# Straighter Flow Matching via a Diffusion-Based Coupling Prior

arXiv: https://arxiv.org/abs/2311.16507 · HTML: https://mlsanity.com/paper/2311.16507/

## Key facts

- Cited by 3 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 26 of its 43 references that are in the map.
- First posted on arXiv 28 Nov 2023.

## 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, 26 of 26)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [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)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [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)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed](https://mlsanity.com/paper/2101.02388/) (2021)
- [FreeDoM: Training-Free Energy-Guided Conditional Diffusion Model](https://mlsanity.com/paper/2303.09833/) (2023)
- [Self-Consuming Generative Models Go MAD](https://mlsanity.com/paper/2307.01850/) (2023)
- [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021)
- [Image Processing Using Multi-Code GAN Prior](https://mlsanity.com/paper/1912.07116/) (2019)
- [Flow Matching in Latent Space](https://mlsanity.com/paper/2307.08698/) (2023)
- [Minimizing Trajectory Curvature of ODE-based Generative Models](https://mlsanity.com/paper/2301.12003/) (2023)
- [Score-based Generative Modeling Secretly Minimizes the Wasserstein Distance](https://mlsanity.com/paper/2212.06359/) (2022)
- [Understanding DDPM Latent Codes Through Optimal Transport](https://mlsanity.com/paper/2202.07477/) (2022)
- [PyTorch Image Quality: Metrics for Image Quality Assessment](https://mlsanity.com/paper/2208.14818/) (2022)

## Built on by (most cited first, 3 of 3)

- [PeRFlow: Piecewise Rectified Flow as Universal Plug-and-Play Accelerator](https://mlsanity.com/paper/2405.07510/) (2024)
- [Immiscible Diffusion: Accelerating Diffusion Training with Noise Assignment](https://mlsanity.com/paper/2406.12303/) (2024)
- [Improved Immiscible Diffusion: Accelerate Diffusion Training by Reducing Its Miscibility](https://mlsanity.com/paper/2505.18521/) (2025)

## Abstract (arXiv)

Flow matching as a paradigm of generative model achieves notable success across various domains. However, existing methods use either multi-round training or knowledge within minibatches, posing challenges in finding a favorable coupling strategy for straightening trajectories to few-step generation. To address this issue, we propose a novel approach, Straighter trajectories of Flow Matching (StraightFM). It straightens trajectories with the coupling strategy from the entire distribution level. More specifically, during training, StraightFM creates couplings of images and noise via one diffusion model as a coupling prior to straighten trajectories for few-step generation. Our coupling strategy can also integrate with the existing coupling direction from real data to noise, improving image quality in few-step generation. Experimental results on pixel space and latent space show that StraightFM yields attractive samples within 5 steps. Moreover, our unconditional StraightFM is seamlessly compatible with training-free multimodal conditional generation, maintaining high-quality image generation in few steps.