mlsanityData to 14 Oct 2026

FlowRefiner: Flow Matching-Based Iterative Refinement for 3D Turbulent Flow Simulation

arXiv 2604.17149 ↗First posted 18 Apr 2026physics.flu-dyn cs.LGcited by 5

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

Abstract (arXiv)

Accurate autoregressive prediction of 3D turbulent flows remains challenging for neural PDE solvers, as small errors in fine-scale structures can accumulate rapidly over rollout. In this paper, we propose FlowRefiner, a flow matching-based iterative refinement framework for 3D turbulent flow simulation. The method replaces stochastic denoising refinement with deterministic ODE-based correction, uses a unified velocity-field regression objective across all refinement stages, and introduces a decoupled sigma schedule that fixes the noise range independently of refinement depth. These design choices yield stable and effective refinement in the small-noise regime. Experiments on large-scale 3D turbulence with rich multi-scale structures show that FlowRefiner achieves state-of-the-art autoregressive prediction accuracy and strong physical consistency. Although developed for turbulent flow simulation, the proposed framework is broadly applicable to iterative refinement problems in scientific modeling.

Key facts. Cited by 5 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 36 of its 46 references that are in the map. First posted on arXiv 18 Apr 2026.

Builds on

36 of 46 references.

Closest ancestors · 12

Same direction, newest first

  1. 2026DiffusionRollout: Uncertainty-Aware Rollout Planning in Long-Horizon PDE Solving14 Feb
  2. 2025Residual-augmented flow matching operators for probabilistic partial differential equations14 Dec
  3. 2025CFO: Learning Continuous-Time PDE Dynamics via Flow-Matched Neural Operators4 Dec
  4. 2025Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraints4 Jun
  5. 2025FourierFlow: Frequency-aware Flow Matching for Generative Turbulence Modeling1 Jun
  6. 2025Generative Latent Neural PDE Solver using Flow Matching28 Mar
  7. 2024On conditional diffusion models for PDE simulations21 Oct
  8. 2024Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modeling13 Sep
  9. 2023Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation4 Sep
  10. 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers10 Aug
  11. 2022Flow Matching for Generative Modeling6 Oct
  12. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 24

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  3. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
  4. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  5. 2018On the Spectral Bias of Neural Networkscited by 1,341
  6. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  7. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 527
  8. 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 413
  9. 2022Message Passing Neural PDE Solverscited by 386
  10. 2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 326
  11. 2023Understanding Diffusion Objectives as the ELBO with Simple Data Augmentationcited by 304
  12. 2021U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flowcited by 297
12 more
  1. 2022Transformer for Partial Differential Equations' Operator Learningcited by 283
  2. 2021Factorized Fourier Neural Operatorscited by 249
  3. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 197
  4. 2024DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Trainingcited by 151
  5. 2023Scalable Transformer for PDE Surrogate Modelingcited by 128
  6. 2024Constrained Synthesis with Projected Diffusion Modelscited by 89
  7. 2023From Zero to Turbulence: Generative Modeling for 3D Flow Simulationcited by 49
  8. 2026Project and Generate: Divergence-Free Neural Operators for Incompressible Flowscited by 7
  9. 2026Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operatorscited by 6
  10. 2026PEST: Physics-Enhanced Swin Transformer for 3D Turbulence Simulationcited by 5
  11. 2026Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computingcited by 4
  12. 2025PDESpectralRefiner: Achieving More Accurate Long Rollouts with Spectral Adjustmentcited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 5.

5 papers.

  1. 2026Physics-Preserving Latent Compression for Zero-Shot Resolution Transfer in 3D Turbulencecited by 3
  2. 2026TIDE: A Physically Diverse 3D Turbulence Benchmark Dataset for Advancing Scientific Machine Learningcited by 1
  3. 2026SolarFlowRefiner: Refinement-Aware Flow Matching for Surface Solar Radiation Downscalingcited by 0
  4. 2026Staying on the Attractor: Supervising Neural Surrogates of 3D Turbulence Where They Leave Itcited by 0
  5. 2026ReAl: Refine neural operators via aligning dynamical flowcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Multi-Fidelity Flow Matching: Cascaded Refinement of PDE Solutions
  2. 2026High-fidelity Three-Dimensional Flow Field Reconstruction Driven by Turbulent Fluid Dynamics
  3. 2026One Scale at a Time: Scale-Autoregressive Modeling for Fluid Flow Distributions
  4. 2026Patched Flow Matching: Generative Wall-Pressure Reconstruction Beyond Training-Domain Scales from Sparse Sensors
  5. 2025Rectified Flows for Fast Multiscale Fluid Flow Modeling
  6. 2025Autoregressive regularized score-based diffusion models for multi-scenarios fluid flow prediction
  7. 2024CoNFiLD-inlet: Synthetic Turbulence Inflow Using Generative Latent Diffusion Models with Neural Fields
  8. 2025Straighten Viscous Rectified Flow via Noise Optimization