Speckle noise strongly affects Synthetic Aperture Radar (SAR) images, causing strong intensity fluctuations that make them difficult to analyze. Although many speckle reduction algorithms have been proposed, how to effectively deal with the spatial correlations of speckle remains an open question, especially in the most recent deep learning approaches. This paper tries to address this problem. Existing approaches to tackle the speckle correlations are described. Then, a standard training strategy for deep learning is proposed. Two models are trained and the increased robustness brought by including a Total Variation (TV) term in the loss function is analyzed on Sentinel-1 images.