# REG: Rectified Gradient Guidance for Conditional Diffusion Models

arXiv: https://arxiv.org/abs/2501.18865 · HTML: https://mlsanity.com/paper/2501.18865/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 31 of its 36 references that are in the map.
- First posted on arXiv 31 Jan 2025.

## Placed in

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

## Builds on (most cited first, 30 of 31)

- [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)
- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (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)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (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)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [Guiding a Diffusion Model with a Bad Version of Itself](https://mlsanity.com/paper/2406.02507/) (2024)
- [MDTv2: Masked Diffusion Transformer is a Strong Image Synthesizer](https://mlsanity.com/paper/2303.14389/) (2023)
- [Applying Guidance in a Limited Interval Improves Sample and Distribution Quality in Diffusion Models](https://mlsanity.com/paper/2404.07724/) (2024)
- [CFG++: Manifold-constrained Classifier Free Guidance for Diffusion Models](https://mlsanity.com/paper/2406.08070/) (2024)
- [End-to-End Diffusion Latent Optimization Improves Classifier Guidance](https://mlsanity.com/paper/2303.13703/) (2023)
- [Classifier-Free Guidance is a Predictor-Corrector](https://mlsanity.com/paper/2408.09000/) (2024)
- [Analysis of Classifier-Free Guidance Weight Schedulers](https://mlsanity.com/paper/2404.13040/) (2024)
- [Rectified Diffusion: Straightness Is Not Your Need in Rectified Flow](https://mlsanity.com/paper/2410.07303/) (2024)
- [A Noise is Worth Diffusion Guidance](https://mlsanity.com/paper/2412.03895/) (2024)
- [What does guidance do? A fine-grained analysis in a simple setting](https://mlsanity.com/paper/2409.13074/) (2024)
- [Theoretical Insights for Diffusion Guidance: A Case Study for Gaussian Mixture Models](https://mlsanity.com/paper/2403.01639/) (2024)
- [Characteristic Guidance: Non-linear Correction for Diffusion Model at Large Guidance Scale](https://mlsanity.com/paper/2312.07586/) (2023)

## Built on by (most cited first, 8 of 8)

- [Stage-wise Dynamics of Classifier-Free Guidance in Diffusion Models](https://mlsanity.com/paper/2509.22007/) (2025)
- [Towards a Golden Classifier-Free Guidance Path via Foresight Fixed Point Iterations](https://mlsanity.com/paper/2510.21512/) (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)
- [Tempered Guided Diffusion](https://mlsanity.com/paper/2605.03712/) (2026)
- [Self-Supervised Learning via Flow-Guided Neural Operator on Time-Series Data](https://mlsanity.com/paper/2602.12267/) (2026)
- [MacroGuide: Topological Guidance for Macrocycle Generation](https://mlsanity.com/paper/2602.14977/) (2026)
- [Learning ω-Powered Conditional Distributions with Importance-Weighted Flow Matching](https://mlsanity.com/paper/2610.16419/) (2026)

## Abstract (arXiv)

Guidance techniques are simple yet effective for improving conditional generation in diffusion models. Albeit their empirical success, the practical implementation of guidance diverges significantly from its theoretical motivation. In this paper, we reconcile this discrepancy by replacing the scaled marginal distribution target, which we prove theoretically invalid, with a valid scaled joint distribution objective. Additionally, we show that the established guidance implementations are approximations to the intractable optimal solution under no future foresight constraint. Building on these theoretical insights, we propose rectified gradient guidance (REG), a versatile enhancement designed to boost the performance of existing guidance methods. Experiments on 1D and 2D demonstrate that REG provides a better approximation to the optimal solution than prior guidance techniques, validating the proposed theoretical framework. Extensive experiments on class-conditional ImageNet and text-to-image generation tasks show that incorporating REG consistently improves FID and Inception/CLIP scores across various settings compared to its absence.