  Magnetic resonance imaging (MRI) is a common and life-saving medical imaging
technique. However, acquiring high signal-to-noise ratio MRI scans requires
long scan times, resulting in increased costs and patient discomfort, and
decreased throughput. Thus, there is great interest in denoising MRI scans,
especially for the subtype of diffusion MRI scans that are severely
SNR-limited. While most prior MRI denoising methods are supervised in nature,
acquiring supervised training datasets for the multitude of anatomies, MRI
scanners, and scan parameters proves impractical. Here, we propose Denoising
Diffusion Models for Denoising Diffusion MRI (DDM$^2$), a self-supervised
denoising method for MRI denoising using diffusion denoising generative models.
Our three-stage framework integrates statistic-based denoising theory into
diffusion models and performs denoising through conditional generation. During
inference, we represent input noisy measurements as a sample from an
intermediate posterior distribution within the diffusion Markov chain. We
conduct experiments on 4 real-world in-vivo diffusion MRI datasets and show
that our DDM$^2$ demonstrates superior denoising performances ascertained with
clinically-relevant visual qualitative and quantitative metrics.
