An on-demand vapor generator includes a vapor chamber configured to produce a vapor and a vapor absorption assembly configured to receive flows of vapor from the vapor chamber. The vapor absorption assembly includes a first vapor-permeable passage having a passage outlet and at least one second vapor-permeable passage that is closed. When vapor absorption assembly receives a flow of vapor from the vapor chamber, the flow of vapor passes through the first vapor-permeable passage to the passage outlet at least substantially without absorption of vapor from the flow of vapor. However, when a flow of vapor is not received from the vapor chamber, vapor entering the vapor absorption assembly from the vapor chamber passes into the first vapor-permeable passage and the at least one second vapor-permeable passage and is at least substantially absorbed.