# Straighten Viscous Rectified Flow via Noise Optimization

arXiv: https://arxiv.org/abs/2507.10218 · HTML: https://mlsanity.com/paper/2507.10218/

## 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 30 of its 34 references that are in the map.
- First posted on arXiv 14 Jul 2025.

## 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, 30 of 30)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2302.04867/) (2023)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed](https://mlsanity.com/paper/2101.02388/) (2021)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [Rectified Flow: A Marginal Preserving Approach to Optimal Transport](https://mlsanity.com/paper/2209.14577/) (2022)
- [Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Models](https://mlsanity.com/paper/2305.18455/) (2023)
- [GENIE: Higher-Order Denoising Diffusion Solvers](https://mlsanity.com/paper/2210.05475/) (2022)
- [ReNO: Enhancing One-step Text-to-Image Models through Reward-based Noise Optimization](https://mlsanity.com/paper/2406.04312/) (2024)
- [Golden Noise for Diffusion Models: A Learning Framework](https://mlsanity.com/paper/2411.09502/) (2024)
- [Banach Wasserstein GAN](https://mlsanity.com/paper/1806.06621/) (2018)
- [DC-Solver: Improving Predictor-Corrector Diffusion Sampler via Dynamic Compensation](https://mlsanity.com/paper/2409.03755/) (2024)
- [Constant Acceleration Flow](https://mlsanity.com/paper/2411.00322/) (2024)
- [Topic-VQ-VAE: Leveraging Latent Codebooks for Flexible Topic-Guided Document Generation](https://mlsanity.com/paper/2312.11532/) (2023)
- [Attack Deterministic Conditional Image Generative Models for Diverse and Controllable Generation](https://mlsanity.com/paper/2403.08294/) (2024)

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

- [Correlation Analysis of Generative Models](https://mlsanity.com/paper/2603.06614/) (2026)
- [Conditional Random Ordered Transport Spaces](https://mlsanity.com/paper/2606.08113/) (2026)
- [Self-Consistent Generative Paths via Admissible Random Variational Transport](https://mlsanity.com/paper/2606.08953/) (2026)
- [QWRF-Net: A Quantum-Wavelet Framework with Rectified Flow for Short-Term Precipitation Nowcasting](https://mlsanity.com/paper/2608.01626/) (2026)

## Abstract (arXiv)

The Reflow operation aims to straighten the inference trajectories of the rectified flow during training by constructing deterministic couplings between noises and images, thereby improving the quality of generated images in single-step or few-step generation. However, we identify critical limitations in Reflow, particularly its inability to rapidly generate high-quality images due to a distribution gap between images in its constructed deterministic couplings and real images. To address these shortcomings, we propose a novel alternative called Straighten Viscous Rectified Flow via Noise Optimization (VRFNO), which is a joint training framework integrating an encoder and a neural velocity field. VRFNO introduces two key innovations: (1) a historical velocity term that enhances trajectory distinction, enabling the model to more accurately predict the velocity of the current trajectory, and (2) the noise optimization through reparameterization to form optimized couplings with real images which are then utilized for training, effectively mitigating errors caused by Reflow's limitations. Comprehensive experiments on synthetic data and real datasets with varying resolutions show that VRFNO significantly mitigates the limitations of Reflow, achieving state-of-the-art performance in both one-step and few-step generation tasks.