Title: One Scale at a Time: Scale-Autoregressive Modeling for Fluid Flow Distributions
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: Diffusion, Generative modelling, Fluid Dynamics, Autoregressive Modelling

Abstract: Analyzing unsteady fluid flows often requires access to the full distribution of possible temporal states, yet conventional PDE solvers are computationally prohibitive and learned time-stepping surrogates quickly accumulate error over long rollouts. Generative models avoid compounding error by sampling states independently, but diffusion and flow-matching methods, while accurate, are limited by the cost of many evaluations over the entire mesh. We introduce scale–autoregressive modeling (SAR) for sampling flows on unstructured meshes hierarchically from coarse to fine: it first generates a low-resolution field, then refines it by progressively sampling higher resolutions conditioned on coarser predictions. This coarse-to-fine factorization improves efficiency by concentrating computation at coarser scales, where uncertainty is greatest, while requiring fewer steps at finer scales. Across unsteady-flow benchmarks of varying complexity, SAR attains substantially lower distributional error and higher per-sample accuracy than state-of-the-art diffusion models based on multi-scale GNNs, while matching or surpassing a flow-matching Transolver (a linear-time transformer) yet running $2$–$7\times$ faster than this depending on the task. Overall, SAR provides a practical tool for fast and accurate estimation of statistical flow quantities (e.g., turbulent kinetic energy and two-point correlations) in real-world settings.

TL;DR: We introduce a scale–autoregressive framework that generates fluid flow distributions on complex meshes up to 7× faster than existing diffusion or flow-matching models, while maintaining or improving accuracy.