The spatial properties of the solar magnetic field are crucial to decoding the physical processes in the solar interior and their interplanetary effects. However, observations from older instruments, such as the Michelson Doppler Imager (MDI), have limited spatial or temporal resolution, which hinders the ability to study small-scale solar features in detail. Super resolving these older datasets is essential for uniform analysis across different solar cycles, enabling better characterization of solar flares, active regions, and magnetic network dynamics. In this work, we introduce a novel diffusion model approach for Super-Resolution and we apply it to MDI magnetograms to match the higher-resolution capabilities of the Helioseismic and Magnetic Imager (HMI). By training a Latent Diffusion Model (LDM) with residuals on downscaled HMI data and fine-tuning it with paired MDI/HMI data, we can enhance the resolution of MDI observations from 2"/pixel to 0.5"/pixel. We evaluate the quality of the reconstructed images by means of classical metrics (e.g., PSNR, SSIM, FID and LPIPS) and we check if physical properties, such as the unsigned magnetic flux or the size of an active region, are preserved. We compare our model with different variations of LDM and Denoising Diffusion Probabilistic models (DDPMs), but also with two deterministic architectures already used in the past for performing the Super-Resolution task. Furthermore, we show with an analysis in the Fourier domain that the LDM with residuals can resolve features smaller than 2", and due to the probabilistic nature of the LDM, we can asses their reliability, in contrast with the deterministic models. Future studies aim to super-resolve the temporal scale of the solar MDI instrument so that we can also have a better overview of the dynamics of the old events.

翻译：太阳磁场的空间特性对于解码太阳内部物理过程及其行星际效应至关重要。然而，来自较旧仪器（如迈克尔逊多普勒成像仪，MDI）的观测数据在空间或时间分辨率上存在局限，这阻碍了对小尺度太阳特征进行详细研究的能力。对这些旧数据集进行超分辨率重建对于跨不同太阳周期的统一分析至关重要，能够更好地表征太阳耀斑、活动区及磁网络动力学。本研究提出了一种新颖的扩散模型方法用于超分辨率任务，并将其应用于MDI磁图数据，以匹配日震与磁场成像仪（HMI）的高分辨率能力。通过在降尺度HMI数据上训练带有残差连接的潜在扩散模型（LDM），并使用配对的MDI/HMI数据进行微调，我们能够将MDI观测的分辨率从2"/像素提升至0.5"/像素。我们通过经典指标（如PSNR、SSIM、FID和LPIPS）评估重建图像的质量，并检验物理特性（如无符号磁通量或活动区尺寸）是否得以保持。我们将所提模型与不同变体的LDM和去噪扩散概率模型（DDPMs）进行比较，同时也与两种过去曾用于超分辨率任务的确定性架构进行对比。此外，通过在傅里叶域的分析，我们证明带有残差连接的LDM能够解析小于2"的特征，并且得益于LDM的概率特性，我们可以评估其可靠性，这与确定性模型形成鲜明对比。未来研究旨在提升太阳MDI仪器的时间尺度分辨率，从而能够更全面地分析历史事件的动态演化过程。