  Magnetic resonance imaging (MRI) is a widely used non-invasive imaging
modality. However, a persistent challenge lies in balancing image quality with
imaging speed. This trade-off is primarily constrained by k-space measurements,
which traverse specific trajectories in the spatial Fourier domain (k-space).
These measurements are often undersampled to shorten acquisition times,
resulting in image artifacts and compromised quality. Generative models learn
image distributions and can be used to reconstruct high-quality images from
undersampled k-space data. In this work, we present the autoregressive image
diffusion (AID) model for image sequences and use it to sample the posterior
for accelerated MRI reconstruction. The algorithm incorporates both
undersampled k-space and pre-existing information. Models trained with fastMRI
dataset are evaluated comprehensively. The results show that the AID model can
robustly generate sequentially coherent image sequences. In 3D and dynamic MRI,
the AID can outperform the standard diffusion model and reduce hallucinations,
due to the learned inter-image dependencies.
