Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priors

This is the official implementation of Blade, a derivative-free Bayesian inversion method that leverages diffusion model priors for solving inverse problems.

Abstract

Derivative-free Bayesian inversion is an important task in many science and engineering applications, particularly when computing the forward model derivative is computationally and practically challenging. Blade produces accurate and well-calibrated posteriors for Bayesian inversion using an ensemble of interacting particles. It leverages powerful data-driven priors based on diffusion models and can handle nonlinear forward models that permit only black-box access (i.e., derivative-free).

Installation

We recommend Linux with Python 3.10+ for the best compatibility. Use uv sync to install the dependencies.

Pretrained Models

This codebase uses pretrained diffusion models from InverseBench. Please download the checkpoints from InverseBench and place them in the checkpoints/ directory.

How to run experiments

Examples: Navier-Stokes Inverse Problems

python main.py algorithm=blade \
    algorithm.method.num_steps=25 \
    algorithm.method.likelihood_steps=50 \
    algorithm.method.guidance_scale=30.0 \
    problem.model.sigma_noise=1.0

scripts/ns.sh contains the commands to run Blade on Navier-Stokes.

Evaluation Metrics

For Navier-Stokes experiments, we extend the original InverseBench evaluation with probabilistic metrics to assess the generated posterior distribution:

Metric	Type	Description
CRPS	Probabilistic	Continuous Ranked Probability Score - measures calibration and sharpness
SSR	Probabilistic	Spread-Skill Ratio - ideal value is 1.0 (SSR < 1: overconfident, SSR > 1: underconfident)

Examples: Linear Gaussian and Gaussian Mixture Problems

# Linear Gaussian with Blade
python gaussian.py algorithm=blade_gaussian

# Gaussian Mixture with Blade
python gmm-exp.py algorithm=blade_gmm

Configuration

The project uses Hydra for configuration management. Configuration files are located in configs/:

• configs/config.yaml - Main configuration with defaults
• configs/algorithm/ - Algorithm-specific configs (blade.yaml, enkg.yaml, etc.)
• configs/pretrain/ - Pretrained model configs
• configs/problem/ - Problem-specific configs

Override any configuration from the command line:

python main.py algorithm=blade algorithm.method.num_steps=50 problem.model.sigma_noise=0.5

Citation

If you find this code useful, please cite our paper:

@article{zheng2025blade,
  title={Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priors},
  author={Zheng, Hongkai and Wang, Austin and Wu, Zihui and Huang, Zhengyu and Baptista, Ricardo and Yue, Yisong},
  journal={arXiv preprint arXiv:2510.10968},
  year={2025}
}

Acknowledgments

This codebase is built upon InverseBench. We thank the authors for their excellent work and for making their code publicly available.

License

This project is licensed under the MIT License - see the LICENSE file for details.