# Latent Space Inference via Paired Autoencoders

arXiv: https://arxiv.org/abs/2601.11397 · HTML: https://mlsanity.com/paper/2601.11397/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 67 references that are in the map.
- First posted on arXiv 16 Jan 2026.

## Builds on (most cited first, 23 of 23)

- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [Adversarial Regularizers in Inverse Problems](https://mlsanity.com/paper/1805.11572/) (2018)
- [PnP-Flow: Plug-and-Play Image Restoration with Flow Matching](https://mlsanity.com/paper/2410.02423/) (2024)
- [Invertible generative models for inverse problems: mitigating representation error and dataset bias](https://mlsanity.com/paper/1905.11672/) (2019)
- [Phase Retrieval Under a Generative Prior](https://mlsanity.com/paper/1807.04261/) (2018)
- [Training-free Linear Image Inverses via Flows](https://mlsanity.com/paper/2310.04432/) (2023)
- [InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences](https://mlsanity.com/paper/2503.11043/) (2025)
- [Stochastic seismic waveform inversion using generative adversarial networks as a geological prior](https://mlsanity.com/paper/1806.03720/) (2018)
- [Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms](https://mlsanity.com/paper/2308.10542/) (2023)
- [PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularization](https://mlsanity.com/paper/2205.12021/) (2022)
- [Learning Regularization Parameters of Inverse Problems via Deep Neural Networks](https://mlsanity.com/paper/2104.06594/) (2021)
- [2DeteCT -- A large 2D expandable, trainable, experimental Computed Tomography dataset for machine learning](https://mlsanity.com/paper/2306.05907/) (2023)
- [Learning from small data sets: Patch-based regularizers in inverse problems for image reconstruction](https://mlsanity.com/paper/2312.16611/) (2023)
- [Paired Autoencoders for Likelihood-free Estimation in Inverse Problems](https://mlsanity.com/paper/2405.13220/) (2024)
- [A Paired Autoencoder Framework for Inverse Problems via Bayes Risk Minimization](https://mlsanity.com/paper/2501.14636/) (2025)
- [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)
- [Deep Optimal Experimental Design for Parameter Estimation Problems](https://mlsanity.com/paper/2406.14003/) (2024)

## Abstract (arXiv)

This work describes a novel data-driven latent space inference framework built on paired autoencoders to handle observational inconsistencies when solving inverse problems. Our approach uses two autoencoders, one for the parameter space and one for the observation space, connected by learned mappings between the autoencoders' latent spaces. These mappings enable a surrogate for regularized inversion and optimization in low-dimensional, informative latent spaces. Our flexible framework can work with partial, noisy, or out-of-distribution data, all while maintaining consistency with the underlying physical models. The paired autoencoders enable reconstruction of corrupted data, and then use the reconstructed data for parameter estimation, which produces more accurate reconstructions compared to paired autoencoders alone and end-to-end encoder-decoders of the same architecture, especially in scenarios with data inconsistencies. We demonstrate our approaches on two imaging examples in medical tomography and geophysical seismic-waveform inversion, but the described approaches are broadly applicable to a variety of inverse problems in scientific and engineering applications.