Abstract: In this study, we train score-based diffusion models to super-resolve gigaparsec-scale cosmological simulations of the 21-cm signal. We examine the impact of network and training dataset size on model performance, demonstrating that a single simulation ($1.25$\% of the dataset) is sufficient for a model to learn the super-resolution task regardless of the initial conditions. Our best-performing model achieve pixelwise $\mathrm{RMSE}\sim0.57\ \mathrm{mK}$ and dimensionless power spectrum residuals from $10^{-2}-10^{-1}\ \mathrm{mK^2}$ for $128^3$, $256^3$ and $512^3$ voxel simulation volumes at redshift $10$. The super-resolution network ultimately allows us to utilize all spatial scales covered by the SKA1-Low instrument, and could in future be employed to help constrain the astrophysics of the early Universe.