# Population Annealing as a Discrete-Time Schr"odinger Bridge

arXiv: https://arxiv.org/abs/2603.16056 · HTML: https://mlsanity.com/paper/2603.16056/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 7 references that are in the map.
- First posted on arXiv 17 Mar 2026.

## Builds on (most cited first, 4 of 4)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [Mathematical understanding of detailed balance condition violation and its application to Langevin dynamics](https://mlsanity.com/paper/1503.02356/) (2015)
- [Sch"odinger Bridge Type Diffusion Models as an Extension of Variational Autoencoders](https://mlsanity.com/paper/2412.18237/) (2024)

## Abstract (arXiv)

We present a theoretical framework that reinterprets Population Annealing (PA) through the lens of the discrete-time Schr"odinger Bridge (SB) problem. We demonstrate that the heuristic reweighting step in PA is derived by analytically solving the Schr"odinger system without iterative computation via instantaneous projection. In addition, we identify the thermodynamic work as the optimal control potential that solves the global variational problem on path space. This perspective unifies non-equilibrium thermodynamics with the geometric framework of optimal transport, interpreting the Jarzynski equality as a consistency condition within the Donsker-Varadhan variational principle, and elucidates the thermodynamic optimality of PA.