# DOLPH: Diffusion Models for Phase Retrieval

arXiv: https://arxiv.org/abs/2211.00529 · HTML: https://mlsanity.com/paper/2211.00529/

## Key facts

- Cited by 4 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 14 of its 26 references that are in the map.
- First posted on arXiv 1 Nov 2022.

## Placed in

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

## Builds on (most cited first, 14 of 14)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [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)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [prDeep: Robust Phase Retrieval with a Flexible Deep Network](https://mlsanity.com/paper/1803.00212/) (2018)
- [Phase Retrieval from Coded Diffraction Patterns](https://mlsanity.com/paper/1310.3240/) (2013)
- [Online Regularization by Denoising with Applications to Phase Retrieval](https://mlsanity.com/paper/1909.02040/) (2019)
- [PhasePack: A Phase Retrieval Library](https://mlsanity.com/paper/1711.10175/) (2017)

## Built on by (most cited first, 4 of 4)

- [Posterior Sampling with Denoising Oracles via Tilted Transport](https://mlsanity.com/paper/2407.00745/) (2024)
- [Diffusion Posterior Sampling for Informed Single-Channel Dereverberation](https://mlsanity.com/paper/2306.12286/) (2023)
- [Poisson-Gaussian Holographic Phase Retrieval with Score-based Image Prior](https://mlsanity.com/paper/2305.07712/) (2023)
- [Uncertainty Quantification in HSI Reconstruction using Physics-Aware Diffusion Priors and Optics-Encoded Measurements](https://mlsanity.com/paper/2511.18473/) (2025)

## Abstract (arXiv)

Phase retrieval refers to the problem of recovering an image from the magnitudes of its complex-valued linear measurements. Since the problem is ill-posed, the recovery requires prior knowledge on the unknown image. We present DOLPH as a new deep model-based architecture for phase retrieval that integrates an image prior specified using a diffusion model with a nonconvex data-fidelity term for phase retrieval. Diffusion models are a recent class of deep generative models that are relatively easy to train due to their implementation as image denoisers. DOLPH reconstructs high-quality solutions by alternating data-consistency updates with the sampling step of a diffusion model. Our numerical results show the robustness of DOLPH to noise and its ability to generate several candidate solutions given a set of measurements.