According to the chemiosmotic theory (chemiosmotic coupling), the energy required to move protons from the mitochondrial matrix to the intermembrane space against a concentration gradient comes most directly from:

4. electrons flowing along the electron transport chain

Explanation:

Oxidative phosphorylation is made up of two closely connected components: the electron transport chain and chemiosmosis. During chemiosmosis, the energy stored in the gradient is used to make ATP. Electrons are passed from one member of the transport chain to another in a series of redox reactions. The proton gradient generated by proton pumping during the electron transport chain is a stored form of energy. When protons flow back down their concentration gradient (from the intermembrane space to the matrix), their only route is through ATP synthase, an enzyme embedded in the inner mitochondrial membrane.