# Unfolding with a Wasserstein Loss

arXiv: https://arxiv.org/abs/2603.20903 · HTML: https://mlsanity.com/paper/2603.20903/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 37 references that are in the map.
- First posted on arXiv 21 Mar 2026.

## Builds on (most cited first, 12 of 12)

- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [OmniFold: A Method to Simultaneously Unfold All Observables](https://mlsanity.com/paper/1911.09107/) (2019)
- [GAN and VAE from an Optimal Transport Point of View](https://mlsanity.com/paper/1706.01807/) (2017)
- [The Landscape of Unfolding with Machine Learning](https://mlsanity.com/paper/2404.18807/) (2024)
- [Efficient Prior Calibration From Indirect Data](https://mlsanity.com/paper/2405.17955/) (2024)
- [Scaffolding Simulations with Deep Learning for High-dimensional Deconvolution](https://mlsanity.com/paper/2105.04448/) (2021)
- [Sharper Exponential Convergence Rates for Sinkhorn's Algorithm in Continuous Settings](https://mlsanity.com/paper/2407.01202/) (2024)
- [Stochastic Inverse Problem: stability, regularization and Wasserstein gradient flow](https://mlsanity.com/paper/2410.00229/) (2024)
- [Efficient Deconvolution in Populational Inverse Problems](https://mlsanity.com/paper/2505.19841/) (2025)
- [Gaussian mixtures closest to a given measure via optimal transport](https://mlsanity.com/paper/2404.19378/) (2024)
- [Wasserstein-Cram'er-Rao Theory of Unbiased Estimation](https://mlsanity.com/paper/2511.07414/) (2025)
- [Robust Sublinear Convergence Rates for Iterative Bregman Projections](https://mlsanity.com/paper/2602.01372/) (2026)

## Abstract (arXiv)

Data unfolding -- the removal of noise or artifacts from measurements -- is a fundamental task across the experimental sciences. Of particular interest are applications in physics, where the dominant approach is Richardson-Lucy (RL) deconvolution. The classical RL approach aims to find denoised data that, once passed through the noise model, is as close as possible to the measured data in terms of Kullback-Leibler (KL) divergence. This requires that the support of the measured data overlaps with the output of the noise model, a hypothesis typically enforced by binning, which introduces numerical error. As a counterpoint, the present work studies an alternative formulation using a Wasserstein loss. We establish sharp conditions for existence and uniqueness of optimizers, answering open questions of Li, et al., regarding necessary conditions for uniqueness in the case of transport map noise models. We then develop a provably convergent generalized Sinkhorn algorithm to compute approximate optimizers. Our algorithm requires only empirical observations of the noise model and measured data and scales with the size of the data, rather than the ambient dimension. Numerical experiments on one- and two-dimensional problems inspired by jet mass unfolding in particle physics demonstrate that the optimal transport approach offers robust, accurate performance compared to classical RL deconvolution, particularly when binning artifacts are significant.