I am not a professional, but let me try to answer.Pls correct me if I make any mistakes. My memory is already abit hazy cos I took this course in my first year.
Other than the sodium potassium pump, the presence of ion channels provides a way for the ions to diffuse through the membrane under the influence of both concentration forces and electrostatic forces. This diffusion helps to balance the membrane potential in the resting state. Ion channels are in fact protein molecules. This might be the thing that your lecturer talked about.
i think you got the idea of this question
but you used the term "diffuse" wrongly:). ions cannot diffuse through the membrane. "diffuse" means there are no facilitated channels needed and it means the substrate molecules cross the barrier spontaneously.