mlsanityData to 14 Oct 2026

Smoothing the Landscape: Causal Structure Learning via Diffusion Denoising Objectives

arXiv 2604.02250 ↗First posted 2 Apr 2026cs.LG stat.MLcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Understanding causal dependencies in observational data is critical for informing decision-making. These relationships are often modeled as Bayesian Networks (BNs) and Directed Acyclic Graphs (DAGs). Existing methods, such as NOTEARS and DAG-GNN, often face issues with scalability and stability in high-dimensional data, especially when there is a feature-sample imbalance. Here, we show that the denoising score matching objective of diffusion models could smooth the gradients for faster, more stable convergence. We also propose an adaptive k-hop acyclicity constraint that improves runtime over existing solutions that require matrix inversion. We name this framework Denoising Diffusion Causal Discovery (DDCD). Unlike generative diffusion models, DDCD utilizes the reverse denoising process to infer a parameterized causal structure rather than to generate data. We demonstrate the competitive performance of DDCDs on synthetic benchmarking data. We also show that our methods are practically useful by conducting qualitative analyses on two real-world examples. Code is available at this url: https://github.com/haozhu233/ddcd.

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 35 of its 73 references that are in the map. First posted on arXiv 2 Apr 2026.

Builds on

35 of 73 references.

Closest ancestors · 4

Same direction, newest first

  1. 2022Diffusion Models for Causal Discovery via Topological Ordering12 Oct
  2. 2022Understanding Diffusion Models: A Unified Perspective25 Aug
  3. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  4. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 31

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  3. 2017Deep Setscited by 1,421
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  5. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 752
  6. 2019DAG-GNN: DAG Structure Learning with Graph Neural Networkscited by 331
  7. 2013Causal Discovery with Continuous Additive Noise Modelscited by 255
  8. 2019Gradient-Based Neural DAG Learningcited by 227
  9. 2020Differentiable Causal Discovery from Interventional Datacited by 218
  10. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 211
  11. 2020DYNOTEARS: Structure Learning from Time-Series Datacited by 200
  12. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 191
19 more
  1. 2021Discrete Graph Structure Learning for Forecasting Multiple Time Seriescited by 171
  2. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 161
  3. 2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 140
  4. 2019Masked Gradient-Based Causal Structure Learningcited by 89
  5. 2013High-dimensional learning of linear causal networks via inverse covariance estimationcited by 87
  6. 2020Weakly Supervised Disentangled Generative Causal Representation Learningcited by 68
  7. 2020DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networkscited by 66
  8. 2019A Graph Autoencoder Approach to Causal Structure Learningcited by 55
  9. 2021DAGs with No Curl: An Efficient DAG Structure Learning Approachcited by 53
  10. 2018Structural Agnostic Modeling: Adversarial Learning of Causal Graphscited by 48
  11. 2021Unsuitability of NOTEARS for Causal Graph Discoverycited by 47
  12. 2019Scaling structural learning with NO-BEARS to infer causal transcriptome networkscited by 39
  13. 2023Structure Learning with Continuous Optimization: A Sober Look and Beyondcited by 36
  14. 2021NTS-NOTEARS: Learning Nonparametric DBNs With Prior Knowledgecited by 33
  15. 2023Stable Differentiable Causal Discoverycited by 31
  16. 2023Optimizing NOTEARS Objectives via Topological Swapscited by 17
  17. 2020Efficient and Scalable Structure Learning for Bayesian Networks: Algorithms and Applicationscited by 11
  18. 2025Penalized FCI for Causal Structure Learning in a Sparse DAG for Biomarker Discovery in Parkinson's Diseasecited by 4
  19. 2025dcFCI: Robust Causal Discovery Under Latent Confounding, Unfaithfulness, and Mixed Datacited by 1

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  6. 2025Diffusion Models: A Mathematical Introduction
  7. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions
  8. 2025Test-Time Scaling of Diffusion Models via Noise Trajectory Search