Scalability of power-law scheduled score-based diffusion and Lazy Diffusion to 3D turbulence, anisotropic spectra, and coupled multiphysics

Determine the scalability of score-based conditional diffusion models equipped with power-law noise schedules and the Lazy Diffusion one-step distillation to fully three-dimensional turbulent flows, to systems exhibiting anisotropic energy spectra, and to coupled multiphysics dynamical systems, beyond the moderate-resolution two-dimensional settings evaluated in this work.

Background

The paper analyzes spectral collapse in standard DDPM forward processes for turbulent power-law spectra and introduces physics-aware modifications: power-law noise schedules to preserve high-wavenumber coherence and a Lazy Diffusion distillation to enable single-step conditional generation. These approaches showed improved spectral fidelity and long-horizon autoregressive stability on two systems: 2D forced Kolmogorov turbulence and regional ocean surface reanalysis.

The authors note that the current demonstrations are at moderate resolutions and in two-dimensional domains. They explicitly state that questions remain about scaling these methods to more complex regimes, specifically fully three-dimensional turbulence, anisotropic spectra, and coupled multiphysics systems, which would test the generality and robustness of the proposed diffusion-based generative framework.