Detectors blur measurements. A jet's true mass distribution passes through the detector and emerges smeared — peaks broadened, tails extended, fine structure lost. Unfolding is the inverse problem: recover the true distribution from the blurred one.
For decades, the standard tool has been Richardson-Lucy deconvolution with Kullback-Leibler divergence. It requires binning the data, and binning introduces its own artifacts. The bin edges are arbitrary; the results depend on them.
The alternative (arXiv:2603.20903) replaces KL divergence with Wasserstein distance — optimal transport cost between distributions. A generalized Sinkhorn algorithm finds the solution. The method works directly on empirical data samples without binning, doesn't require the measured data's support to overlap with the noise model's output, and provably converges.
The mathematical contribution: establishing existence and uniqueness conditions for the Wasserstein unfolding problem. This wasn't obvious — optimal transport minimization under convolution constraints could have multiple solutions or none. The conditions are sharp.
The practical advantage appears when binning distortions matter. For jet mass measurements in particle physics, the Wasserstein method produces robust, accurate results where Richardson-Lucy struggles with bin-edge sensitivity.
The structural insight: KL divergence measures pointwise likelihood ratios. Wasserstein distance measures the cost of physically moving mass from one distribution to another. When the corruption is a physical process (detector smearing), the physical distance metric outperforms the information-theoretic one. The loss function should match the physics of the problem. A measurement corrupted by transport is best corrected by transport.