# Solving Bayesian Inverse Problems via Variational Autoencoders

arXiv: https://arxiv.org/abs/1912.04212 · HTML: https://mlsanity.com/paper/1912.04212/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2019.

## Built on by (most cited first, 30 of 32)

- [Neural Methods for Amortized Inference](https://mlsanity.com/paper/2404.12484/) (2024)
- [Solution of Physics-based Bayesian Inverse Problems with Deep Generative Priors](https://mlsanity.com/paper/2107.02926/) (2021)
- [The efficacy and generalizability of conditional GANs for posterior inference in physics-based inverse problems](https://mlsanity.com/paper/2202.07773/) (2022)
- [InVAErt networks: a data-driven framework for model synthesis and identifiability analysis](https://mlsanity.com/paper/2307.12586/) (2023)
- [Paired Autoencoders for Likelihood-free Estimation in Inverse Problems](https://mlsanity.com/paper/2405.13220/) (2024)
- [Utilizing variational autoencoders in the Bayesian inverse problem of photoacoustic tomography](https://mlsanity.com/paper/2204.06270/) (2022)
- [Phi-DVAE: Physics-Informed Dynamical Variational Autoencoders for Unstructured Data Assimilation](https://mlsanity.com/paper/2209.15609/) (2022)
- [Quantifying uncertainty for deep learning based forecasting and flow-reconstruction using neural architecture search ensembles](https://mlsanity.com/paper/2302.09748/) (2023)
- [Good Things Come in Pairs: Paired Autoencoders for Inverse Problems](https://mlsanity.com/paper/2505.06549/) (2025)
- [Variational Bayes image restoration with compressive autoencoders](https://mlsanity.com/paper/2311.17744/) (2023)
- [A Primer on Variational Inference for Physics-Informed Deep Generative Modelling](https://mlsanity.com/paper/2409.06560/) (2024)
- [Generative AI for Autonomous Driving: A Review](https://mlsanity.com/paper/2505.15863/) (2025)
- [Adversarial Disentanglement by Backpropagation with Physics-Informed Variational Autoencoder](https://mlsanity.com/paper/2506.13658/) (2025)
- [An invertible generative model for forward and inverse problems](https://mlsanity.com/paper/2509.03910/) (2025)
- [Dimension-reduced KRnet maps for high-dimensional Bayesian inverse problems](https://mlsanity.com/paper/2303.00573/) (2023)
- [An autoencoder compression approach for accelerating large-scale inverse problems](https://mlsanity.com/paper/2304.04781/) (2023)
- [Goal-oriented Uncertainty Quantification for Inverse Problems via Variational Encoder-Decoder Networks](https://mlsanity.com/paper/2304.08324/) (2023)
- [Learning WENO for entropy stable schemes to solve conservation laws](https://mlsanity.com/paper/2403.14848/) (2024)
- [Bi-level Guided Diffusion Models for Zero-Shot Medical Imaging Inverse Problems](https://mlsanity.com/paper/2404.03706/) (2024)
- [Diffusion assisted image reconstruction in optoacoustic tomography](https://mlsanity.com/paper/2404.10239/) (2024)
- [Integrating Physics of the Problem into Data-Driven Methods to Enhance Elastic Full-Waveform Inversion with Uncertainty Quantification](https://mlsanity.com/paper/2406.05153/) (2024)
- [Bayesian Inverse Problems Meet Flow Matching: Efficient and Flexible Inference via Transformers](https://mlsanity.com/paper/2503.01375/) (2025)
- [Geometric Autoencoder Priors for Bayesian Inversion: Learn First Observe Later](https://mlsanity.com/paper/2509.19929/) (2025)
- [LLM-Based Test Oracles: Source-of-Authority Taxonomy -- A Systematic Literature Review](https://mlsanity.com/paper/2607.05031/) (2026)
- [Enhanced uncertainty quantification variational autoencoders for the solution of Bayesian inverse problems](https://mlsanity.com/paper/2502.13105/) (2025)
- [Optimal Linear Baseline Models for Scientific Machine Learning](https://mlsanity.com/paper/2508.05831/) (2025)
- [Diffusion for Fusion: Designing Stellarators with Generative AI](https://mlsanity.com/paper/2511.20445/) (2025)
- [Variational Sparse Paired Autoencoders (vsPAIR) for Inverse Problems and Uncertainty Quantification](https://mlsanity.com/paper/2602.02948/) (2026)
- [Multiparameter Uncertainty Mapping in Quantitative Molecular MRI using a Physics-Structured Variational Autoencoder (PS-VAE)](https://mlsanity.com/paper/2602.03317/) (2026)
- [UOTIP: Unbalanced Optimal Transport Map for Unpaired Inverse Problems](https://mlsanity.com/paper/2605.21094/) (2026)

## Abstract (arXiv)

In recent years, the field of machine learning has made phenomenal progress in the pursuit of simulating real-world data generation processes. One notable example of such success is the variational autoencoder (VAE). In this work, with a small shift in perspective, we leverage and adapt VAEs for a different purpose: uncertainty quantification in scientific inverse problems. We introduce UQ-VAE: a flexible, adaptive, hybrid data/model-informed framework for training neural networks capable of rapid modelling of the posterior distribution representing the unknown parameter of interest. Specifically, from divergence-based variational inference, our framework is derived such that most of the information usually present in scientific inverse problems is fully utilized in the training procedure. Additionally, this framework includes an adjustable hyperparameter that allows selection of the notion of distance between the posterior model and the target distribution. This introduces more flexibility in controlling how optimization directs the learning of the posterior model. Further, this framework possesses an inherent adaptive optimization property that emerges through the learning of the posterior uncertainty.