The ions of an electrochemical cell move only due to the presence of electrodes
An electrochemical cell is always described by the movement of ions towards the oppositely charged electrodes.
While this may look like the only movement in an electrochemical cell, very often we tend to overlook the movement of ions in the electrochemical cell due to a concentration gradient. This gradient results in a motion known as diffusion.
To sum it up, the ions moving towards the opposite electrodes due to the electrostatic force of attraction are very small in number. The majority of the movement is because of the diffusion of charged particles from regions of higher concentrations to regions of lower concentration.