# Learning to solve inverse problems using Wasserstein loss

arXiv: https://arxiv.org/abs/1710.10898 · HTML: https://mlsanity.com/paper/1710.10898/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2017.

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- [Surface Topography Characterization Using a Simple Optical Device and Artificial Neural Networks](https://mlsanity.com/paper/2103.08482/) (2021)
- [Unpaired Single-Image Depth Synthesis with cycle-consistent Wasserstein GANs](https://mlsanity.com/paper/2103.16938/) (2021)
- [Synergizing Deep Learning and Full-Waveform Inversion: Bridging Data-Driven and Theory-Guided Approaches for Enhanced Seismic Imaging](https://mlsanity.com/paper/2502.17585/) (2025)
- [A Distributionally Robust Framework for Learned Reconstructions in Inverse Problems](https://mlsanity.com/paper/2606.30230/) (2026)

## Abstract (arXiv)

We propose using the Wasserstein loss for training in inverse problems. In particular, we consider a learned primal-dual reconstruction scheme for ill-posed inverse problems using the Wasserstein distance as loss function in the learning. This is motivated by miss-alignments in training data, which when using standard mean squared error loss could severely degrade reconstruction quality. We prove that training with the Wasserstein loss gives a reconstruction operator that correctly compensates for miss-alignments in certain cases, whereas training with the mean squared error gives a smeared reconstruction. Moreover, we demonstrate these effects by training a reconstruction algorithm using both mean squared error and optimal transport loss for a problem in computerized tomography.