Unveiling the spatial-temporal dynamics: Diffusion-based learning of conditional distribution for range-dependent ocean sound speed field forecasting

Environment-aware underwater acoustic detection and communications demand precise forecasting of the sound speed field (SSF) both temporally and spatially. Toward this goal, recent machine learning models, such as recurrent neural networks and Gaussian process regressions, have outperformed classical autoregressive models. However, from the unified theoretical perspective of conditional distribution learning, there is still significant room for improvement, as existing works have not fully learned the conditional distribution of future SSFs given past SSFs. To address these limitations, in this paper, we leverage the use of diffusion models, the foundation of recent successful deep generative models, such as DALL-E 2 and SORA, to learn the conditional distribution even under limited training data, through careful neural architecture and training strategy design. Our experiments, conducted on real-life South China Sea datasets, confirm that our proposed model outperforms the state-of-the-art baselines in forecasting range-dependent SSFs and the associated underwater transmission losses. Additionally, our model provides reliable confidence intervals that quantify the uncertainties of predictions.