We explore the formation of the intragroup light and intracluster light, representing diffuse lights within groups and clusters, from the point that z = 1.5. For this, we perform multiresolution cosmological N-body simulations using the "galaxy replacement technique" and identify the progenitors in which the diffuse light stars existed when they fell into the groups or clusters. Our findings reveal that typical progenitors contributing to diffuse lights enter the host halo with massive galaxies containing a stellar mass of 10<logMgal[M circle dot]<11 , regardless of the mass or dynamical state of the host halos at z = 0. In cases where the host halos are dynamically unrelaxed or more massive, diffuse lights from massive progenitors with logMgal[M circle dot]>11 are more prominent, with over half of them already preprocessed before entering the host halo. Additionally, we find that the main formation mechanism of diffuse lights is the stripping process of satellites, and a substantial fraction (40%-45%) of diffuse light stars are linked to the merger tree of the brightest cluster galaxy. Remarkably, all trends persist for groups and clusters at higher redshifts. The fraction of diffuse lights in the host halos with a similar mass decreases as the redshift increases, but they are already substantial at z = 1.5 (similar to 10%). However, it is crucial to acknowledge that detection limits related to the observable radius and faint-end surface brightness may obscure numerous diffuse light stars and even alter the main formation channel of diffuse lights.