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Downscaling, or super-resolution, provides decision-makers with detailed, high-resolution information about the potential risks and impacts of climate change, based on climate model output. Machine learning algorithms are proving themselves to be efficient and accurate approaches to downscaling. Here, we show how a generative, diffusion-based approach to downscaling gives accurate downscaled results. We focus on an idealised setting where we recover ERA5 at $0.25\degree$~resolution from coarse grained version at $2\degree$~resolution. The diffusion-based method provides superior accuracy compared to a standard U-Net, particularly at the fine scales, as highlighted by a spectral decomposition. Additionally, the generative approach provides users with a probability distribution which can be used for risk assessment. This research highlights the potential of diffusion-based downscaling techniques in providing reliable and detailed climate predictions.