Precise aerial radio environment characterization is vital for low-altitude airspace planning. However, existing datasets and construction methods lack the high-resolution granularity required for complex aerial spaces, particularly failing to capture spatial variations across both horizontal and vertical dimensions. To address these gaps, this paper introduces FARM, a pioneering foundation model for unified aerial radio map (ARM) construction. FARM is supported by our newly curated, high-granularity full-domain ARM dataset, which features multi-band and multi-antenna configurations, effectively filling a critical void in comprehensive low-altitude radio data. Structurally, FARM leverages a masked autoencoder to extract deep latent representations of the aerial radio environment, which subsequently guide a diffusion-based decoder to synthesize high-fidelity signal distributions through only a few iterative refinement steps. Benefiting from this design, the architecture seamlessly accommodates both condition-based and condition-free ARM construction, providing robust support for diverse signal and environmental priors. Extensive experiments demonstrate that FARM significantly outperforms state-of-the-art benchmarks while exhibiting strong cross-scenario generalization. Crucially, we validate the transferability of FARM on a real-world dataset collected from field tests, proving its robust deployment capability. Ultimately, FARM serves as a foundational infrastructure for the low-altitude economy by enabling autonomous aerial logistics and intelligent urban networking.