Proposes Rex, a family of reversible exponential Runge‑Kutta solvers derived via Lawson methods
Transforms any explicit Runge‑Kutta scheme into a reversible scheme
Provides rigorous theoretical analysis of the resulting solvers
Demonstrates empirical benefits in sampling Boltzmann distributions with flow models
Shows improved image generation and editing performance using diffusion models
Highlights limitations of current inversion approaches (low stability, low convergence order, ODE‑only)
📖 Full Retelling
The authors Zander W. Blasingame and Chen Liu, from the arXiv community, present in a 2025–2026 preprint the Rex family of reversible exponential Runge‑Kutta solvers. Developed by applying Lawson methods to turn any explicit Runge‑Kutta scheme into a reversible one, Rex addresses the non‑inversible errors that arise in standard ODE/SDE solvers used by deep generative models. The paper was first submitted to arXiv on 12 Feb 2025 (v1) and most recently revised on 19 Feb 2026 (v3). These solvers aim to enable exact backward integration for generative models, improving the precision of tasks such as Boltzmann‑distribution sampling, image generation and editing, problems where the current inversion methods suffer from poor stability and low‑order convergence.
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Deep Analysis
Why It Matters
Rex introduces reversible exponential Runge-Kutta solvers that allow neural differential equation models to be inverted exactly, eliminating discretization errors that hinder current generative models. This improves the fidelity of sampling and editing tasks in diffusion and flow models.
Context & Background
Generative models rely on ODE/SDE solvers that accumulate discretization errors when integrating backward
Standard solvers cannot provide exact inversion, leading to instability and low convergence order
Rex applies Lawson methods to convert any explicit Runge-Kutta scheme into a reversible one
What Happens Next
Researchers will likely integrate Rex into popular diffusion frameworks to achieve more accurate sampling and image editing. Further work may extend the approach to stochastic differential equations and explore higher-order convergence.
Frequently Asked Questions
What is a reversible solver?
A reversible solver can integrate a differential equation forward and backward exactly, preserving the trajectory without accumulating discretization errors.
How does Rex improve Boltzmann sampling?
By providing a reversible integration scheme, Rex reduces bias in the sampling process, leading to more accurate Boltzmann distribution estimates.
Original Source
--> Computer Science > Machine Learning arXiv:2502.08834 [Submitted on 12 Feb 2025 ( v1 ), last revised 19 Feb 2026 (this version, v3)] Title: Rex: A Family of Reversible Exponential Runge-Kutta Solvers Authors: Zander W. Blasingame , Chen Liu View a PDF of the paper titled Rex: A Family of Reversible Exponential Runge-Kutta Solvers, by Zander W. Blasingame and Chen Liu View PDF Abstract: Deep generative models based on neural differential equations have quickly become the state-of-the-art for numerous generation tasks across many different applications. These models rely on ODE/SDE solvers which integrate from a prior distribution to the data distribution. In many applications it is highly desirable to then integrate in the other direction. The standard solvers, however, accumulate discretization errors which don't align with the forward trajectory, thereby prohibiting an exact inversion. In applications where the precision of the generative model is paramount this inaccuracy in inversion is often unacceptable. Current approaches to solving the inversion of these models results in significant downstream issues with poor stability and low-order of convergence; moreover, they are strictly limited to the ODE domain. In this work, we propose a new family of reversible exponential Runge-Kutta solvers which we refer to as Rex developed by an application of Lawson methods to convert any explicit Runge-Kutta scheme into a reversible one. In addition to a rigorous theoretical analysis of the proposed solvers, we also empirically demonstrate the utility of Rex on improving the sampling of Boltzmann distributions with flow models, and improving image generation and editing capabilities with diffusion models. Comments: Updated preprint. Added Boltzmann sampling experiments among other things Subjects: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI); Machine Learning (stat.ML) Cite as: arXiv:2502.08834 [cs.LG] (or arXiv:2502.08834v3 [cs.LG] for this version) https://...
