# PeRFlow: Piecewise Rectified Flow as Universal Plug-and-Play Accelerator

arXiv: https://arxiv.org/abs/2405.07510 · HTML: https://mlsanity.com/paper/2405.07510/

## Key facts

- Cited by 97 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 48 of its 55 references that are in the map.
- First posted on arXiv 13 May 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, 30 of 48)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (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)
- [IP-Adapter: Text Compatible Image Prompt Adapter for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2308.06721/) (2023)
- [AnimateDiff: Animate Your Personalized Text-to-Image Diffusion Models without Specific Tuning](https://mlsanity.com/paper/2307.04725/) (2023)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [eDiff-I: Text-to-Image Diffusion Models with an Ensemble of Expert Denoisers](https://mlsanity.com/paper/2211.01324/) (2022)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Wonder3D: Single Image to 3D using Cross-Domain Diffusion](https://mlsanity.com/paper/2310.15008/) (2023)
- [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)
- [MagicVideo: Efficient Video Generation With Latent Diffusion Models](https://mlsanity.com/paper/2211.11018/) (2022)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [Rectified Flow: A Marginal Preserving Approach to Optimal Transport](https://mlsanity.com/paper/2209.14577/) (2022)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)

## Built on by (most cited first, 30 of 97)

- [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024)
- [Pyramidal Flow Matching for Efficient Video Generative Modeling](https://mlsanity.com/paper/2410.05954/) (2024)
- [Diffusion Adversarial Post-Training for One-Step Video Generation](https://mlsanity.com/paper/2501.08316/) (2025)
- [PixelFlow: Pixel-Space Generative Models with Flow](https://mlsanity.com/paper/2504.07963/) (2025)
- [Autoregressive Adversarial Post-Training for Real-Time Interactive Video Generation](https://mlsanity.com/paper/2506.09350/) (2025)
- [Multistep Distillation of Diffusion Models via Moment Matching](https://mlsanity.com/paper/2406.04103/) (2024)
- [One-Step Diffusion Distillation through Score Implicit Matching](https://mlsanity.com/paper/2410.16794/) (2024)
- [EM Distillation for One-step Diffusion Models](https://mlsanity.com/paper/2405.16852/) (2024)
- [Rectified Diffusion: Straightness Is Not Your Need in Rectified Flow](https://mlsanity.com/paper/2410.07303/) (2024)
- [Learning Few-Step Diffusion Models by Trajectory Distribution Matching](https://mlsanity.com/paper/2503.06674/) (2025)
- [Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matching](https://mlsanity.com/paper/2405.18816/) (2024)
- [Adversarial Diffusion Compression for Real-World Image Super-Resolution](https://mlsanity.com/paper/2411.13383/) (2024)
- [SeedVR2: One-Step Video Restoration via Diffusion Adversarial Post-Training](https://mlsanity.com/paper/2506.05301/) (2025)
- [Efficient Diffusion Models: A Comprehensive Survey from Principles to Practices](https://mlsanity.com/paper/2410.11795/) (2024)
- [One Diffusion Step to Real-World Super-Resolution via Flow Trajectory Distillation](https://mlsanity.com/paper/2502.01993/) (2025)
- [MegaTTS 3: Sparse Alignment Enhanced Latent Diffusion Transformer for Zero-Shot Speech Synthesis](https://mlsanity.com/paper/2502.18924/) (2025)
- [Adversarial Distribution Matching for Diffusion Distillation Towards Efficient Image and Video Synthesis](https://mlsanity.com/paper/2507.18569/) (2025)
- [OSV: One Step is Enough for High-Quality Image to Video Generation](https://mlsanity.com/paper/2409.11367/) (2024)
- [Efficient Diffusion Models: A Survey](https://mlsanity.com/paper/2502.06805/) (2025)
- [Variational Rectified Flow Matching](https://mlsanity.com/paper/2502.09616/) (2025)
- [FlashVideo: Flowing Fidelity to Detail for Efficient High-Resolution Video Generation](https://mlsanity.com/paper/2502.05179/) (2025)
- [Diff-Instruct++: Training One-step Text-to-image Generator Model to Align with Human Preferences](https://mlsanity.com/paper/2410.18881/) (2024)
- [Diff2Flow: Training Flow Matching Models via Diffusion Model Alignment](https://mlsanity.com/paper/2506.02221/) (2025)
- [Unleashing Vecset Diffusion Model for Fast Shape Generation](https://mlsanity.com/paper/2503.16302/) (2025)
- [OFTSR: One-Step Flow for Image Super-Resolution with Tunable Fidelity-Realism Trade-offs](https://mlsanity.com/paper/2412.09465/) (2024)
- [Diversity-Preserved Distribution Matching Distillation for Fast Visual Synthesis](https://mlsanity.com/paper/2602.03139/) (2026)
- [LightningDrag: Lightning Fast and Accurate Drag-based Image Editing Emerging from Videos](https://mlsanity.com/paper/2405.13722/) (2024)
- [NitroFusion: High-Fidelity Single-Step Diffusion through Dynamic Adversarial Training](https://mlsanity.com/paper/2412.02030/) (2024)
- [Ultra-Fast Language Generation via Discrete Diffusion Divergence Instruct](https://mlsanity.com/paper/2509.25035/) (2025)
- [AccVideo: Accelerating Video Diffusion Model with Synthetic Dataset](https://mlsanity.com/paper/2503.19462/) (2025)

## Abstract (arXiv)

We present Piecewise Rectified Flow (PeRFlow), a flow-based method for accelerating diffusion models. PeRFlow divides the sampling process of generative flows into several time windows and straightens the trajectories in each interval via the reflow operation, thereby approaching piecewise linear flows. PeRFlow achieves superior performance in a few-step generation. Moreover, through dedicated parameterizations, the PeRFlow models inherit knowledge from the pretrained diffusion models. Thus, the training converges fast and the obtained models show advantageous transfer ability, serving as universal plug-and-play accelerators that are compatible with various workflows based on the pre-trained diffusion models. Codes for training and inference are publicly released. https://github.com/magic-research/piecewise-rectified-flow