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Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlo

Created by
  • Haebom

Author

Filip Ekstr om Kelvinius, Zheng Zhao, Fredrik Lindsten

Outline

This paper contributes to the research direction of utilizing pre-trained generative diffusion models as prior probabilities for solving Bayesian inverse problems. We design a sequential Monte Carlo method for the linear-Gaussian inverse problem, which is based on "decoupled diffusion", where the generation process is designed to allow larger updates for samples. The method is asymptotically accurate, and we demonstrate the effectiveness of the Decoupled Diffusion Sequential Monte Carlo (DDSMC) algorithm on synthetic data as well as protein and image data. We also show how to extend this approach to discrete data.

Takeaways, Limitations

Takeaways:
We present a new efficient and asymptotically accurate sequential Monte Carlo method (DDSMC) for the linear-Gaussian inverse problem.
Validation of the effectiveness of the DDSMC algorithm on synthetic data, protein data, and image data.
Suggesting the possibility of extension to discrete data.
Decoupled diffusion allows for larger sample updates during generation.
Limitations:
Currently limited to linear-Gaussian inverse problems. Extension studies to nonlinear inverse problems are needed.
Analysis and optimization of the computational complexity of the algorithm is required.
More extensive experimental validation in real-world applications is needed.
Because it focuses on performance evaluation for specific data types, generalizability studies for various data types are needed.
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