Explanation for drift current
In zero bias the diffusion current is equal to the drift current. Majority charge carries diffuse from high concentration region to low concentration region and minority charge carriers inside the  depletion region drift according to the electric field of the depletion region.
The tendency for diffusion  never stops because there is always a concentration difference of electrons and holes between the 2 regions (N type and P type).In the beginning when the diode is first made , there isn't a depletion region .The depletion region is created due to the recombination of electrons and holes(majority carriers) at the middle of the junction. Inside the depletion region there is an electric field which opposes the diffusion.But it is not about balance of 'forces' because electrons and holes always want to diffuse from high concentration to low concentration regions. What's happening is while the electric potential of the depletion region is increased it opposes the diffusion of free majority charge carriers.At the same time due to imperfection in making of the diode there are some minority charge carriers(electrons in P type region and holes in N type region).If they become free inside the depletion region they will drift due to the electric potential of the depletion region. But for those minority charge carriers there isnt any 'diffusion force' which will oppose their motion because diffusion isn't a force.The only force both majority and minority charge carriers feel is the electrostatic force of the electric field of the depletion region. But majority charge carriers tend to move anyway opposite to the electric field because of the concentration gradient and the electric field resists that motion while on the other hand free minority charge carriers drift in the direction of the electric field.