Despite the utility of tumour characterisation using quantitative parameter maps from multi-b-value diffusion-weighted MRI (DWI), clinicians often prefer the use of the image with highest diffusion-weighting (b-value), for instance for defining regions of interest (ROIs). However, these images are typically degraded by noise, as they do not utilize the information from the full acquisition. We present a principal component analysis (PCA) approach for model-free denoising of DWI data. PCA-denoising was compared to synthetic MRI, where a diffusion model is fitted for each voxel and a denoised image at a given b-value is generated from the model fit. A quantitative comparison of systematic and random errors was performed on data simulated using several diffusion models (mono-exponential, bi-exponential, stretched-exponential and kurtosis). A qualitative visual comparison was also performed for in vivo images in six healthy volunteers and three pancreatic cancer patients. In simulations, the reduction in random errors from PCA-denoising was substantial (up to 55%) and similar to synthetic MRI (up to 53%). Model-based synthetic MRI denoising resulted in substantial (up to 29% of signal) systematic errors, whereas PCA-denoising was able to denoise without introducing systematic errors (less than 2%). In vivo, the signal-to-noise ratio (SNR) and sharpness of PCA-denoised images were superior to synthetic MRI, resulting in clearer tumour boundaries. In the presence of motion, PCA-denoising did not cause image blurring, unlike image averaging or synthetic MRI. Multi-b-value MRI can be denoised model-free with our PCA-denoising strategy that reduces noise to a level similar to synthetic MRI, but without introducing systematic errors associated with the synthetic MRI method.