# WaveFreqAnchor: Wave-Structural Anchoring and Frequency Correction Diffusion for Training-Free Face Restoration

arXiv: https://arxiv.org/abs/2608.06717 · HTML: https://mlsanity.com/paper/2608.06717/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 36 of its 46 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## 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 36)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [MUSIQ: Multi-scale Image Quality Transformer](https://mlsanity.com/paper/2108.05997/) (2021)
- [Exploring CLIP for Assessing the Look and Feel of Images](https://mlsanity.com/paper/2207.12396/) (2022)
- [VGGFace2: A dataset for recognising faces across pose and age](https://mlsanity.com/paper/1710.08092/) (2017)
- [Image Quality Assessment: Unifying Structure and Texture Similarity](https://mlsanity.com/paper/2004.07728/) (2020)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [How far are we from solving the 2D & 3D Face Alignment problem? (and a dataset of 230,000 3D facial landmarks)](https://mlsanity.com/paper/1703.07332/) (2017)
- [PULSE: Self-Supervised Photo Upsampling via Latent Space Exploration of Generative Models](https://mlsanity.com/paper/2003.03808/) (2020)
- [Towards Real-World Blind Face Restoration with Generative Facial Prior](https://mlsanity.com/paper/2101.04061/) (2021)
- [Towards Robust Blind Face Restoration with Codebook Lookup Transformer](https://mlsanity.com/paper/2206.11253/) (2022)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [Focal Frequency Loss for Image Reconstruction and Synthesis](https://mlsanity.com/paper/2012.12821/) (2020)
- [GAN Prior Embedded Network for Blind Face Restoration in the Wild](https://mlsanity.com/paper/2105.06070/) (2021)
- [Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing](https://mlsanity.com/paper/2407.01521/) (2024)
- [VQFR: Blind Face Restoration with Vector-Quantized Dictionary and Parallel Decoder](https://mlsanity.com/paper/2205.06803/) (2022)
- [DifFace: Blind Face Restoration with Diffused Error Contraction](https://mlsanity.com/paper/2212.06512/) (2022)
- [RestoreFormer: High-Quality Blind Face Restoration from Undegraded Key-Value Pairs](https://mlsanity.com/paper/2201.06374/) (2022)
- [DR2: Diffusion-based Robust Degradation Remover for Blind Face Restoration](https://mlsanity.com/paper/2303.06885/) (2023)
- [Fourier Space Losses for Efficient Perceptual Image Super-Resolution](https://mlsanity.com/paper/2106.00783/) (2021)
- [Prompt-tuning latent diffusion models for inverse problems](https://mlsanity.com/paper/2310.01110/) (2023)
- [PGDiff: Guiding Diffusion Models for Versatile Face Restoration via Partial Guidance](https://mlsanity.com/paper/2309.10810/) (2023)
- [OSDFace: One-Step Diffusion Model for Face Restoration](https://mlsanity.com/paper/2411.17163/) (2024)
- [WaveFace: Authentic Face Restoration with Efficient Frequency Recovery](https://mlsanity.com/paper/2403.12760/) (2024)
- [Survey on Deep Face Restoration: From Non-blind to Blind and Beyond](https://mlsanity.com/paper/2309.15490/) (2023)
- [Efficient Face Super-Resolution via Wavelet-based Feature Enhancement Network](https://mlsanity.com/paper/2407.19768/) (2024)
- [Self-Supervised Selective-Guided Diffusion Model for Old-Photo Face Restoration](https://mlsanity.com/paper/2510.12114/) (2025)

## Abstract (arXiv)

Diffusion-based face restoration that adjusts the sampling trajectory of pre-trained diffusion models has achieved remarkable progress. However, existing approaches provide insufficient constraints during reverse diffusion, causing identity-related structural drift and degraded fidelity under severe degradations. To address this, we propose WaveFreqAnchor, a training-free framework based on Wave-Structural Anchoring and Frequency Correction Diffusion. Specifically, Anchor-Space Wave-Structural Guidance (ASWG) constrains facial structures through anisotropic wave-response consistency, while Multi-scale Wavelet-Fourier Injection (MWFI) aligns the predicted low-frequency subband with the observation by replacing its phase, correcting inconsistencies accumulated during reverse diffusion. For real-world scenes, we further introduce Subband High-Frequency Enhancement (SHE), which performs bounded, spatially masked refinement on the predicted high-frequency subbands to recover fine facial details under unknown compound degradations. Together, these designs effectively preserve facial identity while restoring sharp and realistic facial details. Extensive experiments show that our method consistently outperforms existing methods, achieving high-quality and high-fidelity face restoration.