# Characteristic Guidance: Non-linear Correction for Diffusion Model at Large Guidance Scale

arXiv: https://arxiv.org/abs/2312.07586 · HTML: https://mlsanity.com/paper/2312.07586/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 23 of its 32 references that are in the map.
- First posted on arXiv 11 Dec 2023.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [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)
- [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)
- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2302.04867/) (2023)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [FreeDoM: Training-Free Energy-Guided Conditional Diffusion Model](https://mlsanity.com/paper/2303.09833/) (2023)
- [Improving Sample Quality of Diffusion Models Using Self-Attention Guidance](https://mlsanity.com/paper/2210.00939/) (2022)
- [Refining Generative Process with Discriminator Guidance in Score-based Diffusion Models](https://mlsanity.com/paper/2211.17091/) (2022)
- [FP-Diffusion: Improving Score-based Diffusion Models by Enforcing the Underlying Score Fokker-Planck Equation](https://mlsanity.com/paper/2210.04296/) (2022)
- [On Investigating the Conservative Property of Score-Based Generative Models](https://mlsanity.com/paper/2209.12753/) (2022)
- [ShiftDDPMs: Exploring Conditional Diffusion Models by Shifting Diffusion Trajectories](https://mlsanity.com/paper/2302.02373/) (2023)

## Built on by (most cited first, 26 of 26)

- [Guiding a Diffusion Model with a Bad Version of Itself](https://mlsanity.com/paper/2406.02507/) (2024)
- [Eliminating Oversaturation and Artifacts of High Guidance Scales in Diffusion Models](https://mlsanity.com/paper/2410.02416/) (2024)
- [CFG-Zero*: Improved Classifier-Free Guidance for Flow Matching Models](https://mlsanity.com/paper/2503.18886/) (2025)
- [Diffusion Models without Classifier-free Guidance](https://mlsanity.com/paper/2502.12154/) (2025)
- [Rectified-CFG++ for Flow Based Models](https://mlsanity.com/paper/2510.07631/) (2025)
- [Learn to Guide Your Diffusion Model](https://mlsanity.com/paper/2510.00815/) (2025)
- [Flow Map Distillation Without Data](https://mlsanity.com/paper/2511.19428/) (2025)
- [Normalized Attention Guidance: Universal Negative Guidance for Diffusion Models](https://mlsanity.com/paper/2505.21179/) (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)
- [Towards a Golden Classifier-Free Guidance Path via Foresight Fixed Point Iterations](https://mlsanity.com/paper/2510.21512/) (2025)
- [Dichotomous Diffusion Policy Optimization](https://mlsanity.com/paper/2601.00898/) (2025)
- [DogFit: Domain-guided Fine-tuning for Efficient Transfer Learning of Diffusion Models](https://mlsanity.com/paper/2508.05685/) (2025)
- [Improving Classifier-Free Guidance of Flow Matching via Manifold Projection](https://mlsanity.com/paper/2601.21892/) (2026)
- [DICE: Distilling Classifier-Free Guidance into Text Embeddings](https://mlsanity.com/paper/2502.03726/) (2025)
- [Composable Score-based Graph Diffusion Model for Multi-Conditional Molecular Generation](https://mlsanity.com/paper/2509.09451/) (2025)
- [On the Separability of Information in Diffusion Models](https://mlsanity.com/paper/2509.23937/) (2025)
- [Stay Fair! Ensuring Group Fairness in Diffusion Models Across Guidance Scales](https://mlsanity.com/paper/2605.28036/) (2026)
- [RSTR: Reducing SpatioTemporal Redundancy in Diffusion Transformers](https://mlsanity.com/paper/2512.14096/) (2025)
- [Error as Signal: Stiffness-Aware Diffusion Sampling via Embedded Runge-Kutta Guidance](https://mlsanity.com/paper/2603.03692/) (2026)
- [ModaFlow: Modality-Aware Flow Matching for High-Fidelity Virtual Try-On](https://mlsanity.com/paper/2606.27773/) (2026)
- [TAG: Tangential Amplifying Guidance for Hallucination-Resistant Sampling](https://mlsanity.com/paper/2510.04533/) (2025)
- [Commitment Before Realization: When Classifier-Free Guidance Becomes Unnecessary in Masked Diffusion Language Models](https://mlsanity.com/paper/2608.08082/) (2026)
- [Backward SDEs-based Diffusion for Physics-Constrained Generation](https://mlsanity.com/paper/2609.15702/) (2026)
- [SAGE: Subspace Alignment for Classifier-Free Guidance in Mixture-of-Experts Diffusion Models](https://mlsanity.com/paper/2609.34525/) (2026)
- [Diffusion Editing with Soft Mask: Pixel Level Redo of Image and Video with Adjustable Strength](https://mlsanity.com/paper/2610.00359/) (2026)

## Abstract (arXiv)

Popular guidance for denoising diffusion probabilistic model (DDPM) linearly combines distinct conditional models together to provide enhanced control over samples. However, this approach overlooks nonlinear effects that become significant when guidance scale is large. To address this issue, we propose characteristic guidance, a guidance method that provides first-principle non-linear correction for classifier-free guidance. Such correction forces the guided DDPMs to respect the Fokker-Planck (FP) equation of diffusion process, in a way that is training-free and compatible with existing sampling methods. Experiments show that characteristic guidance enhances semantic characteristics of prompts and mitigate irregularities in image generation, proving effective in diverse applications ranging from simulating magnet phase transitions to latent space sampling.