We present an approach for significantly improving the quantitative analysis of motion in noisy fluorescence microscopic image sequences. The new partial differential equation based method is a general extension of a 2-D nonlinear anisotropic diffusion filtering scheme to a specially adapted 3-D nonlinear anisotropic diffusion filtering scheme, with two spatial image dimensions and the time t in the image sequence as the third dimension. Motion in image sequences is considered as oriented, line-like structures in the spatiotemporal x,y,t domain, which are determined by the structure tensor method. Image enhancement is achieved by a structure adopted smoothing kernel in three dimensions, thereby using the full 3-D information inherent in spatiotemporal image sequences. As an example for low signal-to-noise ratio (SNR) microscopic image sequences we have applied this method to noisy in vitro motility assay data, where fluorescently labeled actin filaments move over a surface of immobilized myosin. With the 3-D anisotropic diffusion filtering the SNR is significantly improved (by a factor of 3.8) and closed object structures are reliably restored, which were originally degraded by noise. Generally, this approach is very valuable for all applications where motion has to be measured quantitatively in low light level fluorescence microscopic image sequences of cellular, subcellular, and molecular processes.