Numerical and experimental data for porescale particle dynamics show intermittent patterns in Lagrangian velocities and accelerations, which manifest in long time intervals of low and short durations of high velocities. This phenomenon is due to the spatial persistence of particle velocities on characteristic heterogeneity length scales. In order to systematically quantify these behaviors and extract the stochastic dynamics of particle motion, we focus on the analysis of Lagrangian velocities sampled equidistantly along trajectories (termed space-Lagrangian velocities). This method removes the intermittency observed under isochrone sampling. The space-Lagrangian velocity series can be quantified by a Markov process that is continuous in distance along streamlines. It is fully parameterized in terms of the flux-weighted Eulerian velocity PDF and the characteristic pore-length. The resulting stochastic particle motion describes a continuous time random walk (CTRW). This approach allows for the process based interpretation of experimental and numerical porescale velocity, acceleration and displacement data for passive and active particles. It provides a framework for the characterization and upscaling of particle transport and dispersion from the pore to the Darcy-scale based on the medium geometry and Eulerian flow attributes. We apply this methodology for the interpretation and quantification of the dispersion of passive and active particles in two- and three-dimensional porescale flows. We quantify dispersion in terms of first passage time distributions, spatial propagators, and the evolution of displacement mean and variance.