We study self-diffusion in complex fluids within dynamic density functional theory and explicitly account for the coupling to the fluctuating background. Applying the formalism to nematic and smectic liquid crystals, we find the temporary cages formed by neighboring particles to compete with permanent barriers in nonuniform systems, resulting in non-Gaussian diffusive motion that in different directions becomes correlated. Qualitative agreement with recent experiments demonstrates the importance of explicitly dealing with time-dependent self-consistent molecular fields.