# Fast Flow Matching based Conditional Independence Tests for Causal Discovery

arXiv: https://arxiv.org/abs/2602.08315 · HTML: https://mlsanity.com/paper/2602.08315/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 24 of its 39 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 24 of 24)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information](https://mlsanity.com/paper/1709.01447/) (2017)
- [Conditional Independence Testing using Generative Adversarial Networks](https://mlsanity.com/paper/1907.04068/) (2019)
- [The Randomized Dependence Coefficient](https://mlsanity.com/paper/1304.7717/) (2013)
- [Double Generative Adversarial Networks for Conditional Independence Testing](https://mlsanity.com/paper/2006.02615/) (2020)
- [FlowTS: Time Series Generation via Rectified Flow](https://mlsanity.com/paper/2411.07506/) (2024)
- [Significance tests of feature relevance for a black-box learner](https://mlsanity.com/paper/2103.04985/) (2021)
- [Causal Discovery with Fewer Conditional Independence Tests](https://mlsanity.com/paper/2406.01823/) (2024)
- [An Asymptotic Test for Conditional Independence using Analytic Kernel Embeddings](https://mlsanity.com/paper/2110.14868/) (2021)
- [Improving Accuracy and Scalability of the PC Algorithm by Maximizing P-value](https://mlsanity.com/paper/1610.00378/) (2016)
- [Conditional Diffusion Models Based Conditional Independence Testing](https://mlsanity.com/paper/2412.11744/) (2024)
- [On the Hardness of Conditional Independence Testing In Practice](https://mlsanity.com/paper/2512.14000/) (2025)
- [Nearest-Neighbor Sampling Based Conditional Independence Testing](https://mlsanity.com/paper/2304.04183/) (2023)
- [Efficient Ensemble Conditional Independence Test Framework for Causal Discovery](https://mlsanity.com/paper/2509.21021/) (2025)
- [From Conditional to Unconditional Independence: Testing Conditional Independence via Transport Maps](https://mlsanity.com/paper/2504.09567/) (2025)
- [Score-based Generative Modeling for Conditional Independence Testing](https://mlsanity.com/paper/2505.23309/) (2025)
- [Testing Conditional Independence via the Spectral Generalized Covariance Measure: Beyond Euclidean Data](https://mlsanity.com/paper/2511.15453/) (2025)

## Abstract (arXiv)

Constraint-based causal discovery methods require a large number of conditional independence (CI) tests, which severely limits their practical applicability due to high computational complexity. Therefore, it is crucial to design an algorithm that accelerates each individual test. To this end, we propose the Flow Matching-based Conditional Independence Test (FMCIT). The proposed test leverages the high computational efficiency of flow matching and requires the model to be trained only once throughout the entire causal discovery procedure, substantially accelerating causal discovery. According to numerical experiments, FMCIT effectively controls type-I error and maintains high testing power under the alternative hypothesis, even in the presence of high-dimensional conditioning sets. In addition, we further integrate FMCIT into a two-stage guided PC skeleton learning framework, termed GPC-FMCIT, which combines fast screening with guided, budgeted refinement using FMCIT. This design yields explicit bounds on the number of CI queries while maintaining high statistical power. Experiments on synthetic and real-world causal discovery tasks demonstrate favorable accuracy-efficiency trade-offs over existing CI testing methods and PC variants.