# Bridging Simulators with Conditional Optimal Transport

arXiv: https://arxiv.org/abs/2510.24631 · HTML: https://mlsanity.com/paper/2510.24631/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 28 Oct 2025.

## Builds on (most cited first, 13 of 13)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Sampling-Based Accuracy Testing of Posterior Estimators for General Inference](https://mlsanity.com/paper/2302.03026/) (2023)
- [Conditional Sampling with Monotone GANs: from Generative Models to Likelihood-Free Inference](https://mlsanity.com/paper/2006.06755/) (2020)
- [Learning to Predict the Cosmological Structure Formation](https://mlsanity.com/paper/1811.06533/) (2018)
- [Dynamic Conditional Optimal Transport through Simulation-Free Flows](https://mlsanity.com/paper/2404.04240/) (2024)
- [Field Level Neural Network Emulator for Cosmological N-body Simulations](https://mlsanity.com/paper/2206.04594/) (2022)
- [Hybrid Physical-Neural ODEs for Fast N-body Simulations](https://mlsanity.com/paper/2207.05509/) (2022)
- [COmoving Computer Acceleration (COCA): N-body simulations in an emulated frame of reference](https://mlsanity.com/paper/2409.02154/) (2024)

## Built on by (most cited first, 1 of 1)

- [When do explicit penalties improve flow matching?](https://mlsanity.com/paper/2610.15689/) (2026)

## Abstract (arXiv)

We propose a new field-level emulator that bridges two simulators using unpaired simulation datasets. Our method leverages a flow-based approach to learn the likelihood transport from one simulator to the other. Since multiple transport maps exist, we employ Conditional Optimal Transport Flow Matching (COT-FM) to ensure that the transformation minimally distorts the underlying structure of the data. We demonstrate the effectiveness of this approach by bridging weak lensing simulators: a Lagrangian Perturbation Theory (LPT) to a N-body Particle-Mesh (PM). We demonstrate that our emulator captures the full correction between the simulators by showing that it enables full-field inference to accurately recover the true posterior, validating its accuracy beyond traditional summary statistics.