Accurate estimation of diffuse horizontal irradiance (DHI) is critical for optimising photovoltaic system performance and energy forecasting yet remains challenging in regions lacking comprehensive ground-based instrumentation. Recent advancements using Vision Transformers (ViTs) trained on extensive sky image datasets have shown promise in replacing costly irradiance measurement equipment, but the scarcity of long-term, high-quality sky imagery significantly restricts practical implementation. Addressing this critical gap, this study proposes a novel dual-framework approach designed for data-scarce scenarios. First, calculated atmospheric parameters, including extraterrestrial irradiance and cyclic time encodings, are integrated to represent sky conditions without utilising any instrumentation. Next, a sequential pipeline initially predicts synthetic global horizontal irradiance (GHI) and uses it as a feature, to refine DHI estimation. Finally, a dual-parallel architecture simultaneously processes raw and overlay-enhanced fisheye sky images. Overlays are generated through unsupervised, physics-informed cloud segmentation to highlight dynamic sky features. Empirical validation is performed using data from the Chilbolton Observatory, chosen for its temperate climate and frequent cloud variability. To simulate data-scarce conditions, models are trained on a single month (e.g., January) and evaluated across a temporally disjoint, full-year test set. Under this setup, the sequential and dual-parallel frameworks achieve RMSE values within 2-3 W/m^2 and 1-6 W/m^2, respectively, of a state-of-the-art ViT trained on the complete dataset. By combining physics-informed modelling with unsupervised segmentation, the proposed method provides a scalable and cost-effective solution for DHI estimation, advancing solar resource assessment in data-constrained environments.