mlsanityData to 7 Oct 2026

Bayesian Conditional Diffusion Models for Versatile Spatiotemporal Turbulence Generation

arXiv 2311.07896 ↗First posted 14 Nov 2023physics.flu-dyn cs.LGcited by 28

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

Abstract (arXiv)

Turbulent flows have historically presented formidable challenges to predictive computational modeling. Traditional numerical simulations often require vast computational resources, making them infeasible for numerous engineering applications. As an alternative, deep learning-based surrogate models have emerged, offering data-drive solutions. However, these are typically constructed within deterministic settings, leading to shortfall in capturing the innate chaotic and stochastic behaviors of turbulent dynamics. We introduce a novel generative framework grounded in probabilistic diffusion models for versatile generation of spatiotemporal turbulence. Our method unifies both unconditional and conditional sampling strategies within a Bayesian framework, which can accommodate diverse conditioning scenarios, including those with a direct differentiable link between specified conditions and generated unsteady flow outcomes, and scenarios lacking such explicit correlations. A notable feature of our approach is the method proposed for long-span flow sequence generation, which is based on autoregressive gradient-based conditional sampling, eliminating the need for cumbersome retraining processes. We showcase the versatile turbulence generation capability of our framework through a suite of numerical experiments, including: 1) the synthesis of LES simulated instantaneous flow sequences from URANS inputs; 2) holistic generation of inhomogeneous, anisotropic wall-bounded turbulence, whether from given initial conditions, prescribed turbulence statistics, or entirely from scratch; 3) super-resolved generation of high-speed turbulent boundary layer flows from low-resolution data across a range of input resolutions. Collectively, our numerical experiments highlight the merit and transformative potential of the proposed methods, making a significant advance in the field of turbulence generation.

Key facts. Cited by 28 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 26 of its 59 references that are in the map. First posted on arXiv 14 Nov 2023.

Builds on

26 of 59 references.

Closest ancestors · 3

Same direction, newest first

  1. 2023Diffusion model based data generation for partial differential equations19 Jun
  2. 2023Debias Coarsely, Sample Conditionally: Statistical Downscaling through Optimal Transport and Probabilistic Diffusion Models24 May
  3. 2022A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction26 Nov

Other references · 23

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Denoising Diffusion Implicit Modelscited by 9,655
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  5. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  6. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  7. 2021Variational Diffusion Modelscited by 1,145
  8. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  9. 2021Machine learning accelerated computational fluid dynamicscited by 461
  10. 2019Machine Learning for Fluid Mechanicscited by 380
  11. 2022Understanding Diffusion Models: A Unified Perspectivecited by 337
  12. 2015A note on the evaluation of generative modelscited by 291
11 more
  1. 2020A Review on Generative Adversarial Networks: Algorithms, Theory, and Applicationscited by 209
  2. 2019Seeing What a GAN Cannot Generatecited by 148
  3. 2021Enhancing Computational Fluid Dynamics with Machine Learningcited by 137
  4. 2016Accelerating Eulerian Fluid Simulation With Convolutional Networkscited by 128
  5. 2022Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamicscited by 44
  6. 2021Generative Modeling of Turbulencecited by 26
  7. 2020Multi-fidelity Generative Deep Learning Turbulent Flowscited by 21
  8. 2023Differentiable hybrid neural modeling for fluid-structure interactioncited by 18
  9. 2018Deep Learning of Turbulent Scalar Mixingcited by 17
  10. 2020Reconstruction of turbulent data with deep generative models for semantic inpainting from TURB-Rot databasecited by 17
  11. 2021Assessments of epistemic uncertainty using Gaussian stochastic weight averaging for fluid-flow regressioncited by 15

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 7; 2025: 11; 2026: 10.

28 papers.

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  1. 2025Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networkscited by 24
  2. 2025FunDiff: Diffusion Models over Function Spaces for Physics-Informed Generative Modelingcited by 19
  3. 2024Generative Learning of the Solution of Parametric Partial Differential Equations Using Guided Diffusion Models and Virtual Observationscited by 16
  4. 2024Data-Driven Stochastic Closure Modeling via Conditional Diffusion Model and Neural Operatorcited by 12
  5. 2025Diffusion-Based Hierarchical Graph Neural Networks for Simulating Nonlinear Solid Mechanicscited by 10
  6. 2025Diff-SPORT: Diffusion-based Sensor Placement Optimization and Reconstruction of Turbulent flows in urban environmentscited by 8
  7. 2024Learning Physics for Unveiling Hidden Earthquake Ground Motions via Conditional Generative Modelingcited by 7
  8. 2024Generative Learning for Forecasting the Dynamics of Complex Systemscited by 6
  9. 2024Generative prediction of flow fields around an obstacle using the diffusion modelcited by 6
  10. 2026D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matchingcited by 5
  11. 2025Rectified Flows for Fast Multiscale Fluid Flow Modelingcited by 4
  12. 2024Model-Agnostic AI Framework with Explicit Time Integration for Long-Term Fluid Dynamics Predictioncited by 3
16 more
  1. 2025CD-TVD: Contrastive Diffusion for 3D Super-Resolution with Scarce High-Resolution Time-Varying Datacited by 3
  2. 2026Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systemscited by 3
  3. 2025Multi-fidelity Reinforcement Learning Control for Complex Dynamical Systemscited by 2
  4. 2025Generative forecasting with joint probability modelscited by 2
  5. 2024Comparison of Generative Learning Methods for Turbulence Surrogatescited by 1
  6. 2026Synergizing Transport-Based Generative Models and Latent Geometry for Stochastic Closure Modelingcited by 1
  7. 2025FoilDiff: A Hybrid Transformer Backbone for Diffusion-based Modelling of 2D Airfoil Flow Fieldscited by 0
  8. 2025Control-Augmented Autoregressive Diffusion for Data Assimilationcited by 0
  9. 2025Learning Temporally Consistent Turbulence Between Sparse Snapshots via Diffusion Modelscited by 0
  10. 2026Coupled Diffusion-Encoder Models for Reconstruction of Flow Fieldscited by 0
  11. 2026Learning noisy phase transition dynamics from stochastic partial differential equationscited by 0
  12. 2026Data Enrichment for Symbolic Regression Using Diffusion Modelscited by 0
  13. 2026Multiscale Hypersonic Boundary Layer Reconstruction via Spectral Binning and Subdomain-wise Conditional Diffusioncited by 0
  14. 2026Patched Flow Matching: Generative Wall-Pressure Reconstruction Beyond Training-Domain Scales from Sparse Sensorscited by 0
  15. 2026A Shortcut to Statistically Steady-State Turbulence with Flow Matchingcited by 0
  16. 2026MoRF-AST: Calibrated Probabilistic Virtual Sensing for Structural Monitoring under Changing Operating Conditionscited by 0

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