Final answer:
During cellular respiration, active transport and facilitated diffusion are the types of cellular transport occurring when protons are pumped across the mitochondrial membrane and then move back through ATP synthase to generate ATP.
Step-by-step explanation:
The type of cellular transport occurring during cellular respiration is facilitated diffusion and active transport. During the electron transport chain (ETC), which is the final stage of cellular respiration, protons (H+ ions) are pumped across the inner mitochondrial membrane by active transport, creating a proton gradient. This gradient represents potential energy, similar to water held behind a dam. Protons then flow back into the mitochondrial matrix through a specialized protein complex known as ATP synthase, which facilitates their movement by passive transport, a process known as facilitated diffusion. The flow of protons through ATP synthase provides the energy necessary to convert ADP to ATP, which is the main energy molecule used by cells.