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

Abstract:

Neural differential equation-based deep generative models currently represent the state-of-the-art for numerous generation tasks. These architectures typically depend on ODE or SDE solvers to integrate from a prior distribution toward the target data distribution. However, in many scenarios, the ability to integrate in the reverse direction is equally critical. Conventional solvers, unfortunately, accumulate discretization errors that prevent exact inversion, rendering them unsuitable for precision-sensitive applications where such inaccuracies are unacceptable. Furthermore, current inversion techniques are constrained to the ODE domain and exhibit limited convergence orders and poor stability.

To address these limitations, we introduce Rex, a suite of reversible exponential (stochastic) Runge-Kutta solvers. Rex is derived by applying Lawson methods to transform any explicit (stochastic) Runge-Kutta scheme into one that is algebraically reversible, applicable to both diffusion ODEs and SDEs. Our work includes a rigorous theoretical framework that proves the method’s arbitrary-order convergence and identifies a non-zero region of linear stability. Empirically, we demonstrate that Rex enables near-machine-precision reconstruction. Additionally, it enhances Boltzmann sampling using flow models, as well as improving performance in image generation and editing tasks with diffusion models.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC