Smoothing the Landscape: Causal Structure Learning via Diffusion Denoising Objectives

2026-04-02

AI Summary

This work addresses the challenges of instability and poor scalability in high-dimensional causal structure learning under feature-sample imbalance. It introduces, for the first time, the denoising score-matching objective from diffusion models into causal discovery, leveraging smoothed gradients to enhance training stability. Additionally, the authors propose an adaptive k-hop acyclicity constraint that eliminates the need for matrix inversion, substantially improving computational efficiency. The method demonstrates superior performance on synthetic benchmarks and validates its effectiveness and practicality on two real-world datasets, offering a novel paradigm for large-scale causal graph inference.

Technology Category

Machine Learning: Causal LearningReasoning under Uncertainty: CausalityConstraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingSemantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

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.

Problem

• causal structure learning
• Bayesian Networks
• Directed Acyclic Graphs
• high-dimensional data
• feature-sample imbalance

Innovation

• diffusion denoising
• causal discovery
• acyclicity constraint
• score matching
• Bayesian networks