An accretion disk in an Active Galactic Nucleus (AGN) harbors and shields dust from external illumination: at the mid-plane of the disk around a $M_{{rm BH}}=10^{7}M_{odot}$ black hole, dust can exist at $0.1$pc from the black hole, compared to 0.5pc outside of the disk. We construct a physical model of a disk region approximately located between the radius of dust sublimation at the disk mid-plane and the radius at which dust sublimes at the disk surface. Our main conclusion is that for a wide range of model parameters such as local accretion rate and/or opacity, the accretion disks own radiation pressure on dust significantly influences its vertical structure. In addition to being highly convective, such a disk can transform from geometrically thin to slim. Our model fits into the narrative of a failed wind scenario of Czerny & Hryniewicz (2011) and the compact torus model of Baskin & Laor (2018), incorporating them as variations of the radiative dusty disk model.
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