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Ultrasound imaging is widely used for real-time, noninvasive diagnosis, but speckle and related artifacts reduce image quality and can hinder interpretation. We present a diffusion-based ultrasound despeckling method built on the Image Restoration Stochastic Differential Equations framework. To enable supervised training, we curate large paired datasets by simulating ultrasound images from speckle-free magnetic resonance images using the Matlab UltraSound Toolbox. The proposed model reconstructs speckle-suppressed images while preserving anatomically meaningful edges and contrast. On a held-out simulated test set, our approach consistently outperforms classical filters and recent learning-based despeckling baselines. We quantify prediction uncertainty via cross-model variance and show that higher uncertainty correlates with higher reconstruction error, providing a practical indicator of difficult or failure-prone regions. Finally, we evaluate sensitivity to simulation probe settings and observe domain shift, motivating diversified training and adaptation for robust clinical deployment.