# Saddle-Free Guidance: Improved On-Manifold Sampling without Labels or Additional Training

arXiv: https://arxiv.org/abs/2511.21863 · HTML: https://mlsanity.com/paper/2511.21863/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 31 of its 33 references that are in the map.
- First posted on arXiv 26 Nov 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)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [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)
- [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)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [CogVideoX: Text-to-Video Diffusion Models with An Expert Transformer](https://mlsanity.com/paper/2408.06072/) (2024)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [Make-An-Audio: Text-To-Audio Generation with Prompt-Enhanced Diffusion Models](https://mlsanity.com/paper/2301.12661/) (2023)
- [Guiding a Diffusion Model with a Bad Version of Itself](https://mlsanity.com/paper/2406.02507/) (2024)
- [Applying Guidance in a Limited Interval Improves Sample and Distribution Quality in Diffusion Models](https://mlsanity.com/paper/2404.07724/) (2024)
- [Diffusion Model-Based Image Editing: A Survey](https://mlsanity.com/paper/2402.17525/) (2024)
- [A Survey on Video Diffusion Models](https://mlsanity.com/paper/2310.10647/) (2023)
- [Exposing flaws of generative model evaluation metrics and their unfair treatment of diffusion models](https://mlsanity.com/paper/2306.04675/) (2023)
- [Self-Rectifying Diffusion Sampling with Perturbed-Attention Guidance](https://mlsanity.com/paper/2403.17377/) (2024)
- [Denoising diffusion models for out-of-distribution detection](https://mlsanity.com/paper/2211.07740/) (2022)
- [Solving Audio Inverse Problems with a Diffusion Model](https://mlsanity.com/paper/2210.15228/) (2022)
- [Unsupervised Out-of-Distribution Detection with Diffusion Inpainting](https://mlsanity.com/paper/2302.10326/) (2023)
- [Smoothed Energy Guidance: Guiding Diffusion Models with Reduced Energy Curvature of Attention](https://mlsanity.com/paper/2408.00760/) (2024)
- [Adversarial Estimation of Topological Dimension with Harmonic Score Maps](https://mlsanity.com/paper/2312.06869/) (2023)
- [A Connection Between Score Matching and Local Intrinsic Dimension](https://mlsanity.com/paper/2510.12975/) (2025)

## Abstract (arXiv)

Score-based generative models require guidance in order to generate plausible, on-manifold samples. The most popular guidance method, Classifier-Free Guidance (CFG), is only applicable in settings with labeled data and requires training an additional unconditional score-based model. More recently, Auto-Guidance adopts a smaller, less capable version of the original model to guide generation. While each method effectively promotes the fidelity of generated data, each requires labeled data or the training of additional models, making it challenging to guide score-based models when (labeled) training data are not available or training new models is not feasible. We make the surprising discovery that the positive curvature of log density estimates in saddle regions provides strong guidance for score-based models. Motivated by this, we develop saddle-free guidance (SFG) which maintains estimates of maximal positive curvature of the log density to guide individual score-based models. SFG has the same computational cost of classifier-free guidance, does not require additional training, and works with off-the-shelf diffusion and flow matching models. Our experiments indicate that SFG achieves state-of-the-art FID and FD-DINOv2 metrics in single-model unconditional ImageNet-512 generation. When SFG is combined with Auto-Guidance, its unconditional samples achieve general state-of-the-art in FD-DINOv2 score. Our experiments with FLUX.1-dev and Stable Diffusion v3.5 indicate that SFG boosts the diversity of output images compared to CFG while maintaining excellent prompt adherence and image fidelity.