Ultrasound images are widespread in medical diagnosis for musculoskeletal, cardiac, and obstetrical imaging due to the efficiency and non-invasiveness of the acquisition methodology. However, the acquired images are degraded by acoustic (e.g. reverberation and clutter) and electronic sources of noise. To improve the Peak Signal to Noise Ratio (PSNR) of the images, previous denoising methods often remove the speckles, which could be informative for radiologists and also for quantitative ultrasound. Herein, a method based on the recent Denoising Diffusion Probabilistic Models (DDPM) is proposed. It iteratively enhances the image quality by eliminating the noise while preserving the speckle texture. It is worth noting that the proposed method is trained in a completely unsupervised manner, and no annotated data is required. The experimental blind test results show that our method outperforms the previous nonlocal means denoising methods in terms of PSNR and Generalized Contrast to Noise Ratio (GCNR) while preserving speckles.