Smoothing the Landscape: Causal Structure Learning via Diffusion Denoising Objectives

TL;DR

This paper introduces DDCD, a new method for causal structure learning that leverages diffusion denoising objectives for improved stability and efficiency, demonstrated on synthetic and real-world data.

Contribution

The paper proposes DDCD, a novel diffusion-based framework for causal discovery that enhances scalability and stability over existing methods.

Findings

DDCD achieves competitive results on synthetic benchmarks.

DDCD demonstrates practical utility in real-world causal analysis.

The method improves convergence stability and runtime efficiency.

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.