We develop a differential geometric framework for regularizing diffusion MRI data. The key idea is to model white matter fibres as 3D space curves and to then extend Parent and Zucker's 2D curve inference approach [Parent, P., Zucker, S., 1989. Trace inference, curvature consistency, and curve detection. IEEE Transactions on Pattern Analysis and Machine Intelligence 11, 823-839] by using a notion of co-helicity to indicate compatibility between fibre orientations at each voxel with those in a local neighborhood. We argue that this provides several advantages over earlier regularization methods. We validate the approach quantitatively on a biological phantom and on synthetic data, and qualitatively on data acquired in vivo from a human brain. We also demonstrate the use of the technique to improve the performance of a fibre tracking algorithm.