Improper insulation and air sealing can cause that. If there wall has no insulation, you get condensation, which will translate to mold.

Thank you both for taking time to respond. Here’s a photo of the carpet pulled back to show the exhaust fan piping below. The black on the wood sub floor is paint, not mold. Mold only seems to grow on the white slanted wood siding / wall. The carpet smells fine and appears mold free too,

Is that a exhaust fan as in from a bathroom and the metal pipe is the moisture being drawn from bathroom and exits/is vented to that spot/under carpet? No wonder there is moisture/mold there if that is the case. If it is vented to outdoors maybe there is a hole in the tube or not attached well to vent. I discovered the vent tube was loose/not attached well, had a hole and squished to the outside vent when I had to replace my bathroom vent fan and moisture was escaping into my attic space, had to replace tube too. The exhaust from bathroom fan needs to be vented to the outside somehow, and carpet certainly shouldn't be blocking either. Was this home recently updated by flippers?

I suspect that Cook's Kitchen nailed it and the mold is because of condensation. The sofa is probably blocking air circulation and is the reason for the mold on that section of the wall.

Thanks everyone. The exhaust duct does vent to outside. It is possible that there is a hole in the ducting, which is allowing the moisture to escape. I am going to keep the sofa away from the wall and make sure nothing is stored back there and see if that makes a difference. Thanks again!

Do you know what is behind the wall? Is it insulation sandwiched between the wall and the roofline? Do you have any ventilation running on the underside of the roofline (between the roofline and the insulation)? Not ventilation as in bath vents, but rather the opportunity for airflow on the underside of the roof sheathing? That needs to breath or you will shorten the life of the roof decking and shingles and you can end up with condensation as a result. It could likely have little to do with the bath vent being there.

You need to go outside and remove the exhaust vent and verify it's correctly connected to the hose.

What type of roofing? If shingles, remove a few to check for leaks.

Do I understand there are the boards we see in your pictures, and the roofing is attached directly to them.

I agree with the Cooks Kitchen. We had a very similar problem. We had a paneled vaulted ceiling, painted white, in a bedroom. There was no insulation in the ceiling...just the wood paneling, then roof paper and then composite shingles. We never had a leak but we would get mold/mildew (it was grey in color) on the ceiling. This room was on the shady side (not sure if that made a difference) of our one story house, not near any bathrooms or laundry. This mold/mildew would build up over time. Every year I would wipe the ceiling with bleach (we had wood-looking linoleum so I didn’t have to worry about bleaching carpet ) . We finally put in a heater with the vents high up in the wall. This ventilation helped a bit but still had to bleach the ceiling every couple years. We are in the process of remodeling this side of the house. Hopefully the insulation will make the difference. In the meantime maybe try a dehumidifier or heater or some fans. Good luck.

By the way we live in San Diego, near the coast. Maybe your living in SF contributes to your problem, as it may have contributed to ours.

Thanks everyone. This is the only place in the house that we have this issue, probably a combination of the exhaust fan condensation and the sofa so close. We think there is a layer of roofing paper between the sloped ceiling and the wood shingles.

My husband is thinking that maybe there is a hole in the exhaust vent duct that is crammed into the 2x4 joist space. We might pull the carpet back and cut into the wood flooring to see if we can see any damage. There is a moldy/musty smell in the room that we can't pinpoint.

Thanks everyone.

NO insulation? That's your issue right there.