on Causal Generative Modeling](https://mlsanity.com/paper/2310.11011/) (2023)

## Abstract (arXiv)

Causal inconsistency arises when the underlying causal graphs captured by generative models like textitNormalizing Flows (NFs) are inconsistent with those specified in causal models like textitStruct Causal Models (SCMs). This inconsistency can cause unwanted issues including the unfairness problem. Prior works to achieve causal consistency inevitably compromise the expressiveness of their models by disallowing hidden layers. In this work, we introduce a new approach: Causally Consistent Normalizing Flow (CCNF). To the best of our knowledge, CCNF is the first causally consistent generative model that can approximate any distribution with multiple layers. CCNF relies on two novel constructs: a sequential representation of SCMs and partial causal transformations. These constructs allow CCNF to inherently maintain causal consistency without sacrificing expressiveness. CCNF can handle all forms of causal inference tasks, including interventions and counterfactuals. Through experiments, we show that CCNF outperforms current approaches in causal inference. We also empirically validate the practical utility of CCNF by applying it to real-world datasets and show how CCNF addresses challenges like unfairness effectively.