Deterministic diffusion models for Lagrangian turbulence: robustness and encoding of extreme events

TL;DR

This paper demonstrates that deterministic diffusion models can reliably generate realistic Lagrangian turbulence trajectories, capturing extreme events and enabling faster sampling while maintaining statistical accuracy.

Contribution

It introduces a robust, deterministic diffusion modeling approach for Lagrangian turbulence that captures extreme events and accelerates generation with minimal accuracy loss.

Findings

Diffusion models are robust across architectures.

Structured features in initial noise relate to extreme events.

Reduced diffusion steps speed up generation with minimal fidelity loss.

Abstract

Modeling Lagrangian turbulence remains a fundamental challenge due to its multiscale, intermittent, and non-Gaussian nature. Recent advances in data-driven diffusion models have enabled the generation of realistic Lagrangian velocity trajectories that accurately reproduce statistical properties across scales and capture rare extreme events. This study investigates three key aspects of diffusion-based modeling for Lagrangian turbulence. First, we assess architectural robustness by comparing a U-Net backbone with a transformer-based alternative, finding strong consistency in generated trajectories, with only minor discrepancies at small scales. Second, leveraging a deterministic variant of diffusion model formulation, namely the deterministic denoising diffusion implicit model (DDIM), we identify structured features in the initial latent noise that align consistently with extreme acceleration events. Third, we explore accelerated generation by reducing the number of diffusion steps, and find that DDIM enables substantial speedups with minimal loss of statistical fidelity. These findings highlight the robustness of diffusion models and their potential for interpretable, scalable modeling of complex turbulent systems.