# Rex: A Family of Reversible Exponential (Stochastic) Runge-Kutta Solvers

arXiv: https://arxiv.org/abs/2502.08834 · HTML: https://mlsanity.com/paper/2502.08834/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2025.

## Built on by (most cited first, 3 of 3)

- [Strong Stochastic Flow Maps](https://mlsanity.com/paper/2606.01086/) (2026)
- [Contrastive Diffusion Alignment: Learning Structured Latents for Controllable Generation](https://mlsanity.com/paper/2510.14190/) (2025)
- [Identifiable World Models from Pretrained Diffusion Representations](https://mlsanity.com/paper/2610.07028/) (2026)

## Abstract (arXiv)

Deep generative models based on neural differential equations have become state-of-the-art for many generation tasks. These models rely on ODE/SDE solvers that integrate from a prior distribution to the data distribution; in many applications it is also highly desirable to integrate in the inverse direction. Standard solvers, however, accumulate discretization errors that prohibit exact inversion, an inaccuracy that is unacceptable in precision-critical applications. Existing inversion methods suffer from poor stability and low order of convergence, and are strictly limited to the ODE setting. In this work, we propose Rex, a family of reversible exponential (stochastic) Runge-Kutta solvers obtained by applying Lawson methods to convert any explicit (stochastic) Runge-Kutta scheme into an algebraically reversible one for both diffusion ODEs and SDEs. Beyond a rigorous theoretical analysis -- establishing arbitrary-order convergence and a non-zero region of linear stability -- we empirically demonstrate that Rex achieves near-machine-precision reconstruction and improves Boltzmann sampling with flow models as well as image generation and editing with diffusion models.