# Exponential convergence rate for Iterative Markovian Fitting

arXiv: https://arxiv.org/abs/2508.02770 · HTML: https://mlsanity.com/paper/2508.02770/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 2 references that are in the map.
- First posted on arXiv 4 Aug 2025.

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

- [Entering the Era of Discrete Diffusion Models: A Benchmark for Schr"odinger Bridges and Entropic Optimal Transport](https://mlsanity.com/paper/2509.23348/) (2025)
- [Minimal-Action Discrete Schr"odinger Bridge Matching for Peptide Sequence Design](https://mlsanity.com/paper/2601.22408/) (2026)

## Abstract (arXiv)

We consider the discrete-time Schr"odinger bridge problem on a finite state space. Although it has been known that the Iterative Markovian Fitting (IMF) algorithm converges in Kullback-Leibler divergence to the ground truth solution, the speed of that convergence remained unquantified. In this work, we establish for the first time that IMF exhibits exponential convergence with an explicit contraction factor.