We study the transport phenomena of colloidal particles embedded within a moving array of obstacles that mimics a dynamic, time‐varying porous material. While colloidal transport in an array of stationary obstacles (“passive” porous media) has been well studied, we lack the fundamental understanding of colloidal diffusion in a nonequilibrium porous environment. We combine Taylor dispersion theory, Brownian dynamics simulations, and optical tweezer experiments to study the transport of tracer colloidal particles in an oscillating lattice of obstacles. We discover that the dispersion of tracer particles is a nonmonotonic function of oscillation frequency and exhibits a maximum that exceeds the Stokes–Einstein–Sutherland diffusivity in the absence of obstacles. By solving the Smoluchowski equation using a generalized dispersion framework, we demonstrate that the enhanced transport of the tracers depends critically on both the direct interparticle interactions with the obstacles and the fluid‐mediated, hydrodynamic interactions generated by the moving obstacles.