# Accelerating Guided Diffusion Sampling with Splitting Numerical Methods

arXiv: https://arxiv.org/abs/2301.11558 · HTML: https://mlsanity.com/paper/2301.11558/

## Key facts

- Cited by 13 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 42 references that are in the map.
- First posted on arXiv 27 Jan 2023.

## Placed in

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

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

- [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)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed](https://mlsanity.com/paper/2101.02388/) (2021)
- [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021)
- [Score-Based Generative Modeling with Critically-Damped Langevin Diffusion](https://mlsanity.com/paper/2112.07068/) (2021)
- [EGSDE: Unpaired Image-to-Image Translation via Energy-Guided Stochastic Differential Equations](https://mlsanity.com/paper/2207.06635/) (2022)
- [UNIT-DDPM: UNpaired Image Translation with Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2104.05358/) (2021)
- [Learning to Efficiently Sample from Diffusion Probabilistic Models](https://mlsanity.com/paper/2106.03802/) (2021)
- [gDDIM: Generalized denoising diffusion implicit models](https://mlsanity.com/paper/2206.05564/) (2022)
- [Guided Diffusion Model for Adversarial Purification](https://mlsanity.com/paper/2205.14969/) (2022)
- [Guided Diffusion Model for Adversarial Purification from Random Noise](https://mlsanity.com/paper/2206.10875/) (2022)
- [Enhancing Diffusion-Based Image Synthesis with Robust Classifier Guidance](https://mlsanity.com/paper/2208.08664/) (2022)

## Built on by (most cited first, 13 of 13)

- [DPM-Solver-v3: Improved Diffusion ODE Solver with Empirical Model Statistics](https://mlsanity.com/paper/2310.13268/) (2023)
- [Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2307.11494/) (2023)
- [A Comprehensive Survey on Knowledge Distillation of Diffusion Models](https://mlsanity.com/paper/2304.04262/) (2023)
- [Efficient Integrators for Diffusion Generative Models](https://mlsanity.com/paper/2310.07894/) (2023)
- [EVODiff: Entropy-aware Variance Optimized Diffusion Inference](https://mlsanity.com/paper/2509.26096/) (2025)
- [A Survey of Emerging Applications of Diffusion Probabilistic Models in MRI](https://mlsanity.com/paper/2311.11383/) (2023)
- [Robust Guided Diffusion for Offline Black-Box Optimization](https://mlsanity.com/paper/2410.00983/) (2024)
- [STORK: Faster Diffusion And Flow Matching Sampling By Resolving Both Stiffness And Structure-Dependence](https://mlsanity.com/paper/2505.24210/) (2025)
- [Diffusion Sampling with Momentum for Mitigating Divergence Artifacts](https://mlsanity.com/paper/2307.11118/) (2023)
- [Mitigating the Contractivity Trap in Diffusion ODEs via Stein Stabilization](https://mlsanity.com/paper/2606.07835/) (2026)
- [SSSD-ECG-nle: New Label Embeddings with Structured State-Space Models for ECG generation](https://mlsanity.com/paper/2407.11108/) (2024)
- [Elucidating the Preconditioning in Consistency Distillation](https://mlsanity.com/paper/2502.02922/) (2025)
- [Variance-Reduction Guidance: Sampling Trajectory Optimization for Diffusion Models](https://mlsanity.com/paper/2510.21792/) (2025)

## Abstract (arXiv)

Guided diffusion is a technique for conditioning the output of a diffusion model at sampling time without retraining the network for each specific task. One drawback of diffusion models, however, is their slow sampling process. Recent techniques can accelerate unguided sampling by applying high-order numerical methods to the sampling process when viewed as differential equations. On the contrary, we discover that the same techniques do not work for guided sampling, and little has been explored about its acceleration. This paper explores the culprit of this problem and provides a solution based on operator splitting methods, motivated by our key finding that classical high-order numerical methods are unsuitable for the conditional function. Our proposed method can re-utilize the high-order methods for guided sampling and can generate images with the same quality as a 250-step DDIM baseline using 32-58% less sampling time on ImageNet256. We also demonstrate usage on a wide variety of conditional generation tasks, such as text-to-image generation, colorization, inpainting, and super-resolution.