How does carbon dioxide from respiration diffuse out of the leaf during the night?
Do stomata close completely during night?
Leaves have no need to 'exhale' carbon dioxide - it gets consumed by photosynthesis.
Elsewhere in the plant, metabolic processes produce carbon dioxide. This escapes via inter-cellular gas channels that, in woody plants, terminate as lenticels (little pores) on the stem surface. Oxygen for metabolism diffuses into the plant in the same inter-cellular spaces as carbon dioxide diffuses out.
With roots, the oxygen necessary for metabolic processes is dissolved in water.
If you've meant to ask about leaf adsorption of carbon dioxide and when stomata close, it depends on what carbon fixation scheme the plant exhibits, CAM, C4, or C3.
You might want to also consult an answer I gave to a similar question previously posed here.
Land plants might do better to keep their CO2 to use in the morning, unless they produce way too much of it.
CO2 is present in air at concentration around 0.03%. (In recent years it's gone up to 0.04%.) That's a low concentration to work against.
Remember, in the daytime those plants are sending water vapor and O2 OUT the stomata. It's a pressure gradient. Why let CO2 out at night and then depend on it coming IN against the flow the next day?
Plants have ways to grab onto CO2 so it won't just drift away. They convert it to things that aren't gases -- oxaloacetic acid or malate, or 3-phosphoglycerate, or possibly others that haven't been noticed yet.
These compounds can be stored. Then restore the CO2 precisely when and where it is needed.
Some CO2 gets this treatment at the roots (where CO2 concentration can sometimes be as high as 8%) and the storage compounds then get sent toward the leaves along with water and minerals.