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The paper introduces Denoising Diffusion Causal Discovery (DDCD), a novel framework for learning causal structures from observational data. DDCD leverages the denoising score matching objective of diffusion models to smooth gradients, leading to faster and more stable convergence, particularly in high-dimensional, feature-sample imbalanced settings. The method also incorporates an adaptive k-hop acyclicity constraint to improve runtime performance, demonstrating competitive results on synthetic benchmarks and practical utility on real-world datasets.
Diffusion models, typically used for generation, can now efficiently learn causal structures by smoothing gradients and avoiding expensive matrix inversions.
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.
