# Paired Autoencoders for Likelihood-free Estimation in Inverse Problems

arXiv: https://arxiv.org/abs/2405.13220 · HTML: https://mlsanity.com/paper/2405.13220/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 64 references that are in the map.
- First posted on arXiv 21 May 2024.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [A Survey on Generative Diffusion Model](https://mlsanity.com/paper/2209.02646/) (2022)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [InversionNet: A Real-Time and Accurate Full Waveform Inversion with CNNs and continuous CRFs](https://mlsanity.com/paper/1811.07875/) (2018)
- [Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustness](https://mlsanity.com/paper/2305.17289/) (2023)
- [Solving Linear Inverse Problems Using GAN Priors: An Algorithm with Provable Guarantees](https://mlsanity.com/paper/1802.08406/) (2018)
- [A Plug-and-Play Method for Controlled Text Generation](https://mlsanity.com/paper/2109.09707/) (2021)
- [Neural Proximal Gradient Descent for Compressive Imaging](https://mlsanity.com/paper/1806.03963/) (2018)
- [Anomaly Detection With Conditional Variational Autoencoders](https://mlsanity.com/paper/2010.05531/) (2020)
- [Solving Bayesian Inverse Problems via Variational Autoencoders](https://mlsanity.com/paper/1912.04212/) (2019)
- [Likelihood-Free Parameter Estimation with Neural Bayes Estimators](https://mlsanity.com/paper/2208.12942/) (2022)
- [A prior regularized full waveform inversion using generative diffusion models](https://mlsanity.com/paper/2306.12776/) (2023)
- [Deep D-bar: Real time Electrical Impedance Tomography Imaging with Deep Neural Networks](https://mlsanity.com/paper/1711.03180/) (2017)
- [Solving Inverse Problems by Joint Posterior Maximization with Autoencoding Prior](https://mlsanity.com/paper/2103.01648/) (2021)
- [Neural Density Estimation and Likelihood-free Inference](https://mlsanity.com/paper/1910.13233/) (2019)
- [Learning Regularization Parameters of Inverse Problems via Deep Neural Networks](https://mlsanity.com/paper/2104.06594/) (2021)
- [Total-variation regularization strategies in full-waveform inversion](https://mlsanity.com/paper/1608.06159/) (2016)
- [Solving Electrical Impedance Tomography with Deep Learning](https://mlsanity.com/paper/1906.03944/) (2019)
- [Deep Learning Methods for Solving Linear Inverse Problems: Research Directions and Paradigms](https://mlsanity.com/paper/2007.13290/) (2020)
- [WISE: full-Waveform variational Inference via Subsurface Extensions](https://mlsanity.com/paper/2401.06230/) (2023)
- [DRIP: Deep Regularizers for Inverse Problems](https://mlsanity.com/paper/2304.00015/) (2023)
- [An Over Complete Deep Learning Method for Inverse Problems](https://mlsanity.com/paper/2402.04653/) (2024)

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

- [Good Things Come in Pairs: Paired Autoencoders for Inverse Problems](https://mlsanity.com/paper/2505.06549/) (2025)
- [Latent Twins](https://mlsanity.com/paper/2509.20615/) (2025)
- [Optimal Linear Baseline Models for Scientific Machine Learning](https://mlsanity.com/paper/2508.05831/) (2025)
- [Neural Optimal Design of Experiment for Inverse Problems](https://mlsanity.com/paper/2512.23763/) (2025)
- [Latent Space Inference via Paired Autoencoders](https://mlsanity.com/paper/2601.11397/) (2026)
- [Variational Sparse Paired Autoencoders (vsPAIR) for Inverse Problems and Uncertainty Quantification](https://mlsanity.com/paper/2602.02948/) (2026)

## Abstract (arXiv)

We consider the solution of nonlinear inverse problems where the forward problem is a discretization of a partial differential equation. Such problems are notoriously difficult to solve in practice and require minimizing a combination of a data-fit term and a regularization term. The main computational bottleneck of typical algorithms is the direct estimation of the data misfit. Therefore, likelihood-free approaches have become appealing alternatives. Nonetheless, difficulties in generalization and limitations in accuracy have hindered their broader utility and applicability. In this work, we use a paired autoencoder framework as a likelihood-free estimator for inverse problems. We show that the use of such an architecture allows us to construct a solution efficiently and to overcome some known open problems when using likelihood-free estimators. In particular, our framework can assess the quality of the solution and improve on it if needed. We demonstrate the viability of our approach using examples from full waveform inversion and inverse electromagnetic imaging.