A Physics-Informed Multi-Scale Diffusion Model Framework for Physical Field Imputation from Randomly Missing Data

Abstract Non-intrusive optical measurement techniques are widely used to obtain high-resolution pressure, temperature, and velocity fields, but they often suffer from random data loss caused by geometric obstruction, surface reflection, or illumination non-uniformity. Conventional reconstruction methods usually depend on high-fidelity CFD priors or large paired datasets, which limits their flexibility for arbitrary missing patterns and scarce experimental samples. This study proposes a Physics-Informed Multi-Scale Resampled Denoising Diffusion Probabilistic Model (MSR-DDPM) for missing-data reconstruction in optical flow measurements. The method shifts the reconstruction paradigm from deterministic mapping to probabilistic distribution modeling. Three features are introduced: a multi-scale hierarchical reconstruction strategy that reduces computational cost by 56% and improves stability; embedded physics-informed constraints, including divergence and gradient-continuity terms, to enhance physical consistency and reduce dependence on large training datasets; and an optional conditional diffusion module that incorporates auxiliary low-fidelity data for extreme missing-data scenarios. The framework is validated for incompressible velocity-field imputation using turbine cascade passage data, demonstrating its ability to recover complex unsteady flow structures. For missing ratios of 10%-45%, MSR-DDPM achieves high-accuracy reconstruction with Symmetric Mean Absolute Percentage Error (SMAPE) below 6% without auxiliary data. Under more severe missing ratios of 45%-65%, auxiliary guidance substantially recovers flow details and reduces reconstruction errors by approximately 60%. These results indicate that MSR-DDPM offers a flexible, data-efficient, and physically consistent solution for missing-data imputation in complex experimental flow measurements.