# Rectified Diffusion Guidance for Conditional Generation

arXiv: https://arxiv.org/abs/2410.18737 · HTML: https://mlsanity.com/paper/2410.18737/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 28 of its 31 references that are in the map.
- First posted on arXiv 24 Oct 2024.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 28 of 28)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [Conceptual 12M: Pushing Web-Scale Image-Text Pre-Training To Recognize Long-Tail Visual Concepts](https://mlsanity.com/paper/2102.08981/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [Common Diffusion Noise Schedules and Sample Steps are Flawed](https://mlsanity.com/paper/2305.08891/) (2023)
- [Composer: Creative and Controllable Image Synthesis with Composable Conditions](https://mlsanity.com/paper/2302.09778/) (2023)
- [Guiding a Diffusion Model with a Bad Version of Itself](https://mlsanity.com/paper/2406.02507/) (2024)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [Projected GANs Converge Faster](https://mlsanity.com/paper/2111.01007/) (2021)
- [Exposing flaws of generative model evaluation metrics and their unfair treatment of diffusion models](https://mlsanity.com/paper/2306.04675/) (2023)
- [Learning Multi-dimensional Human Preference for Text-to-Image Generation](https://mlsanity.com/paper/2405.14705/) (2024)
- [Classifier-Free Guidance is a Predictor-Corrector](https://mlsanity.com/paper/2408.09000/) (2024)
- [What does guidance do? A fine-grained analysis in a simple setting](https://mlsanity.com/paper/2409.13074/) (2024)

## Built on by (most cited first, 18 of 18)

- [CFG-Zero*: Improved Classifier-Free Guidance for Flow Matching Models](https://mlsanity.com/paper/2503.18886/) (2025)
- [Rectified-CFG++ for Flow Based Models](https://mlsanity.com/paper/2510.07631/) (2025)
- [Feedback Guidance of Diffusion Models](https://mlsanity.com/paper/2506.06085/) (2025)
- [Stage-wise Dynamics of Classifier-Free Guidance in Diffusion Models](https://mlsanity.com/paper/2509.22007/) (2025)
- [Learn to Guide Your Diffusion Model](https://mlsanity.com/paper/2510.00815/) (2025)
- [Normalized Attention Guidance: Universal Negative Guidance for Diffusion Models](https://mlsanity.com/paper/2505.21179/) (2025)
- [Angle Domain Guidance: Latent Diffusion Requires Rotation Rather Than Extrapolation](https://mlsanity.com/paper/2506.11039/) (2025)
- [REG: Rectified Gradient Guidance for Conditional Diffusion Models](https://mlsanity.com/paper/2501.18865/) (2025)
- [CFG-Ctrl: Control-Based Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2603.03281/) (2026)
- [Momentum Guidance: Plug-and-Play Guidance for Flow Models](https://mlsanity.com/paper/2602.20360/) (2026)
- [Studying Classifier(-Free) Guidance From a Classifier-Centric Perspective](https://mlsanity.com/paper/2503.10638/) (2025)
- [MAMBO-G: Magnitude-Aware Mitigation for Boosted Guidance](https://mlsanity.com/paper/2508.03442/) (2025)
- [Improving Diffusion Generalization with Weak-to-Strong Segmented Guidance](https://mlsanity.com/paper/2603.20584/) (2026)
- [ModaFlow: Modality-Aware Flow Matching for High-Fidelity Virtual Try-On](https://mlsanity.com/paper/2606.27773/) (2026)
- [Manifold-Optimal Guidance: A Unified Riemannian Control View of Diffusion Guidance](https://mlsanity.com/paper/2603.11509/) (2026)
- [Exploring Motion-Language Alignment for Text-driven Motion Generation](https://mlsanity.com/paper/2604.02973/) (2026)
- [Adversarial Learning of Classifier-Free Guidance Schedules](https://mlsanity.com/paper/2608.14038/) (2026)
- [Classifier-Free Guidance in Flow Matching: Non-Autonomous Potentials, Overshoot, and Posterior-Mean Control](https://mlsanity.com/paper/2609.24287/) (2026)

## Abstract (arXiv)

Classifier-Free Guidance (CFG), which combines the conditional and unconditional score functions with two coefficients summing to one, serves as a practical technique for diffusion model sampling. Theoretically, however, denoising with CFG textitcannot be expressed as a reciprocal diffusion process, which may consequently leave some hidden risks during use. In this work, we revisit the theory behind CFG and rigorously confirm that the improper configuration of the combination coefficients (textiti.e., the widely used summing-to-one version) brings about expectation shift of the generative distribution. To rectify this issue, we propose ReCFG with a relaxation on the guidance coefficients such that denoising with method strictly aligns with the diffusion theory. We further show that our approach enjoys a textbftextitclosed-form solution given the guidance strength. That way, the rectified coefficients can be readily pre-computed via traversing the observed data, leaving the sampling speed barely affected. Empirical evidence on real-world data demonstrate the compatibility of our post-hoc design with existing state-of-the-art diffusion models, including both class-conditioned ones (textite.g., EDM2 on ImageNet) and text-conditioned ones (textite.g., SD3 on CC12M), without any retraining. Code is available at hrefhttps://github.com/thuxmf/recfghttps://github.com/thuxmf/recfg.