Imaging through scattering is challenging, as even a thin layer can randomly perturb light propagation and obscure hidden objects. Accurate closed-form modeling of forward scattering remains difficult, particularly for dynamically varying or thick layers. Here, we introduce a plug-and-play inverse solver based on video diffusion models with a physically grounded forward model tailored to dynamic scattering layers. Our method extends Diffusion Posterior Sampling (DPS) to the spatio-temporal domain, thereby capturing statistical correlations between video frames and scattered signals more effectively. Leveraging these temporal correlations, our approach recovers high-resolution spatial details that spatial-only methods typically fail to reconstruct. We also propose an inference-time optimization with a lightweight mapping network, enabling joint estimation of low-dimensional forward-model parameters without additional training. This joint optimization significantly enhances adaptability to unknown, time-varying degradations, making our method suitable for blind inverse scattering problems. We validate across diverse conditions, including different scene types, layer thicknesses, and scene-layer distances. And real-world experiments using multiple datasets confirm the robustness and effectiveness of our approach, even under real noise and forward-model approximation mismatches. Finally, we validate our method as a general video-restoration framework across dehazing, deblurring, inpainting, and blind restoration under complex optical aberrations.

Fourier phase retrieval is a classical problem of restoring a signal only from the measured magnitude of its Fourier transform. Although Fienup-type algorithms, which use prior knowledge in both spatial and Fourier domains, have been widely used in practice, they can often stall in local minima. Convex relaxation methods such as PhaseLift and PhaseCut may offer performance guarantees, but these algorithms are usually computationally expensive for practical use. To address this problem, here we propose a novel unsupervised feed-forward neural network for Fourier phase retrieval which generates high quality reconstruction immediately. Unlike the existing deep learning approaches that use a neural network as a regularization term or an end-to-end blackbox model for supervised training, our algorithm is a feed-forward neural network implementation of physics-driven constraints in an unsupervised learning framework. Specifically, our network is composed of two generators: one for the phase estimation using PhaseCut loss, followed by another generator for image reconstruction, all of which are trained simultaneously without matched data. The link to the classical Fienup-type algorithms and the recent symmetry-breaking learning approach is also revealed. Extensive experiments demonstrate that the proposed method outperforms all existing approaches in Fourier phase retrieval problems.