# I2I-PR: Deep Iterative Refinement for Phase Retrieval using Image-to-Image Diffusion Models

arXiv: https://arxiv.org/abs/2507.09609 · HTML: https://mlsanity.com/paper/2507.09609/

## 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 31 of its 64 references that are in the map.
- First posted on arXiv 13 Jul 2025.

## 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 31)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Exploring CLIP for Assessing the Look and Feel of Images](https://mlsanity.com/paper/2207.12396/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Deblurring via Stochastic Refinement](https://mlsanity.com/paper/2112.02475/) (2021)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (2023)
- [GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium](https://mlsanity.com/paper/1706.08500/) (2017)
- [Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration](https://mlsanity.com/paper/2303.11435/) (2023)
- [Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing](https://mlsanity.com/paper/2407.01521/) (2024)
- [Direct Diffusion Bridge using Data Consistency for Inverse Problems](https://mlsanity.com/paper/2305.19809/) (2023)
- [Optimization and Generalization of Shallow Neural Networks with Quadratic Activation Functions](https://mlsanity.com/paper/2006.15459/) (2020)
- [prDeep: Robust Phase Retrieval with a Flexible Deep Network](https://mlsanity.com/paper/1803.00212/) (2018)
- [Iterative α-(de)Blending: a Minimalist Deterministic Diffusion Model](https://mlsanity.com/paper/2305.03486/) (2023)
- [Low Photon Count Phase Retrieval Using Deep Learning](https://mlsanity.com/paper/1806.10029/) (2018)
- [The Numerics of Phase Retrieval](https://mlsanity.com/paper/2004.05788/) (2020)
- [On the use of deep learning for phase recovery](https://mlsanity.com/paper/2308.00942/) (2023)
- [Deep Iterative Reconstruction for Phase Retrieval](https://mlsanity.com/paper/1904.11301/) (2019)
- [Learning Fourier-Constrained Diffusion Bridges for MRI Reconstruction](https://mlsanity.com/paper/2308.01096/) (2023)
- [Phase Retrieval Using Conditional Generative Adversarial Networks](https://mlsanity.com/paper/1912.04981/) (2019)
- [Deep Learning for Accelerated and Robust MRI Reconstruction: a Review](https://mlsanity.com/paper/2404.15692/) (2024)
- [The Douglas-Rachford Algorithm for Convex and Nonconvex Feasibility Problems](https://mlsanity.com/paper/1904.09148/) (2019)
- [Beyond Griffin-Lim: Improved Iterative Phase Retrieval for Speech](https://mlsanity.com/paper/2205.05496/) (2022)
- [Deep Plug-and-Play HIO Approach for Phase Retrieval](https://mlsanity.com/paper/2411.18967/) (2024)

## Abstract (arXiv)

Phase retrieval aims to recover a signal from intensity-only measurements, a fundamental problem in many fields such as imaging, holography, optical computing, crystallography, and microscopy. Although there are several well-known phase retrieval algorithms, including classical alternating projection-based solvers, the reconstruction performance often remains sensitive to initialization and measurement noise. Recently, diffusion models have gained traction in various image reconstruction tasks, yielding significant theoretical insights and practical advances. In this work, we introduce a deep iterative refinement framework that redefines the role of diffusion models in phase retrieval. Instead of generating images from random noise, our method starts with multiple physically consistent initial estimates and iteratively refines them through a learned image-to-image diffusion process. This enables data-driven phase retrieval that is both interpretable and robust, leveraging the strengths of classical solvers while mitigating their weaknesses. Furthermore, we propose an enhanced initialization strategy that integrates classical algorithms with a novel acceleration mechanism to obtain reliable initial estimates. During inference, we adopt a geometric self-ensemble strategy based on input flipping, together with output aggregation to further improve the final reconstruction quality. Comprehensive experiments demonstrate that our approach achieves substantial gains in both training efficiency and reconstruction quality, consistently outperforming classical and recent state-of-the-art methods. These results highlight the potential of diffusion-driven refinement as an effective and general framework for robust phase retrieval across diverse applications. The source code and trained models are available at https://github.com/METU-SPACE-Lab/I2I-PR-for-Phase-Retrieval