# WaveDM: Wavelet-Based Diffusion Models for Image Restoration

arXiv: https://arxiv.org/abs/2305.13819 · HTML: https://mlsanity.com/paper/2305.13819/

## Key facts

- Cited by 47 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 100 of its 132 references that are in the map.
- First posted on arXiv 23 May 2023.

## Placed in

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

## Builds on (most cited first, 30 of 100)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (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)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (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)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [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)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [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)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Image Super-Resolution Using Very Deep Residual Channel Attention Networks](https://mlsanity.com/paper/1807.02758/) (2018)
- [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)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)

## Built on by (most cited first, 30 of 47)

- [Diffusion Model-Based Image Editing: A Survey](https://mlsanity.com/paper/2402.17525/) (2024)
- [Diffusion Models, Image Super-Resolution And Everything: A Survey](https://mlsanity.com/paper/2401.00736/) (2024)
- [A Fourier Space Perspective on Diffusion Models](https://mlsanity.com/paper/2505.11278/) (2025)
- [Token Caching for Diffusion Transformer Acceleration](https://mlsanity.com/paper/2409.18523/) (2024)
- [KV Inversion: KV Embeddings Learning for Text-Conditioned Real Image Action Editing](https://mlsanity.com/paper/2309.16608/) (2023)
- [PFB-Diff: Progressive Feature Blending Diffusion for Text-driven Image Editing](https://mlsanity.com/paper/2306.16894/) (2023)
- [MagicEraser: Erasing Any Objects via Semantics-Aware Control](https://mlsanity.com/paper/2410.10207/) (2024)
- [FEC: Three Finetuning-free Methods to Enhance Consistency for Real Image Editing](https://mlsanity.com/paper/2309.14934/) (2023)
- [Conditioning diffusion models by explicit forward-backward bridging](https://mlsanity.com/paper/2405.13794/) (2024)
- [On the Asymptotic Mean Square Error Optimality of Diffusion Models](https://mlsanity.com/paper/2403.02957/) (2024)
- [Edit-Your-Motion: Space-Time Diffusion Decoupling Learning for Video Motion Editing](https://mlsanity.com/paper/2405.04496/) (2024)
- [RealRestorer: Towards Generalizable Real-World Image Restoration with Large-Scale Image Editing Models](https://mlsanity.com/paper/2603.25502/) (2026)
- [Dual-Schedule Inversion: Training- and Tuning-Free Inversion for Real Image Editing](https://mlsanity.com/paper/2412.11152/) (2024)
- [Latent Wavelet Diffusion For Ultra-High-Resolution Image Synthesis](https://mlsanity.com/paper/2506.00433/) (2025)
- [Edge-preserving noise for diffusion models](https://mlsanity.com/paper/2410.01540/) (2024)
- [Bootstrap Diffusion Model Curve Estimation for High Resolution Low-Light Image Enhancement](https://mlsanity.com/paper/2309.14709/) (2023)
- [SpecRef: A Fast Training-free Baseline of Specific Reference-Condition Real Image Editing](https://mlsanity.com/paper/2401.03433/) (2024)
- [A Wavelet Diffusion GAN for Image Super-Resolution](https://mlsanity.com/paper/2410.17966/) (2024)
- [CasDyF-Net: Image Dehazing via Cascaded Dynamic Filters](https://mlsanity.com/paper/2409.08510/) (2024)
- [Multi-scale Generative Modeling for Fast Sampling](https://mlsanity.com/paper/2411.09356/) (2024)
- [DualSpec: Text-to-spatial-audio Generation via Dual-Spectrogram Guided Diffusion Model](https://mlsanity.com/paper/2502.18952/) (2025)
- [Quaternion Wavelet-Conditioned Diffusion Models for Image Super-Resolution](https://mlsanity.com/paper/2505.00334/) (2025)
- [DFDNet: Dynamic Frequency-Guided De-Flare Network](https://mlsanity.com/paper/2507.17489/) (2025)
- [WDT-MD: Wavelet Diffusion Transformers for Microaneurysm Detection in Fundus Images](https://mlsanity.com/paper/2511.08987/) (2025)
- [Seal2Real: Prompt Prior Learning on Diffusion Model for Unsupervised Document Seal Data Generation and Realisation](https://mlsanity.com/paper/2310.00546/) (2023)
- [Global Spatial-Temporal Information-based Residual ConvLSTM for Video Space-Time Super-Resolution](https://mlsanity.com/paper/2407.08466/) (2024)
- [Controlling the Latent Diffusion Model for Generative Image Shadow Removal via Residual Generation](https://mlsanity.com/paper/2412.02322/) (2024)
- [Leveraging Contrast Information for Efficient Document Shadow Removal](https://mlsanity.com/paper/2504.00385/) (2025)
- [Computationally Efficient Diffusion Models in Medical Imaging: A Comprehensive Review](https://mlsanity.com/paper/2505.07866/) (2025)
- [Diffusion Transformer meets Multi-level Wavelet Spectrum for Single Image Super-Resolution](https://mlsanity.com/paper/2511.01175/) (2025)

## Abstract (arXiv)

Latest diffusion-based methods for many image restoration tasks outperform traditional models, but they encounter the long-time inference problem. To tackle it, this paper proposes a Wavelet-Based Diffusion Model (WaveDM). WaveDM learns the distribution of clean images in the wavelet domain conditioned on the wavelet spectrum of degraded images after wavelet transform, which is more time-saving in each step of sampling than modeling in the spatial domain. To ensure restoration performance, a unique training strategy is proposed where the low-frequency and high-frequency spectrums are learned using distinct modules. In addition, an Efficient Conditional Sampling (ECS) strategy is developed from experiments, which reduces the number of total sampling steps to around 5. Evaluations on twelve benchmark datasets including image raindrop removal, rain steaks removal, dehazing, defocus deblurring, demoir'eing, and denoising demonstrate that WaveDM achieves state-of-the-art performance with the efficiency that is comparable to traditional one-pass methods and over 100× faster than existing image restoration methods using vanilla diffusion models.