Compared with other medical-imaging modalities, ultrasound (US) imaging is a valuable way to examine the body's internal organs, and two-dimensional (2D) imaging is currently the most common technique used in clinical diagnoses. Conventional 2D US imaging systems are highly flexible cost-effective imaging tools that permit operators to observe and record images of a large variety of thin anatomical sections in real time. Recently, 3D US imaging has also been gaining popularity due to its considerable advantages over 2D US imaging. It reduces dependency on the operator and provides better qualitative and quantitative information for an effective diagnosis. Furthermore, it provides a 3D view, which allows the observation of volume information. The major shortcoming of any type of US imaging is the presence of speckle noise. Hence, speckle reduction is vital in providing a better clinical diagnosis. The key objective of any speckle-reduction algorithm is to attain a speckle-free image while preserving the important anatomical features. In this paper we introduce a nonlinear multi-scale complex wavelet-diffusion based algorithm for speckle reduction and sharp-edge preservation of 2D and 3D US images. In the proposed method we use a Rayleigh and Maxwell-mixture model for 2D and 3D US images, respectively, where a genetic algorithm is used in combination with an expectation maximization method to estimate mixture parameters. Experimental results using both 2D and 3D synthetic, physical phantom, and clinical data demonstrate that our proposed algorithm significantly reduces speckle noise while preserving sharp edges without discernible distortions. The proposed approach performs better than the state-of-the-art approaches in both qualitative and quantitative measures.