Autoregressive neural surrogate models can dramatically accelerate simulations of dynamical systems, but they often suffer from error accumulation over long time horizons. This work , led by Qi Liu, introduces a unifying framework that formalizes the trade-off between short-term accuracy and long-term consistency, which most previous approaches handled heuristically. Building on this, the authors propose a new hyperparameter-free method: Self-refining Neural Surrogate (SNS), based on conditional diffusion. SNS can iteratively refine its own predictions or enhance existing models, delivering stable and accurate simulations even over very long time scales.