# Uncertainty quantification for ptychography using normalizing flows

arXiv: https://arxiv.org/abs/2111.00745 · HTML: https://mlsanity.com/paper/2111.00745/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 47 references that are in the map.
- First posted on arXiv 1 Nov 2021.

## Builds on (most cited first, 23 of 23)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [WaveGlow: A Flow-based Generative Network for Speech Synthesis](https://mlsanity.com/paper/1811.00002/) (2018)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [VideoFlow: A Conditional Flow-Based Model for Stochastic Video Generation](https://mlsanity.com/paper/1903.01434/) (2019)
- [Latent Normalizing Flows for Discrete Sequences](https://mlsanity.com/paper/1901.10548/) (2019)
- [Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imaging](https://mlsanity.com/paper/2010.14462/) (2020)
- [Phase recovery and holographic image reconstruction using deep learning in neural networks](https://mlsanity.com/paper/1705.04286/) (2017)
- [Lensless computational imaging through deep learning](https://mlsanity.com/paper/1702.08516/) (2017)
- [Solving inverse problems using conditional invertible neural networks](https://mlsanity.com/paper/2007.15849/) (2020)
- [Likelihood-informed dimension reduction for nonlinear inverse problems](https://mlsanity.com/paper/1403.4680/) (2014)
- [Deep autoregressive neural networks for high-dimensional inverse problems in groundwater contaminant source identification](https://mlsanity.com/paper/1812.09444/) (2018)
- [Reliable deep-learning-based phase imaging with uncertainty quantification](https://mlsanity.com/paper/1901.02038/) (2019)
- [Learning by example: fast reliability-aware seismic imaging with normalizing flows](https://mlsanity.com/paper/2104.06255/) (2021)
- [Multigrid Optimization for Large-Scale Ptychographic Phase Retrieval](https://mlsanity.com/paper/1810.05628/) (2018)
- [Advanced Denoising for X-ray Ptychography](https://mlsanity.com/paper/1811.02081/) (2018)

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

- [Uncertainty Quantification for Deep Unrolling-Based Computational Imaging](https://mlsanity.com/paper/2207.00698/) (2022)
- [Conditional score-based diffusion models for solving inverse problems in mechanics](https://mlsanity.com/paper/2406.13154/) (2024)
- [Conformalized Generative Bayesian Imaging: An Uncertainty Quantification Framework for Computational Imaging](https://mlsanity.com/paper/2504.07696/) (2025)
- [Integrating Generative and Physics-Based Models for Ptychographic Imaging with Uncertainty Quantification](https://mlsanity.com/paper/2412.10882/) (2024)

## Abstract (arXiv)

Ptychography, as an essential tool for high-resolution and nondestructive material characterization, presents a challenging large-scale nonlinear and non-convex inverse problem; however, its intrinsic photon statistics create clear opportunities for statistical-based deep learning approaches to tackle these challenges, which has been underexplored. In this work, we explore normalizing flows to obtain a surrogate for the high-dimensional posterior, which also enables the characterization of the uncertainty associated with the reconstruction: an extremely desirable capability when judging the reconstruction quality in the absence of ground truth, spotting spurious artifacts and guiding future experiments using the returned uncertainty patterns. We demonstrate the performance of the proposed method on a synthetic sample with added noise and in various physical experimental settings.