Progressive Coupling Method for Diffusion Posterior Sampling in Ptychography

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.

Ptychographic imaging at synchrotron and X-ray free-electron laser sources requires densely overlapping scans, which limits throughput and increases dose; extending coherent diffractive imaging to overlap-free operation on extended samples remains an open problem. We present a self-supervised inverse-mapping network for single-frame Fresnel coherent diffraction imaging (CDI) and overlapped ptychography with fixed, pre-estimated probes. The learned neural network reconstructs individual object patches from either one diffraction frame or several overlapping measurements at a time. In single-frame mode, the phase diversity provided by the curved-wavefront probe at the off-focus sample position removes the requirement for overlap constraints, enabling sparser scans and proportionally lower dose at fixed exposure. On synthetic line patterns, reconstructed amplitude SSIM exceeds 0.90 in single-frame mode with the curved probe and reaches 0.952-0.968 with overlap constraints. Optimization of the network via a Poisson negative log likelihood objective, rather than the more common mean absolute error, yields 10-fold improved photon-dose efficiency at doses below $10^5$ photons per image, where shot noise typically limits resolution. In addition to these synthetic studies, we demonstrate robust single-frame reconstruction of extended samples using ptychographic datasets from APS and LCLS, with end-to-end reconstruction of a 10,304-frame workload approximately $36\times$ faster than a highly optimized iterative solver. Together, these results unify single-frame Fresnel CDI and overlapped ptychography within one self-supervised framework, supporting dose-efficient, high-throughput imaging at modern light sources.

Solving severely ill-posed imaging inverse problems requires recovering image structures that are unobservable or weakly constrained by the measurements. Diffusion models provide expressive learned priors for inferring such missing information, while posterior sampling incorporates measurement consistency along the reverse process. Standard diffusion posterior samplers, however, rely on instantaneous measurement-aware estimates, without explicitly exploiting information carried by previous posterior corrections. We introduce Consecutive Posterior Fusion Denoising Diffusion Null-Space Models (CPF-DDNM), an inference-time strategy that fuses consecutive measurement-aware estimates to improve the diffusive recovery of unobservable image structures, without requiring retraining or additional denoiser evaluations. We instantiate this principle within DDNM, whose range/null-space decomposition reveals that consecutive fusion preserves the measurement-determined component while acting exclusively on the prior-driven null-space estimate. We thus provide a geometric interpretation of CPF-DDNM and a local error analysis that characterizes the optimal time-dependent fusion coefficient, including the extrapolative regime. Experiments on sparse-view and simulated low-dose computed tomography, as well as medical image super-resolution, show consistent improvements over DDNM and competitive performance against diffusion-based inverse solvers.