# Turbulence Scaling from Deep Learning Diffusion Generative Models

arXiv: https://arxiv.org/abs/2311.06112 · HTML: https://mlsanity.com/paper/2311.06112/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 10 Nov 2023.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 10 of 10)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [A Denoising Diffusion Model for Fluid Field Prediction](https://mlsanity.com/paper/2301.11661/) (2023)
- [Synthetic Lagrangian Turbulence by Generative Diffusion Models](https://mlsanity.com/paper/2307.08529/) (2023)
- [Generative Modeling of Turbulence](https://mlsanity.com/paper/2112.02548/) (2021)
- [From Deep to Physics-Informed Learning of Turbulence: Diagnostics](https://mlsanity.com/paper/1810.07785/) (2018)
- [Generative Adversarial Networks to infer velocity components in rotating turbulent flows](https://mlsanity.com/paper/2301.07541/) (2023)
- [Neural Network Complexity of Chaos and Turbulence](https://mlsanity.com/paper/2211.15382/) (2022)
- [Generative convective parametrization of dry atmospheric boundary layer](https://mlsanity.com/paper/2307.14857/) (2023)

## Built on by (most cited first, 8 of 8)

- [A Probabilistic Approach to Wildfire Spread Prediction Using a Denoising Diffusion Surrogate Model](https://mlsanity.com/paper/2507.00761/) (2025)
- [Binned Spectral Power Loss for Improved Prediction of Chaotic Systems](https://mlsanity.com/paper/2502.00472/) (2025)
- [Autoregressive regularized score-based diffusion models for multi-scenarios fluid flow prediction](https://mlsanity.com/paper/2505.24145/) (2025)
- [Generative Urban Flow Modeling: From Geometry to Airflow with Graph Diffusion](https://mlsanity.com/paper/2512.14725/) (2025)
- [Divergence-Free Diffusion Models for Incompressible Fluid Flows](https://mlsanity.com/paper/2601.19368/) (2026)
- [Non-equilibrium active noise enhances generative memory in diffusion models](https://mlsanity.com/paper/2411.07233/) (2024)
- [Implicit Augmentation from Distributional Symmetry in Turbulence Super-Resolution](https://mlsanity.com/paper/2509.20683/) (2025)
- [Spectrally Regularized Latent Flow Matching for Turbulence Generation](https://mlsanity.com/paper/2606.11691/) (2026)

## Abstract (arXiv)

Complex spatial and temporal structures are inherent characteristics of turbulent fluid flows and comprehending them poses a major challenge. This comprehesion necessitates an understanding of the space of turbulent fluid flow configurations. We employ a diffusion-based generative model to learn the distribution of turbulent vorticity profiles and generate snapshots of turbulent solutions to the incompressible Navier-Stokes equations. We consider the inverse cascade in two spatial dimensions and generate diverse turbulent solutions that differ from those in the training dataset. We analyze the statistical scaling properties of the new turbulent profiles, calculate their structure functions, energy power spectrum, velocity probability distribution function and moments of local energy dissipation. All the learnt scaling exponents are consistent with the expected Kolmogorov scaling. This agreement with established turbulence characteristics provides strong evidence of the model's capability to capture essential features of real-world turbulence.