It has been found in in vitro experiments that cytoskeletal filaments driven by molecular motors show finite diffusion in sliding motion even in the long filament limit [Imafuku, Y. et al. Biophys. J. 1996, 70, 878-886. Noda, N. et al. Biophysics 2005, 1, 45-53]. This anomalous fluctuation can be evidence for cooperativity among the motors in action because fluctuation should be averaged out for a long filament if the action of each motor is independent. In order to understand the nature of the fluctuation in molecular motors, we perform numerical simulations and analyze velocity correlation in three existing models that are known to show some kind of cooperativity and/or large diffusion coefficient, i.e., the Sekimoto-Tawada model [Sekimoto, K.; Tawada, K. Phys. Rev. Lett. 1995, 75, 180], the Prost model [Prost, J. et al. Phys. Rev. Lett. 1994, 72, 2652], and the Duke model [Duke, T. Proc. Nail. Acad. Sci. U.S.A. 1999, 96, 2770]. It is shown that the Prost model and the Duke model do not give a finite diffusion in the long filament limit, in spite of the collective action of motors. On the other hand, the Sekimoto-Tawada model has been shown to give a diffusion coefficient that is independent of filament length, but it comes from the long time correlation whose time scale is proportional to filament length, and our simulations show. that such a long correlation time conflicts with the experimental time scales. We conclude that none of the three models represent experimental findings. In order to explain the observed anomalous diffusion, we have to search for a mechanism that will allow both the amplitude and the time scale of the velocity correlation to be independent of the filament length.