# Accelerating Score-based Generative Models with Preconditioned Diffusion Sampling

arXiv: https://arxiv.org/abs/2207.02196 · HTML: https://mlsanity.com/paper/2207.02196/

## Key facts

- Cited by 19 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 39 references that are in the map.
- First posted on arXiv 5 Jul 2022.

## 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)
- [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)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [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)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [Score-Based Generative Modeling with Critically-Damped Langevin Diffusion](https://mlsanity.com/paper/2112.07068/) (2021)
- [Gotta Go Fast When Generating Data with Score-Based Models](https://mlsanity.com/paper/2105.14080/) (2021)
- [Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1512.07666/) (2015)

## Built on by (most cited first, 19 of 19)

- [Diffusion Probabilistic Model Made Slim](https://mlsanity.com/paper/2211.17106/) (2022)
- [Wavelet Diffusion Models are fast and scalable Image Generators](https://mlsanity.com/paper/2211.16152/) (2022)
- [Diffusion Models Beat GANs on Topology Optimization](https://mlsanity.com/paper/2208.09591/) (2022)
- [Multiscale Structure Guided Diffusion for Image Deblurring](https://mlsanity.com/paper/2212.01789/) (2022)
- [Conversion Between CT and MRI Images Using Diffusion and Score-Matching Models](https://mlsanity.com/paper/2209.12104/) (2022)
- [WaveDM: Wavelet-Based Diffusion Models for Image Restoration](https://mlsanity.com/paper/2305.13819/) (2023)
- [Multi-Architecture Multi-Expert Diffusion Models](https://mlsanity.com/paper/2306.04990/) (2023)
- [ExposureDiffusion: Learning to Expose for Low-light Image Enhancement](https://mlsanity.com/paper/2307.07710/) (2023)
- [HiDiffusion: Unlocking Higher-Resolution Creativity and Efficiency in Pretrained Diffusion Models](https://mlsanity.com/paper/2311.17528/) (2023)
- [FRDiff : Feature Reuse for Universal Training-free Acceleration of Diffusion Models](https://mlsanity.com/paper/2312.03517/) (2023)
- [Image generation with shortest path diffusion](https://mlsanity.com/paper/2306.00501/) (2023)
- [Preconditioned Score-based Generative Models](https://mlsanity.com/paper/2302.06504/) (2023)
- [Solving Linear Inverse Problems using Higher-Order Annealed Langevin Diffusion](https://mlsanity.com/paper/2305.05014/) (2023)
- [Hitchhiker's guide on the relation of Energy-Based Models with other generative models, sampling and statistical physics: a comprehensive review](https://mlsanity.com/paper/2406.13661/) (2024)
- [Preconditioned Langevin Dynamics with Score-Based Generative Models for Infinite-Dimensional Linear Bayesian Inverse Problems](https://mlsanity.com/paper/2505.18276/) (2025)
- [Efficient Combinatorial Optimization via Heat Diffusion](https://mlsanity.com/paper/2403.08757/) (2024)
- [Inverse design with conditional cascaded diffusion models](https://mlsanity.com/paper/2408.08526/) (2024)
- [TS-Diff: Two-Stage Diffusion Model for Low-Light RAW Image Enhancement](https://mlsanity.com/paper/2505.04281/) (2025)
- [PID-controlled Langevin Dynamics for Faster Sampling of Generative Models](https://mlsanity.com/paper/2511.12603/) (2025)

## Abstract (arXiv)

Score-based generative models (SGMs) have recently emerged as a promising class of generative models. However, a fundamental limitation is that their inference is very slow due to a need for many (e.g., 2000) iterations of sequential computations. An intuitive acceleration method is to reduce the sampling iterations which however causes severe performance degradation. We investigate this problem by viewing the diffusion sampling process as a Metropolis adjusted Langevin algorithm, which helps reveal the underlying cause to be ill-conditioned curvature. Under this insight, we propose a model-agnostic preconditioned diffusion sampling (PDS) method that leverages matrix preconditioning to alleviate the aforementioned problem. Crucially, PDS is proven theoretically to converge to the original target distribution of a SGM, no need for retraining. Extensive experiments on three image datasets with a variety of resolutions and diversity validate that PDS consistently accelerates off-the-shelf SGMs whilst maintaining the synthesis quality. In particular, PDS can accelerate by up to 29x on more challenging high resolution (1024x1024) image generation.