# Deep Variational Inverse Scattering

arXiv: https://arxiv.org/abs/2212.04309 · HTML: https://mlsanity.com/paper/2212.04309/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 40 references that are in the map.
- First posted on arXiv 8 Dec 2022.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [A Variational U-Net for Conditional Appearance and Shape Generation](https://mlsanity.com/paper/1804.04694/) (2018)
- [Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imaging](https://mlsanity.com/paper/2010.14462/) (2020)
- [Evaluating Uncertainty Quantification in End-to-End Autonomous Driving Control](https://mlsanity.com/paper/1811.06817/) (2018)
- [Composing Normalizing Flows for Inverse Problems](https://mlsanity.com/paper/2002.11743/) (2020)
- [Trumpets: Injective Flows for Inference and Inverse Problems](https://mlsanity.com/paper/2102.10461/) (2021)
- [Data-Driven Model Reduction for the Bayesian Solution of Inverse Problems](https://mlsanity.com/paper/1403.4290/) (2014)
- [A Comparison of Uncertainty Estimation Approaches in Deep Learning Components for Autonomous Vehicle Applications](https://mlsanity.com/paper/2006.15172/) (2020)
- [Conditional Injective Flows for Bayesian Imaging](https://mlsanity.com/paper/2204.07664/) (2022)
- [Deep Bayesian inference for seismic imaging with tasks](https://mlsanity.com/paper/2110.04825/) (2021)
- [Faster Uncertainty Quantification for Inverse Problems with Conditional Normalizing Flows](https://mlsanity.com/paper/2007.07985/) (2020)
- [Implicit Neural Representation for Mesh-Free Inverse Obstacle Scattering](https://mlsanity.com/paper/2206.02027/) (2022)
- [j-Wave: An open-source differentiable wave simulator](https://mlsanity.com/paper/2207.01499/) (2022)
- [Fast uncertainty quantification of reservoir simulation with variational U-Net](https://mlsanity.com/paper/1907.00718/) (2019)

## Built on by (most cited first, 2 of 2)

- [Deep Injective Prior for Inverse Scattering](https://mlsanity.com/paper/2301.03092/) (2023)
- [A Model-Guided Neural Network Method for the Inverse Scattering Problem](https://mlsanity.com/paper/2512.10123/) (2025)

## Abstract (arXiv)

Inverse medium scattering solvers generally reconstruct a single solution without an associated measure of uncertainty. This is true both for the classical iterative solvers and for the emerging deep learning methods. But ill-posedness and noise can make this single estimate inaccurate or misleading. While deep networks such as conditional normalizing flows can be used to sample posteriors in inverse problems, they often yield low-quality samples and uncertainty estimates. In this paper, we propose U-Flow, a Bayesian U-Net based on conditional normalizing flows, which generates high-quality posterior samples and estimates physically-meaningful uncertainty. We show that the proposed model significantly outperforms the recent normalizing flows in terms of posterior sample quality while having comparable performance with the U-Net in point estimation.