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.

A.1 Motivation For what purpose was the dataset created?

This dataset covers various topics and is suitable for instruction-tuning general-purpose LLMs for diverse clinical use cases.

Theworddistributions of topics, their optimal transports to the word distributions of documents, and the embeddings of words are learned in a unified framework. When learning thetopic model, weleverage adistilled underlying distance matrix toupdate the topic distributions and smoothly calculate the corresponding optimal transports.

This work was supported by Institute of Information & Communications Technology Planning & Evaluation (IITP) grant (No.2019-0-00075, Artificial Intelligence Graduate School Program(KAIST)), National Research Foundation of Korea (NRF) grant (NRF2020H1D3A2A03100945) andDataVoucher grant(2021-DV-I-P-00114), funded bythe Koreagovernment(MSIT). The dataset contains question-SQL pairs if the question is answerable. Are relationships between individual instances made explicit (e.g., users' movie ratings, socialnetworklinks)? N/A. Arethereanyerrors,sourcesofnoise,orredundanciesinthedataset? Question templates are created to have slots that are later filled with pre-defined values and records from the database. EHRSQL is based on patients in MIMIC-III and eICU.