# DiffPR: Diffusion-Based Phase Reconstruction via Frequency-Decoupled Learning

arXiv: https://arxiv.org/abs/2506.11183 · HTML: https://mlsanity.com/paper/2506.11183/

## 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 24 of its 41 references that are in the map.
- First posted on arXiv 12 Jun 2025.

## Placed in

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

## Builds on (most cited first, 24 of 24)

- [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)
- [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)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed](https://mlsanity.com/paper/2101.02388/) (2021)
- [Fast Sampling of Diffusion Models via Operator Learning](https://mlsanity.com/paper/2211.13449/) (2022)
- [TRACT: Denoising Diffusion Models with Transitive Closure Time-Distillation](https://mlsanity.com/paper/2303.04248/) (2023)
- [Phase recovery and holographic image reconstruction using deep learning in neural networks](https://mlsanity.com/paper/1705.04286/) (2017)
- [PhaseGAN: A deep-learning phase-retrieval approach for unpaired datasets](https://mlsanity.com/paper/2011.08660/) (2020)
- [Calibration-free quantitative phase imaging using data-driven aberration modeling](https://mlsanity.com/paper/2007.13038/) (2020)

## Abstract (arXiv)

Oversmoothing remains a persistent problem when applying deep learning to off-axis quantitative phase imaging (QPI). End-to-end U-Nets favour low-frequency content and under-represent fine, diagnostic detail. We trace this issue to spectral bias and show that the bias is reinforced by high-level skip connections that feed high-frequency features directly into the decoder. Removing those deepest skips thus supervising the network only at a low resolution significantly improves generalisation and fidelity. Building on this insight, we introduce DiffPR, a two-stage frequency-decoupled framework. Stage 1: an asymmetric U-Net with cancelled high-frequency skips predicts a quarter-scale phase map from the interferogram, capturing reliable low-frequency structure while avoiding spectral bias. Stage 2: the upsampled prediction, lightly perturbed with Gaussian noise, is refined by an unconditional diffusion model that iteratively recovers the missing high-frequency residuals through reverse denoising. Experiments on four QPI datasets (B-Cell, WBC, HeLa, 3T3) show that DiffPR outperforms strong U-Net baselines, boosting PSNR by up to 1.1 dB and reducing MAE by 11 percent, while delivering markedly sharper membrane ridges and speckle patterns. The results demonstrate that cancelling high-level skips and delegating detail synthesis to a diffusion prior is an effective remedy for the spectral bias that limits conventional phase-retrieval networks.