The paper describes an approach to combine a diffusion-based regularizer normally used for optical flow problems, with a curvature-based regularizer used for image registration problems. Both problems are defined on a time-sequence of images, i.e., on \(\Omega \times \mathbb {T}\), where \(\Omega \subset \mathbb {R}^2\) represents a space of images, and time \(t\in \mathbb {T}=[0,t_{max}]\), \(t,t_{max}\in \mathbb {N}\). The combined regularizer allows to handle both problems with the same solver. The authors note, however, that one can not expect to achieve the same accuracy using this generalized approach, as it is obtained, e.g., in very accurate optical models with advanced data term. The resulting system of fourth-order partial differential equations is discretized using the standard five-point finite difference scheme. The system of linear equations is solved using the mutligrid method. The authors present some convergence rates, timing and investigate the visual quality of the obtained motion or deformation field for academic as well as real-world images. A discussion about possible generalizations concludes the paper.