Progressive Coupling Method for Diffusion Posterior Sampling in Ptychography

Yihan Qiu; Mingtao Huang; Tianyuan Li; Shudong Li; Yuan Shen

cs.LGOct 28, 2026

Progressive Coupling Method for Diffusion Posterior Sampling in Ptychography

Authors: Yihan Qiu, Mingtao Huang, Tianyuan Li, Shudong Li, Yuan Shen

Organizations: Department of Electronic Engineering, Beijing National Research Center for Information Science and Technology (BNRist), Tsinghua University, Beijing 100084, China

Abstract

Ptychography is a computational imaging method that reconstructs a sample from overlapping diffraction measurements. This technique relies on these overlapping measurements to provide the redundancy information needed for robust reconstruction, but dense scanning increases acquisition time and data volume. Reducing scan overlaps can improve measurement efficiency but weakens the physical constraints available for reconstruction. Diffusion models provide strong learned prior information, offering a promising approach to compensate for the loss of measurement redundancy. However, effectively utilizing this prior information under weak measurement constraints remains a challenge. We propose a progressive coupling posterior sampling (PCPS) method, which allows for a broader exploration of the solution space under high uncertainty while maintaining stronger diffusion-guided consistency as the reconstruction becomes more refined. Experiments on real X-ray ptychographic data at various scan overlaps demonstrate that PCPS consistently improves reconstruction accuracy compared to traditional iterative methods and existing diffusion posterior samplers, especially at low overlaps. These results show that diffusion priors can reduce the measurement redundancy required for accurate ptychography reconstruction.

Figures & tables

Fig. 1: Overview of PCPS. For a transition from noise level $t$ to $s<t$ , the denoiser produces $\hat{x}_{0}(x_{t})$ , measurement refinement with $y$ and $\mathcal{A}$ yields $x_{0|y}$ , and the Gaussian coupling combines the refined clean estimate, the residual of the current noisy state, and fresh Gaussian noise to sample $x_{s}$ . The predetermined coefficient $\lambda_{s,t}$ increases toward the clean endpoint.

100 steps
Method	60%	50%	40%	30%	20%
DPS	0.390±0.335	0.347±0.195	0.374±0.107	0.408±0.229	0.446±0.079
LSQ-ML	0.182±0.030	0.256±0.042	0.304±0.051	0.403±0.064	0.508±0.077
DAPS	0.113±0.004	0.133±0.005	0.145±0.006	0.165±0.006	0.181±0.006
DAPS++	0.125±0.009	0.143±0.015	0.158±0.016	0.205±0.022	0.262±0.047
PCPS	0.106±0.007	0.118±0.008	0.125±0.008	0.140±0.009	0.151±0.008

TABLE I: stitched complex NRMSE at different scan overlaps. reported as mean ± standard deviation over the test objects.

Fig. 2: Qualitative reconstructions at 40% overlap. The top and bottom rows show the amplitude and phase, respectively. The scale bar denotes 500 nm.

Fig. 3: Accuracy–runtime tradeoff at 40% overlap for different sampling budgets. Labels indicate the number of sampling steps. Lower-left points provide better tradeoffs.

Fig. 4: Coupling schedule analysis. (a) Compared coupling schedules. (b) NRMSE difference relative to the full-width cosine schedule across scan overlaps.

Image Reconstruction

Image reconstruction recovers images, volumes, or scenes from incomplete, noisy, indirect, or compressed measurements using physical models and learned priors.

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Image Reconstruction Learning-Augmented Algorithms

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Iterative ptychographic reconstruction algorithms are widely used for coherent diffractive imaging but can exhibit slow convergence under realistic experimental conditions. We propose a machine learning-augmented approach that accelerates iterative ptychographic reconstruction by introducing a learned fast-forward operator applied during reconstruction. Following an initial warm-up using standard iterations, the fast-forward operator advances the reconstruction toward a more converged state, after which conventional iterative updates are resumed. This strategy preserves the physical consistency and flexibility of established ptychographic solvers while reducing the number of iterations required for convergence. The model is trained on diverse ptychographic datasets and evaluated on experimental data acquired in a different year, demonstrating robustness and temporal generalization. Compared with conventional iterative solvers, the machine learning-augmented method achieves comparable reconstruction quality while converging faster in terms of Poisson negative log-likelihood, yielding over a two-fold reduction in wall-clock time. The approach has been integrated into an existing reconstruction pipeline and deployed in production at a synchrotron beamline, demonstrating practicality for real-time experimental operation.

Abstract

Image Reconstruction

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