# Position-Blind Ptychography: Viability of image reconstruction via data-driven variational inference

arXiv: https://arxiv.org/abs/2509.25269 · HTML: https://mlsanity.com/paper/2509.25269/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 114 references that are in the map.
- First posted on arXiv 28 Sep 2025.

## Builds on (most cited first, 30 of 41)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [AudioLDM: Text-to-Audio Generation with Latent Diffusion Models](https://mlsanity.com/paper/2301.12503/) (2023)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Score-Based Diffusion Models as Principled Priors for Inverse Imaging](https://mlsanity.com/paper/2304.11751/) (2023)
- [Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imaging](https://mlsanity.com/paper/2010.14462/) (2020)
- [The troublesome kernel -- On hallucinations, no free lunches and the accuracy-stability trade-off in inverse problems](https://mlsanity.com/paper/2001.01258/) (2020)
- [Fast Diffusion EM: a diffusion model for blind inverse problems with application to deconvolution](https://mlsanity.com/paper/2309.00287/) (2023)
- [The Numerics of Phase Retrieval](https://mlsanity.com/paper/2004.05788/) (2020)
- [Real-time coherent diffraction inversion using deep generative networks](https://mlsanity.com/paper/1806.03992/) (2018)
- [Variational Bayesian Imaging with an Efficient Surrogate Score-based Prior](https://mlsanity.com/paper/2309.01949/) (2023)
- [Flow Matching: Markov Kernels, Stochastic Processes and Transport Plans](https://mlsanity.com/paper/2501.16839/) (2025)
- [Joint ptycho-tomography with deep generative priors](https://mlsanity.com/paper/2009.09498/) (2020)
- [Deep Ptych: Subsampled Fourier Ptychography using Generative Priors](https://mlsanity.com/paper/1812.11065/) (2018)
- [Solving Fourier ptychographic imaging problems via neural network modeling and TensorFlow](https://mlsanity.com/paper/1803.03434/) (2018)
- [Using Automatic Differentiation as a General Framework for Ptychographic Reconstruction](https://mlsanity.com/paper/1902.03920/) (2019)
- [Noise-robust latent vector reconstruction in ptychography using deep generative models](https://mlsanity.com/paper/2311.07580/) (2023)

## Built on by (most cited first, 1 of 1)

- [A neural operator view on U-Nets for inverse imaging problems](https://mlsanity.com/paper/2608.05839/) (2026)

## Abstract (arXiv)

In this work, we present and investigate the novel blind inverse problem of position-blind ptychography, i.e., ptychographic phase retrieval without any knowledge of scan positions, which then must be recovered jointly with the image. The motivation for this problem comes from single-particle diffractive X-ray imaging, where particles in random orientations are illuminated and a set of diffraction patterns is collected. If one uses a highly focused X-ray beam, the measurements would also become sensitive to the beam positions relative to each particle and therefore ptychographic, but these positions are also unknown. We investigate the viability of image reconstruction in a simulated, simplified 2-D variant of this difficult problem, using variational inference with modern data-driven image priors in the form of score-based diffusion models. We find that, with the right illumination structure and a strong prior, one can achieve reliable and successful image reconstructions even under measurement noise, in all except the most difficult evaluated imaging scenario.