# Plug-in estimation of Schr\\"odinger bridges Source: [Plug-in estimation of Schr\\"odinger bridges]() Collection index: [llms.txt]() Data updated: 2025-10-25T17:30:28.657Z Authors: Aram-Alexandre Pooladian, Jonathan Niles-Weed Published: 2024-08-21T15:07:25.000Z ## Abstract We propose a procedure for estimating the Schr\\"odinger bridge between two probability distributions. Unlike existing approaches, our method does not require iteratively simulating forward and backward diffusions or training neural networks to fit unknown drifts. Instead, we show that the potentials obtained from solving the static entropic optimal transport problem between the source and target samples can be modified to yield a natural plug-in estimator of the time-dependent drift that defines the bridge between two measures. Under minimal assumptions, we show that our proposal, which we call the \\emph{Sinkhorn bridge}, provably estimates the Schr\\"odinger bridge with a rate of convergence that depends on the intrinsic dimensionality of the target measure. Our approach combines results from the areas of sampling, and theoretical and statistical entropic optimal transport. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Intermediate distribution restoration on Single-cell data (intermediate time points ti for i in {1, 2, 3})](): Intermediate distribution restoration; Single-cell data (intermediate time points ti for i in {1, 2, 3}); W1 Score: 0.818. ## Original sources and implementation [Original paper]() [PDF]()