mlsanityData to 14 Oct 2026

When Additive Noise Meets Unobserved Mediators: Bivariate Denoising Diffusion for Causal Discovery

arXiv 2506.23374 ↗First posted 29 Jun 2025cs.LGcited by 1

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Distinguishing cause and effect from bivariate observational data is a foundational problem in many disciplines, but challenging without additional assumptions. Additive noise models (ANMs) are widely used to enable sample-efficient bivariate causal discovery. However, conventional ANM-based methods fail when unobserved mediators corrupt the causal relationship between variables. This paper makes three key contributions: first, we rigorously characterize why standard ANM approaches break down in the presence of unmeasured mediators. Second, we demonstrate that prior solutions for hidden mediation are brittle in finite sample settings, limiting their practical utility. To address these gaps, we propose Bivariate Denoising Diffusion (BiDD) for causal discovery, a method designed to handle latent noise introduced by unmeasured mediators. Unlike prior methods that infer directionality through mean squared error loss comparisons, our approach introduces a novel independence test statistic: during the noising and denoising processes for each variable, we condition on the other variable as input and evaluate the independence of the predicted noise relative to this input. We prove asymptotic consistency of BiDD under the ANM, and conjecture that it performs well under hidden mediation. Experiments on synthetic and real-world data demonstrate consistent performance, outperforming existing methods in mediator-corrupted settings while maintaining strong performance in mediator-free settings.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 33 of its 70 references that are in the map. First posted on arXiv 29 Jun 2025.

Builds on

33 of 70 references.

Closest ancestors · 3

Same direction, newest first

  1. 2022Diffusion Models for Causal Discovery via Topological Ordering12 Oct
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  3. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 30

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  2. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 752
  3. 2013Causal Discovery with Continuous Additive Noise Modelscited by 255
  4. 2019Learning Sparse Nonparametric DAGscited by 207
  5. 2019Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishingcited by 191
  6. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 191
  7. 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 178
  8. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 161
  9. 2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 140
  10. 2016Identifying Causal Effects With Proxy Variables of an Unmeasured Confoundercited by 139
  11. 2019Lagging Inference Networks and Posterior Collapse in Variational Autoencoderscited by 124
  12. 2022Score matching enables causal discovery of nonlinear additive noise modelscited by 111
18 more
  1. 2021Efficient Neural Causal Discovery without Acyclicity Constraintscited by 82
  2. 2013Learning Equivalence Classes of Bayesian Networks Structurescited by 77
  3. 2022Learning to Induce Causal Structurecited by 68
  4. 2022Greedy Relaxations of the Sparsest Permutation Algorithmcited by 64
  5. 2022On the Identifiability and Estimation of Causal Location-Scale Noise Modelscited by 56
  6. 2023Scalable Causal Discovery with Score Matchingcited by 45
  7. 2023Causal Discovery with Score Matching on Additive Models with Arbitrary Noisecited by 43
  8. 2023A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive Noise Modelscited by 28
  9. 2020Identifying effects of multiple treatments in the presence of unmeasured confoundingcited by 16
  10. 2023Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modelingcited by 16
  11. 2024Ordering-Based Causal Discovery for Linear and Nonlinear Relationscited by 13
  12. 2019Causal Discovery with Cascade Nonlinear Additive Noise Modelscited by 10
  13. 2024Score matching through the roof: linear, nonlinear, and latent variables causal discoverycited by 10
  14. 2024Hybrid Top-Down Global Causal Discovery with Local Search for Linear and Nonlinear Additive Noise Modelscited by 5
  15. 2025Causal Additive Models with Unobserved Causal Paths and Backdoor Pathscited by 5
  16. 2023Causal Discovery via Conditional Independence Testing with Proxy Variablescited by 3
  17. 2023De-confounding causal inference using latent multiple-mediator pathwayscited by 2
  18. 2024LoSAM: Local Search in Additive Noise Models with Mixed Mechanisms and General Noise for Global Causal Discoverycited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Consistency evaluation of benchmarks used for causal discoverycited by 1

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