  We perform a systematic survey of active galactic nucleus (AGN) continuum
lags using $\sim$3 day cadence $gri$-band light curves from the Zwicky
Transient Facility. We select a sample of 94 type 1 AGN at $z<0.8$ with
significant and consistent inter-band lags based on the interpolated
cross-correlation function method and the Bayesian method JAVELIN. Within the
framework of the lamp-post reprocessing model, our findings are: 1) The
continuum emission (CE) sizes inferred from the data are larger than the disk
sizes predicted by the standard thin disk model; 2) For a subset of the sample,
the CE size exceeds the theoretical limit of the self-gravity radius (12
lt-days) for geometrically thin disks; 3) The CE size scales with continuum
luminosity as $R_{\mathrm{CE}} \propto L^{0.48\pm0.04}$ with a scatter of 0.2
dex, analogous to the well-known radius-luminosity relation of broad
H$\mathrm{\beta}$. These findings suggest a significant contribution of diffuse
continuum emission from the broad-line region (BLR) to AGN continuum lags. We
find that the $R_{\mathrm{CE}}-L$ relation can be explained by a
photoionization model that assumes $\sim$23% of the total flux comes from the
diffuse BLR emission. In addition, the ratio of the CE size and model-predicted
disk size anti-correlates with the continuum luminosity, indicative of a
potential non-disk BLR lag contribution evolving with luminosity. Finally, a
robust positive correlation between CE size and black hole mass is detected.
