Molecular clouds at the Galactic center (GC) have environments considerably different from their disk counterparts. The GC may therefore provide important clues about how the environment affects star formation. Interestingly, while the inner 50 pc of our Galaxy include a remarkable population of high-mass stars, the initial mass function (IMF) appears to be consistent with a Salpeter slope down to. We show here that the loss of turbulent pressure due to ambipolar diffusion and the damping of Alfvén and fast MHD waves can lead to the formation of dense condensations exceeding their Jeans limit. The fragmentation and subsequent collapse of these condensations is similar to the diffusion-driven protostellar collapse mechanism expected to occur within nearby ``regular'' molecular clouds. As such, a Salpeter IMF at the GC is not surprising, though the short dynamical timescales associated with the GC molecular clouds may help explain the lower star formation efficiency observed from this region.