# A domain-decomposed VAE method for Bayesian inverse problems

arXiv: https://arxiv.org/abs/2301.05708 · HTML: https://mlsanity.com/paper/2301.05708/

## Key facts

- Cited by 6 papers in the map (data through 7 Oct 2026).
- Builds on 6 of its 39 references that are in the map.
- First posted on arXiv 9 Jan 2023.

## Builds on (most cited first, 6 of 6)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [D3M: A deep domain decomposition method for partial differential equations](https://mlsanity.com/paper/1909.12236/) (2019)
- [Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural network](https://mlsanity.com/paper/1710.09196/) (2017)
- [Bayesian multiscale deep generative model for the solution of high-dimensional inverse problems](https://mlsanity.com/paper/2102.03169/) (2021)

## Built on by (most cited first, 6 of 6)

- [Monte Carlo guided Diffusion for Bayesian linear inverse problems](https://mlsanity.com/paper/2308.07983/) (2023)
- [VI-DGP: A variational inference method with deep generative prior for solving high-dimensional inverse problems](https://mlsanity.com/paper/2302.11173/) (2023)
- [Bayesian ECG reconstruction using denoising diffusion generative models](https://mlsanity.com/paper/2401.05388/) (2023)
- [Noise-Adaptive Diffusion Sampling for Inverse Problems Without Task-Specific Tuning](https://mlsanity.com/paper/2604.16919/) (2026)
- [Dimension-reduced KRnet maps for high-dimensional Bayesian inverse problems](https://mlsanity.com/paper/2303.00573/) (2023)
- [Variational Autoencoder for Generating Broader-Spectrum prior Proposals in Markov chain Monte Carlo Methods](https://mlsanity.com/paper/2507.00020/) (2025)

## Abstract (arXiv)

Bayesian inverse problems are often computationally challenging when the forward model is governed by complex partial differential equations (PDEs). This is typically caused by expensive forward model evaluations and high-dimensional parameterization of priors. This paper proposes a domain-decomposed variational auto-encoder Markov chain Monte Carlo (DD-VAE-MCMC) method to tackle these challenges simultaneously. Through partitioning the global physical domain into small subdomains, the proposed method first constructs local deterministic generative models based on local historical data, which provide efficient local prior representations. Gaussian process models with active learning address the domain decomposition interface conditions. Then inversions are conducted on each subdomain independently in parallel and in low-dimensional latent parameter spaces. The local inference solutions are post-processed through the Poisson image blending procedure to result in an efficient global inference result. Numerical examples are provided to demonstrate the performance of the proposed method.