This repository contains the code for our paper When Additive Noise Meets Unobserved Mediators: Bivariate Denoising for Causal Discovery

When using this code, please cite the following:

@inproceedings{
    bidd2025,
    title={When Additive Noise Meets Unobserved Mediators: Bivariate Denoising Diffusion for Causal Discovery},
    author={Dominik Meier and Sujai Hiremath and Promit Ghosal and Kyra Gan},
    booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
    year={2025},
    url={https://arxiv.org/abs/2503.04556}
}

You can install this package directly:

# Install from source
git clone https://github.com/XPerianer/diffusion-discovery
cd diffusion-discovery
pip install -e .

Then use the bidd function in your code. See demo_script for a simple example.

The bidd function takes a config argument for configuring how to run.

Most important options:

• epochs: (int) Number of training epochs (default: 2000)
• hidden_dim: (int) Size of the hidden layers in the neural network (default: 512)
• num_blocks: (int) Number of residual blocks in the model (default: 2)
• learning_rate: (float) Learning rate for training (default: 1e-4)
• train_test_split: (float) Fraction of data used for training (default: 0.8)

For all available options, see diffusion_discovery/simple_interface.py.

For more advanced usages, like reusing of the trained diffusion model, you can use the structure of diffusion_discovery/simple_interface.py, and call the functions themselves.

For our experiments, we used python3.11. We recommend setting up a conda environment:

conda create -n discovery311 python=3.11; conda activate discovery311; conda install pytorch torchvision torchaudio -c pytorch-nightly

Then installing the requirements with:

pip install -r requirements.txt

To install additional requirements for baselines and NPEET, you can run

bash install_requirements.bash

The repository includes automated tests via GitHub Actions:

Verifies that:

• The package installs correctly across Python 3.10-3.11
• The bidd function can be imported and executed
• The demo script runs successfully

Runs the test suite to verify functionality for data generation:

# Install test dependencies
pip install -e ".[test]"

# Run all tests
pytest


# Reproduce the experimental results for BiDD

We provide three different scripts to run the experiments, which use the `sacred` package to generate test files:
- `experiments/run_diffusion.py` runs BiDD.
- `experiments/run_canm.py` runs CANM.
- `experiments/run_baselines.py` runs the baselines.

To run the experiments for the different mechanism tables, run:
```bash
cd experiments
python run_experiments_mechanism_table.py

To run the experiments for the depth and sample size tables, run:

cd experiments
python run_experiments_depth_tanh_uniform.py
python run_experiments_sample_size_tanh_uniform.py

To run the experiments for the Tübingen cause-effect pair, run:

cd experiments
python run_experiments_tuebingen_3000.py

The experiment scripts generate data in the results folder, which can be analyzed using Jupyter notebook .ipynb files in the experiments/ folder.

Key analysis notebooks include:

• experiments/data_analysis_diffusion_mechanism_table.ipynb
• experiments/data_analysis_diffusion_depth_table.ipynb
• experiments/data_analysis_diffusion_sample_size_table.ipynb
• experiments/data_analysis_tuebingen.ipynb