First, we need a membrane material which is highly permeable with respect to water and water vapor, but as impermeable as possible with respect to all other components of air. This is not an impossible requirement, as such materials do already exist.
Alternate two layers of this membrane with two
layers of spacer, and roll it up into a cylinder, such that we have a very large surface area in a small volume of space. Mechanically, this will be very similar to the core of a reverse osmosis water purifier.
Pass air from inside the building across one side of the membrane (at atmospheric pressure) while maintaining a partial vacuum on the other side of the membrane.
Water vapor will diffuse across the membrane from the side with the higher partial pressure to the side with the lower partial pressure -- in this case, from the air into the partial vacuum.
The partial vacuum is maintained by a compressor, which continuously transfers water vapor into a condenser. Heat is removed from the condenser by passing the dehumidified air around it. Condensate is continuously removed from the condenser by means of a condensate pump, and transferred either into a container or down a drain.
After the dehumidified air has passed through the condenser, it's returned to the inside of the building.
Ideally, there would be no air inside the condenser to interfere with condensation of water vapor, but in practice, a small vacuum pump will be need to discard the small amount of noncondensable gasses which will inevitably diffuse through the membrane. Most likely, the vacuum pump would be operated intermittently, activated either by an oxygen sensor, or by pressure and temperature sensors. If oxygen is present in the steam, or if the temperature is below water's boiling point for that pressure, then the vacuum pump must be activated.
To provide even greater comfort for the occupants of the house, the condenser could be cooled using air from outside the building, much like an air conditioner; in this case, the condensate could be sprayed onto the outside of the condenser, so that it's evaporation would help cool the condenser.
As a further improvement, we can improve both efficiency and elegance by replacing the condenser with a second membrane air handler, and blow outside air across this second membrane.
As long as the pressure of the pure steam inside the second membrane is higher than the partial pressure of water vapor outside the membrane, water molecules will diffuse through the membrane from inside to outside... even though the steam's total pressure will be much less than atmospheric pressure. In a small way, this is similar to evaporation, but without a phase change.