ICML 2025

Thermalizer: Stable autoregressive neural emulation of spatiotemporal chaos
Christian Pedersen 1 2 Laure Zanna 1 2 Joan Bruna 1 2
Abstract
Autoregressive surrogate models (or emulators)
of spatiotemporal systems provide an avenue for
fast, approximate predictions, with broad applica-
tions across science and engineering. At inference
time, however, these models are generally unable
to provide predictions over long time rollouts due
to accumulation of errors leading to diverging tra-
jectories. In essence, emulators operate out of
distribution, and controlling the online distribu-
tion quickly becomes intractable in large-scale
settings. To address this fundamental issue, and
focusing on time-stationary systems admitting an
invariant measure, we leverage diffusion models
to obtain an implicit estimator of the score of this
invariant measure. We show that this model of
the score function can be used to stabilize autore-
gressive emulator rollouts by applying on-the-fly
denoising during inference, a process we call ther-
malization. Thermalizing an emulator rollout is
shown to extend the time horizon of stable pre-
dictions by two orders of magnitude in complex
systems exhibiting turbulent and chaotic behav-
ior, opening up a novel application of diffusion
models in the context of neural emulation.
1. Introduction
The modeling of dynamical systems is a cornerstone task
in the physical sciences and engineering, with applications
across weather (Pathak et al., 2022; Watt-Meyer et al., 2023;
Lam et al., 2023; Lang et al., 2024) and climate modeling
(Kochkov et al., 2024; Subel & Zanna, 2024; Lupin-Jimenez
et al., 2025). The standard approach to modeling these sys-
tems is to solve the underlying partial differential equation
(PDE) describing the system using numerical methods. In
the case of high-dimensional systems, the computational
1Courant Institute of Mathematical Sciences, New York Univer-
sity, USA 2Center for Data Science, New York University, USA.
Correspondence ...