mlsanityData to 7 Oct 2026

Synthetic Lagrangian Turbulence by Generative Diffusion Models

arXiv 2307.08529 ↗First posted 17 Jul 2023physics.flu-dyn cond-mat.stat-mech cs.CEcited by 31

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

Lagrangian turbulence lies at the core of numerous applied and fundamental problems related to the physics of dispersion and mixing in engineering, bio-fluids, atmosphere, oceans, and astrophysics. Despite exceptional theoretical, numerical, and experimental efforts conducted over the past thirty years, no existing models are capable of faithfully reproducing statistical and topological properties exhibited by particle trajectories in turbulence. We propose a machine learning approach, based on a state-of-the-art diffusion model, to generate single-particle trajectories in three-dimensional turbulence at high Reynolds numbers, thereby bypassing the need for direct numerical simulations or experiments to obtain reliable Lagrangian data. Our model demonstrates the ability to reproduce most statistical benchmarks across time scales, including the fat-tail distribution for velocity increments, the anomalous power law, and the increased intermittency around the dissipative scale. Slight deviations are observed below the dissipative scale, particularly in the acceleration and flatness statistics. Surprisingly, the model exhibits strong generalizability for extreme events, producing events of higher intensity and rarity that still match the realistic statistics. This paves the way for producing synthetic high-quality datasets for pre-training various downstream applications of Lagrangian turbulence.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 19 of its 94 references that are in the map. First posted on arXiv 17 Jul 2023.

Builds on

19 of 94 references.

Closest ancestors · 1

Same direction, newest first

  1. 2022A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction26 Nov

Other references · 18

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Language Models are Few-Shot Learnerscited by 32,199
  3. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  4. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  5. 2020Denoising Diffusion Implicit Modelscited by 9,655
  6. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  7. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  8. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  9. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Stepscited by 1,961
  10. 2016WaveNet: A Generative Model for Raw Audiocited by 1,710
  11. 2019Machine Learning for Fluid Mechanicscited by 380
  12. 2018Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networkscited by 155
6 more
  1. 2022Wavelet Score-Based Generative Modelingcited by 61
  2. 2020Convolutional-network models to predict wall-bounded turbulence from wall quantitiescited by 46
  3. 2014Accurate and Conservative Estimates of MRF Log-likelihood using Reverse Annealingcited by 18
  4. 2020Reconstruction of turbulent data with deep generative models for semantic inpainting from TURB-Rot databasecited by 17
  5. 2023Optimal tracking strategies in a turbulent flowcited by 5
  6. 2022Neural network based generation of a 1-dimensional stochastic field with turbulent velocity statisticscited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 8; 2025: 14; 2026: 6.

31 papers.

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  1. 2025Why Diffusion Models Don't Memorize: The Role of Implicit Dynamical Regularization in Trainingcited by 78
  2. 2024Wavelet Diffusion Neural Operatorcited by 28
  3. 2025Generative Latent Neural PDE Solver using Flow Matchingcited by 28
  4. 2025Physics vs Distributions: Pareto Optimal Flow Matching with Physics Constraintscited by 26
  5. 2024Data-Driven Stochastic Closure Modeling via Conditional Diffusion Model and Neural Operatorcited by 12
  6. 2024PiRD: Physics-informed Residual Diffusion for Flow Field Reconstructioncited by 10
  7. 2023Turbulence Scaling from Deep Learning Diffusion Generative Modelscited by 8
  8. 2025Diff-SPORT: Diffusion-based Sensor Placement Optimization and Reconstruction of Turbulent flows in urban environmentscited by 8
  9. 2025The wall confronting large language modelscited by 8
  10. 2024Generative prediction of flow fields around an obstacle using the diffusion modelcited by 6
  11. 2024DiffBatt: A Diffusion Model for Battery Degradation Prediction and Synthesiscited by 6
  12. 2025Accurate and scalable deep Maxwell solvers using multilevel iterative methodscited by 5
19 more
  1. 2024Understanding complex crowd dynamics with generative neural simulatorscited by 4
  2. 2025FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulationcited by 4
  3. 2025From Uncertain to Safe: Conformal Adaptation of Diffusion Models for Safe PDE Controlcited by 3
  4. 2025Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systemscited by 3
  5. 2023A multiscale and multicriteria Generative Adversarial Network to synthesize 1-dimensional turbulent fieldscited by 2
  6. 2023The Universal Statistical Structure and Scaling Laws of Chaos and Turbulencecited by 2
  7. 2026PODiff: Latent Diffusion in Proper Orthogonal Decomposition Space for Scientific Super-Resolutioncited by 2
  8. 2026Least-Action-Guided Diffusion for Physical Extrapolationcited by 2
  9. 2024Stochastic Reconstruction of Gappy Lagrangian Turbulent Signals by Conditional Diffusion Modelscited by 1
  10. 2026Capturing non-Markovian dynamics in non-equilibrium stochastic systems using flow matchingcited by 1
  11. 2024Mixing Artificial and Natural Intelligence: From Statistical Mechanics to AI and Back to Turbulencecited by 0
  12. 2025Slim multi-scale convolutional autoencoder-based reduced-order models for interpretable features of a complex dynamical systemcited by 0
  13. 2025Data-driven Mori-Zwanzig modeling of Lagrangian particle dynamics in turbulent flowscited by 0
  14. 2025Deep Generative Model for Human Mobility Behaviorcited by 0
  15. 2025Reconstructing Multi-Scale Physical Fields from Extremely Sparse Measurements with an Autoencoder-Diffusion Cascadecited by 0
  16. 2025Learning Temporally Consistent Turbulence Between Sparse Snapshots via Diffusion Modelscited by 0
  17. 2026Explainable deep learning reveals the physical mechanisms behind the turbulent kinetic energy equationcited by 0
  18. 2026Annealed Co-Generation: Disentangling Variables via Progressive Pairwise Modelingcited by 0
  19. 2026Transformers Learn the Optimal DDPM Denoiser for Multi-Token GMMscited by 0

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