This paper introduces and evaluates a post-processing technique for fast denoising of diffusion-weighted magnetic resonance imaging (dMRI) data. The technique leverages the intrinsic redundancy in dMRI data and universal properties of the eigenspectrum of random covariance matrices to remove noise-only principal components, thereby enhancing the signal-to-noise ratio (SNR) and improving the quality of parameter maps. By studying the statistics of residuals, the method demonstrates that it suppresses local signal fluctuations solely originating from thermal noise, preserving fine anatomical details. The technique is applied to simulated and in vivo dMRI data, showing improved precision in estimating diffusion parameters and fiber orientations without compromising accuracy or spatial resolution. The proposed method, denoted as MPPCA, outperforms state-of-the-art techniques such as adaptive non-local means (ANLM) and second-order total generalized variation (TGV) in terms of signal preservation and accuracy. The paper also discusses the limitations and potential applications of the method, emphasizing its ability to selectively suppress noise while preserving the underlying signal.This paper introduces and evaluates a post-processing technique for fast denoising of diffusion-weighted magnetic resonance imaging (dMRI) data. The technique leverages the intrinsic redundancy in dMRI data and universal properties of the eigenspectrum of random covariance matrices to remove noise-only principal components, thereby enhancing the signal-to-noise ratio (SNR) and improving the quality of parameter maps. By studying the statistics of residuals, the method demonstrates that it suppresses local signal fluctuations solely originating from thermal noise, preserving fine anatomical details. The technique is applied to simulated and in vivo dMRI data, showing improved precision in estimating diffusion parameters and fiber orientations without compromising accuracy or spatial resolution. The proposed method, denoted as MPPCA, outperforms state-of-the-art techniques such as adaptive non-local means (ANLM) and second-order total generalized variation (TGV) in terms of signal preservation and accuracy. The paper also discusses the limitations and potential applications of the method, emphasizing its ability to selectively suppress noise while preserving the underlying signal.