Data-driven learning of atmospheric turbulence phase screens via diffusion models

Atmospheric turbulence induces stochastic refractive index fluctuations that degrade the performance of optical systems such as free-space communications and long-range imaging. To simulate these effects, traditional methods typically employ phase screens. However, the generation of these screens is often constrained by a reliance on fixed prior assumptions, such as the Kolmogorov power spectrum, making the accurate modeling of complex non-Kolmogorov turbulence a persistent challenge. Data-driven methods, particularly GANs, have been used to learn phase screen statistics directly from observations, but suffer from training instability and mode collapse. Here, we propose a phase diffusion model (PDM) framework with phase representation to generate high-fidelity phase screens by learning the statistical distribution from data generated by a physics-based simulator. While our framework is capable of learning from real-world observations, this work uses data from the generalized spectrum to demonstrate high-fidelity replication of complex, non-Kolmogorov statistics. Quantitative evaluations reveal that the PDM achieves superior accuracy, attaining a Fréchet distance of 1.28 and a normalized root mean squared error (NRMSE) of merely 2.44% even on limited datasets, all while maintaining high computational efficiency and reducing training time. Furthermore, the generated samples serve as effective data extension for deep learning models, enhancing downstream task performance. This approach establishes diffusion models as a stable and practical framework for atmospheric turbulence simulation.