Rectified Flows for Fast Multiscale Fluid Flow Modeling

• URL: http://arxiv.org/abs/2506.03111v1
• Date: Tue, 03 Jun 2025 17:40:39 GMT
• Title: Rectified Flows for Fast Multiscale Fluid Flow Modeling
• Authors: Victor Armegioiu, Yannick Ramic, Siddhartha Mishra,
• Abstract summary: We introduce a rectified flow framework that learns a time-dependent velocity field.<n>Our method makes each integration step much more effective, using as few as eight steps.<n> Experiments on challenging multiscale flow benchmarks show that rectified flows recover the same posterior distributions as diffusion models.
• Score: 11.597597438962026
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The statistical modeling of fluid flows is very challenging due to their multiscale dynamics and extreme sensitivity to initial conditions. While recently proposed conditional diffusion models achieve high fidelity, they typically require hundreds of stochastic sampling steps at inference. We introduce a rectified flow framework that learns a time-dependent velocity field, transporting input to output distributions along nearly straight trajectories. By casting sampling as solving an ordinary differential equation (ODE) along this straighter flow field, our method makes each integration step much more effective, using as few as eight steps versus (more than) 128 steps in standard score-based diffusion, without sacrificing predictive fidelity. Experiments on challenging multiscale flow benchmarks show that rectified flows recover the same posterior distributions as diffusion models, preserve fine-scale features that MSE-trained baselines miss, and deliver high-resolution samples in a fraction of inference time.

Related papers

• ProReflow: Progressive Reflow with Decomposed Velocity [52.249464542399636]
  Flow matching aims to reflow the diffusion process of diffusion models into a straight line for a few-step and even one-step generation.<n>We introduce progressive reflow, which progressively reflows the diffusion models in local timesteps until the whole diffusion progresses.<n>We also introduce aligned v-prediction, which highlights the importance of direction matching in flow matching over magnitude matching.
  arXiv  Detail & Related papers  (2025-03-05T04:50:53Z)
• Importance Corrected Neural JKO Sampling [0.0]
  We combine continuous normalizing flows (CNFs) with rejection-resampling steps based on importance weights.<n>The arising model can be trained iteratively, reduces the reverse Kullback-Leibler (KL) loss function in each step and allows to generate iid samples.<n> Numerical examples show that our method yields accurate results on various test distributions including high-dimensional multimodal targets.
  arXiv  Detail & Related papers  (2024-07-29T22:49:59Z)
• Consistency Flow Matching: Defining Straight Flows with Velocity Consistency [97.28511135503176]
  We introduce Consistency Flow Matching (Consistency-FM), a novel FM method that explicitly enforces self-consistency in the velocity field. Preliminary experiments demonstrate that our Consistency-FM significantly improves training efficiency by converging 4.4x faster than consistency models.
  arXiv  Detail & Related papers  (2024-07-02T16:15:37Z)
• Provable Statistical Rates for Consistency Diffusion Models [87.28777947976573]
  Despite the state-of-the-art performance, diffusion models are known for their slow sample generation due to the extensive number of steps involved. This paper contributes towards the first statistical theory for consistency models, formulating their training as a distribution discrepancy minimization problem.
  arXiv  Detail & Related papers  (2024-06-23T20:34:18Z)
• Flow Map Matching [15.520853806024943]
  Flow map matching is an algorithm that learns the two-time flow map of an underlying ordinary differential equation. We show that flow map matching leads to high-quality samples with significantly reduced sampling cost compared to diffusion or interpolant methods.
  arXiv  Detail & Related papers  (2024-06-11T17:41:26Z)
• Fast Samplers for Inverse Problems in Iterative Refinement Models [19.099632445326826]
  We propose a plug-and-play framework for constructing efficient samplers for inverse problems. Our method can generate high-quality samples in as few as 5 conditional sampling steps and outperforms competing baselines requiring 20-1000 steps.
  arXiv  Detail & Related papers  (2024-05-27T21:50:16Z)
• Boosting Diffusion Models with Moving Average Sampling in Frequency Domain [101.43824674873508]
  Diffusion models rely on the current sample to denoise the next one, possibly resulting in denoising instability. In this paper, we reinterpret the iterative denoising process as model optimization and leverage a moving average mechanism to ensemble all the prior samples. We name the complete approach "Moving Average Sampling in Frequency domain (MASF)"
  arXiv  Detail & Related papers  (2024-03-26T16:57:55Z)
• Fast Sampling via Discrete Non-Markov Diffusion Models with Predetermined Transition Time [49.598085130313514]
  We propose discrete non-Markov diffusion models (DNDM), which naturally induce the predetermined transition time set.<n>This enables a training-free sampling algorithm that significantly reduces the number of function evaluations.<n>We study the transition from finite to infinite step sampling, offering new insights into bridging the gap between discrete and continuous-time processes.
  arXiv  Detail & Related papers  (2023-12-14T18:14:11Z)
• Fast Sampling of Diffusion Models via Operator Learning [74.37531458470086]
  We use neural operators, an efficient method to solve the probability flow differential equations, to accelerate the sampling process of diffusion models. Compared to other fast sampling methods that have a sequential nature, we are the first to propose a parallel decoding method. We show our method achieves state-of-the-art FID of 3.78 for CIFAR-10 and 7.83 for ImageNet-64 in the one-model-evaluation setting.
  arXiv  Detail & Related papers  (2022-11-24T07:30:27Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.