# Unfolding Time: Generative Modeling for Turbulent Flows in 4D

arXiv: https://arxiv.org/abs/2406.11390 · HTML: https://mlsanity.com/paper/2406.11390/

## Key facts

- Cited by 4 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 15 of its 23 references that are in the map.
- First posted on arXiv 17 Jun 2024.

## 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, 15 of 15)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Delving Deeper into Convolutional Networks for Learning Video Representations](https://mlsanity.com/paper/1511.06432/) (2015)
- [Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2307.11494/) (2023)
- [From Zero to Turbulence: Generative Modeling for 3D Flow Simulation](https://mlsanity.com/paper/2306.01776/) (2023)
- [Learning the Dynamics of Physical Systems from Sparse Observations with Finite Element Networks](https://mlsanity.com/paper/2203.08852/) (2022)
- [Add and Thin: Diffusion for Temporal Point Processes](https://mlsanity.com/paper/2311.01139/) (2023)
- [Assessing Robustness via Score-Based Adversarial Image Generation](https://mlsanity.com/paper/2310.04285/) (2023)

## Built on by (most cited first, 4 of 4)

- [Generative prediction of flow fields around an obstacle using the diffusion model](https://mlsanity.com/paper/2407.00735/) (2024)
- [Generative Modeling with Bayesian Sample Inference](https://mlsanity.com/paper/2502.07580/) (2025)
- [Accelerating the discovery of steady-states of planetary interior dynamics with machine learning](https://mlsanity.com/paper/2408.17298/) (2024)
- [Coupled Diffusion-Encoder Models for Reconstruction of Flow Fields](https://mlsanity.com/paper/2601.07946/) (2026)

## Abstract (arXiv)

A recent study in turbulent flow simulation demonstrated the potential of generative diffusion models for fast 3D surrogate modeling. This approach eliminates the need for specifying initial states or performing lengthy simulations, significantly accelerating the process. While adept at sampling individual frames from the learned manifold of turbulent flow states, the previous model lacks the capability to generate sequences, hindering analysis of dynamic phenomena. This work addresses this limitation by introducing a 4D generative diffusion model and a physics-informed guidance technique that enables the generation of realistic sequences of flow states. Our findings indicate that the proposed method can successfully sample entire subsequences from the turbulent manifold, even though generalizing from individual frames to sequences remains a challenging task. This advancement opens doors for the application of generative modeling in analyzing the temporal evolution of turbulent flows, providing valuable insights into their complex dynamics.