# Rectified Noise: A Generative Model Using Positive-incentive Noise

arXiv: https://arxiv.org/abs/2511.07911 · HTML: https://mlsanity.com/paper/2511.07911/

## Key facts

- Cited by 7 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 27 of its 40 references that are in the map.
- First posted on arXiv 11 Nov 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, 27 of 27)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [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)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Movie Gen: A Cast of Media Foundation Models](https://mlsanity.com/paper/2410.13720/) (2024)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Generating Images with Sparse Representations](https://mlsanity.com/paper/2103.03841/) (2021)
- [On the Importance of Noise Scheduling for Diffusion Models](https://mlsanity.com/paper/2301.10972/) (2023)
- [U-GAT-IT: Unsupervised Generative Attentional Networks with Adaptive Layer-Instance Normalization for Image-to-Image Translation](https://mlsanity.com/paper/1907.10830/) (2019)
- [Solving Schr"odinger Bridges via Maximum Likelihood](https://mlsanity.com/paper/2106.02081/) (2021)
- [Theoretical guarantees for sampling and inference in generative models with latent diffusions](https://mlsanity.com/paper/1903.01608/) (2019)
- [Improved Techniques for Maximum Likelihood Estimation for Diffusion ODEs](https://mlsanity.com/paper/2305.03935/) (2023)
- [Enhance Vision-Language Alignment with Noise](https://mlsanity.com/paper/2412.10817/) (2024)
- [Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusions](https://mlsanity.com/paper/2302.07261/) (2023)
- [Learn Beneficial Noise as Graph Augmentation](https://mlsanity.com/paper/2505.19024/) (2025)
- [NFIG: Multi-Scale Autoregressive Image Generation via Frequency Ordering](https://mlsanity.com/paper/2503.07076/) (2025)
- [Adv-CPG: A Customized Portrait Generation Framework with Facial Adversarial Attacks](https://mlsanity.com/paper/2503.08269/) (2025)
- [Object-AVEdit: An Object-level Audio-Visual Editing Model](https://mlsanity.com/paper/2510.00050/) (2025)

## Built on by (most cited first, 7 of 7)

- [GRPO-RM: Fine-Tuning Representation Models via GRPO-Driven Reinforcement Learning](https://mlsanity.com/paper/2511.15256/) (2025)
- [ViewMask-1-to-3: Multi-View Consistent Image Generation via Multimodal Discrete Diffusion Models](https://mlsanity.com/paper/2512.14099/) (2025)
- [Safeguarding Text-to-Image Generative Models Against Unauthorized Knowledge Distillation](https://mlsanity.com/paper/2605.22060/) (2026)
- [Multi-Intent Spoken Language Understanding: Methods, Trends, and Challenges](https://mlsanity.com/paper/2512.11258/) (2025)
- [Latent Noise Mask for Reducing Visual Redundancy in Multimodal Large Language Models](https://mlsanity.com/paper/2606.30168/) (2026)
- [Miles: Metric Learning with Expandable Subspace for Pre-Trained Model-Based Class-Incremental Learning](https://mlsanity.com/paper/2607.17593/) (2026)
- [Representation Learning in Diffusion and Flow-based Model: An Application Aspect](https://mlsanity.com/paper/2608.24068/) (2026)

## Abstract (arXiv)

Rectified Flow (RF) has been widely used as an effective generative model. Although RF is primarily based on probability flow Ordinary Differential Equations (ODE), recent studies have shown that injecting noise through reverse-time Stochastic Differential Equations (SDE) for sampling can achieve superior generative performance. Inspired by Positive-incentive Noise (pi-noise), we propose an innovative generative algorithm to train pi-noise generators, namely Rectified Noise (RN), which improves the generative performance by injecting pi-noise into the velocity field of pre-trained RF models. After introducing the Rectified Noise pipeline, pre-trained RF models can be efficiently transformed into pi-noise generators. We validate Rectified Noise by conducting extensive experiments across various model architectures on different datasets. Notably, we find that: (1) RF models using Rectified Noise reduce FID from 10.16 to 9.05 on ImageNet-1k. (2) The models of pi-noise generators achieve improved performance with only 0.39% additional training parameters.