Does growing a vertical garden on a wall of home cause mold?

I'm not sure. Indoors or outdoors would probably make a difference, but if the garden is not always wet and has air circulation and a chance to dry, probably not. There would probably need to be some barrier between the walls of the house and the plants, some effective method of watering with a way for excess water to drain off, and a way to circulate air. Good luck!

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Put waterproofing spray on the wall or plastic

Are you speaking of a seepage wall? I know someone that created one and got all kinds of surprise growth. They lived on Hawaii and had lots of air circulation. Here in hot humid indiana I bet you would get mold as I had a leak under the sink and it was super damaging with mold. Guess this sounds like an i-dont-know answer but lots to consider. Can you house stand the extra humidity? What will be your base? Sterilized or wild rock? Maybe a small try on a table arrangement? Good luck! Our friends creation was lovely.

Waterproofing spray should do it!