We employ all -atom molecular dynamics simulations up to microsecond time scales to study diffusion of fullerene nanoparticles (C-60 and its derivative PCBM) in a polyimide matrix above its glass transition temperature. A detailed examination of the fullerene mobility in the embedding polymer system reveals the presence of different diffusion regimes (ballistic, subdiffusive, and normal diffusive). The microscopic origin of the observed subdiffusive regime is discussed by comparing the behavior to the one displayed by different anomalous diffusion processes, namely, continuous time random walk (CTRW), random walk on a fractal (RWF), and fractional Langevin equation (FLE). A series of statistical tests suggests that the FLE framework is the more appropriate one to describe subdiffusion of fullerenes in our system. Furthermore, a comprehensive analysis of the self -part of the van Hove function shows that the normal diffusion regime observed at long times displays a nonclassical behavior characterized by the simultaneous presence of several Gaussian peaks. We ascribe this behavior to a mechanism of diffusion by hopping. Until recently, it was commonly believed that hopping of tracer particles in polymer systems is only relevant for particle sizes that are of the order of the reptation tube diameter (dr), while smaller particles are considered to slip through the entanglement mesh. However, our results provide direct evidence for hopping as a relevant mechanism for diffusion of particles whose sizes are commensurate with the correlation length of the polymer system. These results emphasize the importance of local interactions at the atomic level for the understanding of nanoparticle dynamics in polymer melts.