# Rectified Diffusion: Straightness Is Not Your Need in Rectified Flow

arXiv: https://arxiv.org/abs/2410.07303 · HTML: https://mlsanity.com/paper/2410.07303/

## Key facts

- Cited by 61 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 59 of its 71 references that are in the map.
- First posted on arXiv 9 Oct 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 59)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [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)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [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)
- [Make-A-Video: Text-to-Video Generation without Text-Video Data](https://mlsanity.com/paper/2209.14792/) (2022)
- [Scaling Autoregressive Models for Content-Rich Text-to-Image Generation](https://mlsanity.com/paper/2206.10789/) (2022)
- [Conceptual 12M: Pushing Web-Scale Image-Text Pre-Training To Recognize Long-Tail Visual Concepts](https://mlsanity.com/paper/2102.08981/) (2021)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2305.01569/) (2023)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [eDiff-I: Text-to-Image Diffusion Models with an Ensemble of Expert Denoisers](https://mlsanity.com/paper/2211.01324/) (2022)
- [Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesis](https://mlsanity.com/paper/2306.09341/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)

## Built on by (most cited first, 30 of 61)

- [MMaDA: Multimodal Large Diffusion Language Models](https://mlsanity.com/paper/2505.15809/) (2025)
- [Taming Rectified Flow for Inversion and Editing](https://mlsanity.com/paper/2411.04746/) (2024)
- [Yume: An Interactive World Generation Model](https://mlsanity.com/paper/2507.17744/) (2025)
- [GestureLSM: Latent Shortcut based Co-Speech Gesture Generation with Spatial-Temporal Modeling](https://mlsanity.com/paper/2501.18898/) (2025)
- [Adversarial Distribution Matching for Diffusion Distillation Towards Efficient Image and Video Synthesis](https://mlsanity.com/paper/2507.18569/) (2025)
- [GS-DiT: Advancing Video Generation with Pseudo 4D Gaussian Fields through Efficient Dense 3D Point Tracking](https://mlsanity.com/paper/2501.02690/) (2025)
- [UniEdit-Flow: Unleashing Inversion and Editing in the Era of Flow Models](https://mlsanity.com/paper/2504.13109/) (2025)
- [SnapGen-V: Generating a Five-Second Video within Five Seconds on a Mobile Device](https://mlsanity.com/paper/2412.10494/) (2024)
- [DepthLab: From Partial to Complete](https://mlsanity.com/paper/2412.18153/) (2024)
- [Training-free Diffusion Acceleration with Bottleneck Sampling](https://mlsanity.com/paper/2503.18940/) (2025)
- [Diffusion-NPO: Negative Preference Optimization for Better Preference Aligned Generation of Diffusion Models](https://mlsanity.com/paper/2505.11245/) (2025)
- [Beyond Optimal Transport: Model-Aligned Coupling for Flow Matching](https://mlsanity.com/paper/2505.23346/) (2025)
- [Manifold-Aware Exploration for Reinforcement Learning in Video Generation](https://mlsanity.com/paper/2603.21872/) (2026)
- [MeanAudio: Fast and Faithful Text-to-Audio Generation with Mean Flows](https://mlsanity.com/paper/2508.06098/) (2025)
- [RayFlow: Instance-Aware Diffusion Acceleration via Adaptive Flow Trajectories](https://mlsanity.com/paper/2503.07699/) (2025)
- [Few-Step Diffusion via Score identity Distillation](https://mlsanity.com/paper/2505.12674/) (2025)
- [WideRange4D: Enabling High-Quality 4D Reconstruction with Wide-Range Movements and Scenes](https://mlsanity.com/paper/2503.13435/) (2025)
- [LinVideo: A Post-Training Framework towards O(n) Attention in Efficient Video Generation](https://mlsanity.com/paper/2510.08318/) (2025)
- [Distilling Diffusion Models to Efficient 3D LiDAR Scene Completion](https://mlsanity.com/paper/2412.03515/) (2024)
- [CurveFlow: Curvature-Guided Flow Matching for Image Generation](https://mlsanity.com/paper/2508.15093/) (2025)
- [Stable Consistency Tuning: Understanding and Improving Consistency Models](https://mlsanity.com/paper/2410.18958/) (2024)
- [Bures-Wasserstein Flow Matching for Graph Generation](https://mlsanity.com/paper/2506.14020/) (2025)
- [Taming Diffusion Transformer for Efficient Mobile Video Generation in Seconds](https://mlsanity.com/paper/2507.13343/) (2025)
- [REG: Rectified Gradient Guidance for Conditional Diffusion Models](https://mlsanity.com/paper/2501.18865/) (2025)
- [Conceptrol: Concept Control of Zero-shot Personalized Image Generation](https://mlsanity.com/paper/2503.06568/) (2025)
- [UniGlyph: Unified Segmentation-Conditioned Diffusion for Precise Visual Text Synthesis](https://mlsanity.com/paper/2507.00992/) (2025)
- [Score Distillation of Flow Matching Models](https://mlsanity.com/paper/2509.25127/) (2025)
- [Learning Straight Flows: Variational Flow Matching for Efficient Generation](https://mlsanity.com/paper/2511.17583/) (2025)
- [Stream-DiffVSR: Low-Latency Streamable Video Super-Resolution via Auto-Regressive Diffusion](https://mlsanity.com/paper/2512.23709/) (2025)
- [S2DiT: Sandwich Diffusion Transformer for Mobile Streaming Video Generation](https://mlsanity.com/paper/2601.12719/) (2026)

## Abstract (arXiv)

Diffusion models have greatly improved visual generation but are hindered by slow generation speed due to the computationally intensive nature of solving generative ODEs. Rectified flow, a widely recognized solution, improves generation speed by straightening the ODE path. Its key components include: 1) using the diffusion form of flow-matching, 2) employing boldsymbol v-prediction, and 3) performing rectification (a.k.a. reflow). In this paper, we argue that the success of rectification primarily lies in using a pretrained diffusion model to obtain matched pairs of noise and samples, followed by retraining with these matched noise-sample pairs. Based on this, components 1) and 2) are unnecessary. Furthermore, we highlight that straightness is not an essential training target for rectification; rather, it is a specific case of flow-matching models. The more critical training target is to achieve a first-order approximate ODE path, which is inherently curved for models like DDPM and Sub-VP. Building on this insight, we propose Rectified Diffusion, which generalizes the design space and application scope of rectification to encompass the broader category of diffusion models, rather than being restricted to flow-matching models. We validate our method on Stable Diffusion v1-5 and Stable Diffusion XL. Our method not only greatly simplifies the training procedure of rectified flow-based previous works (e.g., InstaFlow) but also achieves superior performance with even lower training cost. Our code is available at https://github.com/G-U-N/Rectified-Diffusion.