The UV/optical light curves of active galactic nuclei (AGNs) may be roughly characterized by aperiodic fractional flux variations of similar to 10% on timescales of 1 month. The physical mechanism(s) responsible remain ill defined. We present a structure function analysis, i.e., measure the power distribution over a range of timescales tau, of 13 AGNs to constrain the origin of UV/optical emission. On timescales tau similar to 5- 60 days, the mean UV and optical power-density spectra (PDS) are equivalent. This may suggest that the underlying energy generating mechanism is identical. The combined UV/optical PDS is P(f) proportional to f(-alpha) with alpha = 2.13(-0.06)(+0.22). For sources with measured X-ray PDS indices, we find they are indistinguishable from their UV/optical counterparts. This supports scenarios whereby X-rays are generated via Compton upscattering of UV photons, to later radiatively drive optical variations. At the same time, we present evidence for characteristic variability timescales tau (char) of similar to 5-100 days in 10 sources. These variability timescales combined with reverberation based masses M suggest a M-tau (char) relationship; higher mass systems have larger characteristic timescales. The UV tau (cha)r may possibly reflect dynamical or accretion disk thermal timescales. We find suggestive evidence for a dichotomy, at tau similar to 30 days and M similar to 10(7) M-circle dot, between short- and long-timescale optical variations. These optical variations may be attributable to dynamical and accretion disk thermal or starburst activity timescales, respectively.