We perform a systematic survey of active galactic nuclei (AGNs) continuum lags using ~3days cadence gri-band light curves from the Zwicky Transient Facility. We select a sample of 94 type 1 AGNs 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_CE_{propto}L^0.48+/-0.04^ with a scatter of 0.2dex, analogous to the well-known radius-luminosity relation of broad H{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_CE_-L relation can be explained by a photoionization model that assumes ~23% of the total flux comes from the diffuse BLR emission. In addition, the ratio of the CE size and model-predicted disk size anticorrelates with the continuum luminosity, which is indicative of a potential nondisk BLR lag contribution evolving with the luminosity. Finally, a robust positive correlation between the CE size and black hole mass is detected.