The radius valley, a prominent feature in the observed distribution of exoplanet radii, separates smaller super-Earths from larger sub-Neptunes. Traditionally, this gap is attributed to the loss of primordial H/He envelopes atop rocky cores. However, planet formation models predict that water-rich planets migrate from regions outside the snowline toward the star. This study uses an advanced coupled formation and evolution model to investigate the origin of the radius valley. By treating water as vapor mixed with H/He, the model naturally reproduces the observed valley at the correct location. The results indicate that the valley separates less massive, in-situ rocky super-Earths from more massive, ex-situ water-rich sub-Neptunes. The occurrence drop at larger radii, known as the radius cliff, is also matched by planets with water-dominated envelopes. The model's synthetic distribution of radii agrees quantitatively with observations for close-in planets, provided that atmospheric photoevaporation is also acting, populating the super-Earth peak with evaporated rocky cores. This provides a hybrid theoretical explanation for the radius gap and cliff, combining both formation (orbital migration) and evolution (atmospheric escape) processes. The study highlights the importance of including realistic physics, such as different phases of water, in models to accurately reproduce the observed planetary radius distribution.The radius valley, a prominent feature in the observed distribution of exoplanet radii, separates smaller super-Earths from larger sub-Neptunes. Traditionally, this gap is attributed to the loss of primordial H/He envelopes atop rocky cores. However, planet formation models predict that water-rich planets migrate from regions outside the snowline toward the star. This study uses an advanced coupled formation and evolution model to investigate the origin of the radius valley. By treating water as vapor mixed with H/He, the model naturally reproduces the observed valley at the correct location. The results indicate that the valley separates less massive, in-situ rocky super-Earths from more massive, ex-situ water-rich sub-Neptunes. The occurrence drop at larger radii, known as the radius cliff, is also matched by planets with water-dominated envelopes. The model's synthetic distribution of radii agrees quantitatively with observations for close-in planets, provided that atmospheric photoevaporation is also acting, populating the super-Earth peak with evaporated rocky cores. This provides a hybrid theoretical explanation for the radius gap and cliff, combining both formation (orbital migration) and evolution (atmospheric escape) processes. The study highlights the importance of including realistic physics, such as different phases of water, in models to accurately reproduce the observed planetary radius distribution.