Soft condensed matter, involving such diverse systems as synthetic or biological macromolecules to colloids, is a fast growing research area due to its scientific and technological relevance. Beyond scaling theories of simple model systems the dynamics and rheology of complex fluids have been extensively studied through various experimental techniques and computer simulations. While these techniques typically address a single dynamic quantity it is a challenge to develop simulation methodologies that can directly access different dynamic quantities as well as a broad range of length and time scales of specific systems. Here we present a hierarchical simulation approach to overcome these problems. We predict polymer dynamics over a broad spectrum of length and time scales ranging from segmental relaxation on the monomer level to long time chain diffusion. As an example we study various dynamical modes of atactic polystyrene melts of molecular weights relevant to polymer processing (up to 50,000 g/mol) without any adjustable parameter and compare the results to experiments.