Polarimetric Synthetic Aperture Radar (PolSAR) imagery is a valuable tool for Earth observation. This imaging technique finds wide application in various fields, including agriculture, forestry, geology, and disaster monitoring. However, due to the inherent presence of speckle noise, filtering is often necessary to improve the interpretability and reliability of PolSAR data. The effectiveness of a speckle filter is measured by its ability to attenuate fluctuations without introducing artifacts or degrading spatial and polarimetric information. Recent advancements in this domain leverage the power of deep learning. These approaches adopt a supervised learning strategy, which requires a large amount of speckle-free images that are costly to produce. In contrast, this paper presents PolSAR2PolSAR, a semi-supervised learning strategy that only requires, from the sensor under consideration, pairs of noisy images of the same location and acquired in the same configuration (same incidence angle and mode as during the revisit of the satellite on its orbit). Our approach applies to a wide range of sensors. Experiments on Radarsat-2 and RCM data demonstrate the capacity of the proposed method to effectively reduce speckle noise and retrieve fine details.