In this talk, we study nonlinear drift-diffusion equations of porous medium and fast diffusion types with a measure-valued external force. We first consider the case without drift to emphasize the influence of measure data and the nonlinear diffusion structure. Then, we establish the existence of nonnegative weak solutions that satisfy suitable gradient estimates when the drift term belongs to a sub-scaling class associated with the $L^1$ space. For divergence-free drifts, this requirement can be further relaxed to a scaling class, allowing a broader range of nonlinear diffusion behaviors.