Autoregressive surrogate models (emulators) make fast predictions for dynamical systems but become unstable over time due to error buildup. This study , led by Chris Pedersen, introduces thermalization, a technique leveraging diffusion models to adaptively correct errors during inference. By stabilizing predictions, it extends emulated rollouts of chaotic and turbulent systems by several orders of magnitude. This breakthrough application of diffusion models enhances the utility of emulators, and can be applied to autoregressive models across science and engineering.