In perfusion MRI (p-MRI) exams, short-axis (SA) image sequences are captured at multiple slice levels along the long-axis of the heart during the transit of a vascular contrast agent (Gd-DTPA) through the cardiac chambers and muscle. Compensating cardio-thoracic motions is a requirement for enabling computer-aided quantitative assessment of myocardial ischaemia from contrast-enhanced p-MRI sequences. The classical paradigm consists of registering each sequence frame on a reference image using some intensity-based matching criterion. In this paper, we introduce a novel unsupervised method for the spatio-temporal groupwise registration of cardiac p-MRI exams based on normalized mutual information (NMI) between high-dimensional feature distributions. Here, local contrast enhancement curves are used as a dense set of spatio-temporal features, and statistically matched through variational optimization to a target feature distribution derived from a registered reference template. The hard issue of probability density estimation in high-dimensional state spaces is bypassed by using consistent geometric entropy estimators, allowing NMI to be computed directly from feature samples. Specifically, a computationally efficient kth-nearest neighbor (kNN) estimation framework is retained, leading to closed-form expressions for the gradient flow of NMI over finite- and infinite-dimensional motion spaces. This approach is applied to the groupwise alignment of cardiac p-MRI exams using a free-form Deformation (FFD) model for cardio-thoracic motions. Experiments on simulated and natural datasets suggest its accuracy and robustness for registering p-MRI exams comprising more than 30 frames. For randomized FFD transformations, estimated B-spline parameters correlate to 94% with ground-truth values. Processing natural data further suggests that the technique allows for reliably computing clinically-relevant perfusion indices, enabling a multiparametric quantitative assessment which strongly correlates with expert-based qualitative diagnosis.