# Fast and Stable Diffusion Inverse Solver with History Gradient Update

arXiv: https://arxiv.org/abs/2307.12070 · HTML: https://mlsanity.com/paper/2307.12070/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 23 of its 30 references that are in the map.
- First posted on arXiv 22 Jul 2023.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Implicit Diffusion Models for Continuous Super-Resolution](https://mlsanity.com/paper/2303.16491/) (2023)
- [Focal Frequency Loss for Image Reconstruction and Synthesis](https://mlsanity.com/paper/2012.12821/) (2020)
- [Image Restoration with Mean-Reverting Stochastic Differential Equations](https://mlsanity.com/paper/2301.11699/) (2023)
- [Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency](https://mlsanity.com/paper/2307.08123/) (2023)
- [Solving 3D Inverse Problems using Pre-trained 2D Diffusion Models](https://mlsanity.com/paper/2211.10655/) (2022)
- [Parallel Diffusion Models of Operator and Image for Blind Inverse Problems](https://mlsanity.com/paper/2211.10656/) (2022)

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

- [Regularization by Texts for Latent Diffusion Inverse Solvers](https://mlsanity.com/paper/2311.15658/) (2023)
- [You Only Need One Step: Fast Super-Resolution with Stable Diffusion via Scale Distillation](https://mlsanity.com/paper/2401.17258/) (2024)
- [Rethinking Diffusion Posterior Sampling: From Conditional Score Estimator to Maximizing a Posterior](https://mlsanity.com/paper/2501.18913/) (2025)
- [LATINO-PRO: LAtent consisTency INverse sOlver with PRompt Optimization](https://mlsanity.com/paper/2503.12615/) (2025)
- [Consistency Model is an Effective Posterior Sample Approximation for Diffusion Inverse Solvers](https://mlsanity.com/paper/2403.12063/) (2024)
- [Posterior sampling via Langevin dynamics based on generative priors](https://mlsanity.com/paper/2410.02078/) (2024)
- [Enhancing Diffusion Model Stability for Image Restoration via Gradient Management](https://mlsanity.com/paper/2507.06656/) (2025)
- [Iterative CT Reconstruction via Latent Variable Optimization of Shallow Diffusion Models](https://mlsanity.com/paper/2408.03156/) (2024)

## Abstract (arXiv)

Diffusion models have recently been recognised as efficient inverse problem solvers due to their ability to produce high-quality reconstruction results without relying on pairwise data training. Existing diffusion-based solvers utilize Gradient Descent strategy to get a optimal sample solution. However, these solvers only calculate the current gradient and have not utilized any history information of sampling process, thus resulting in unstable optimization progresses and suboptimal solutions. To address this issue, we propose to utilize the history information of the diffusion-based inverse solvers. In this paper, we first prove that, in previous work, using the gradient descent method to optimize the data fidelity term is convergent. Building on this, we introduce the incorporation of historical gradients into this optimization process, termed History Gradient Update (HGU). We also provide theoretical evidence that HGU ensures the convergence of the entire algorithm. It's worth noting that HGU is applicable to both pixel-based and latent-based diffusion model solvers. Experimental results demonstrate that, compared to previous sampling algorithms, sampling algorithms with HGU achieves state-of-the-art results in medical image reconstruction, surpassing even supervised learning methods. Additionally, it achieves competitive results on natural images.