Since diffusion-open roofs breathe, I also think that there are wall structures that breathe. Why not? If the sd value decreases from inside to outside, that should physically not be a problem.
With stone houses, I'm not so sure, but the phenomenon of visible stones through the exterior plaster speaks, in my opinion, for the theory that moisture is conducted outwards from the inside.
And how much water needs how much time to pass through the entire structure? And how much water does the house breathe in through the walls? It surely is not a one-way street
Here are a few quotes from the internet that everyone can understand and verify: It is true that numerous porous building materials are air-permeable in the sense of Pettenkofer. However, air transport through the pore structure can only be initiated by a difference in air pressure between the two sides of a wall. Since the air pressure inside a building usually hardly differs from the outside air pressure, there is no driving force for such a transport process.
Every building material is in a moisture equilibrium with its environment. Depending on its location, a moisture equilibrium and a typical water content in the component are established. A component is in moisture equilibrium with the water vapor content of the indoor and outdoor air. This is very dry in winter (30% relative humidity) and the indoor air is more humid (around 30–60% relative humidity). The migration of water vapor molecules is based on their temperature-induced random motion (energy charge) and their concentration gradient inside/outside. In a normal household, about 5 to 10 liters of water per day are released as water vapor through breathing, transpiration (by humans and houseplants), cooking, etc. Of this, only 1–3% can be discharged outward through the walls by water vapor diffusion, since all building materials resist diffusion.
Moisture production in living spaces varies greatly, for example through cooking, showering, sleeping, etc. Temporarily high peak values of humidity with condensation at cooler spots such as thermal bridges or “frost flowers” on poorly insulated windows are prevented or mitigated by water vapor sorption in all hygroscopic interior claddings of all components (plasters, wood materials, fiberboards). Sorption is a natural property of all mineral building materials and has no driving mechanism. The sorbed amounts are given off again to the room air when the room air’s water vapor load decreases again through cooking, bathing, etc. They must be ventilated out of the indoor air. There is no alternative to active ventilation.
Usually, wall surfaces are not the only sorption-capable surfaces in the room. Textiles such as carpets, curtains, or upholstered furniture usually have even greater sorption capacities than wall materials and can have very large surface areas. Furnishings made of untreated wood can also contribute to sorption to some extent. However, moisture equilibrium is also established in the closed system, and moisture can only be removed from the system by ventilating in drier air. If this happens, the moisture peaks occurring in living areas are only of relatively short duration, so the sorbed moisture has little time to penetrate deeply into the wall before it is desorbed again.
Moisture buffering also requires a sufficient possibility to release the absorbed moisture again. With regular strong moisture loads, e.g., in the bathroom, a “breathable” wall surface might be disadvantageous if it absorbs moisture and appears dry so that ventilation for drying is no longer sufficient and mold develops over the long term. Here a surface that is neither “breathable” nor absorbent (such as tiles) would be safer, where condensation water is clearly visible and the need to ventilate is made obvious.