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Discoloured ceramic tiles.
You didn t indicate whether the tile is a glazed ceramic tile or an unglazed ceramic tile or whether either of those types of ceramic tile were porcelain body tiles.
If the tiles have been around for a while your tile restoration may just include a good cleaning to restore their shine.
To give your tiles a deep clean take a bucket of hot water and add a couple of drops of mild dish.
Someone mentioned they are ceramic and absorb water.
Likely not so coincidentally there is a 4 strip of adhesive vapor barrier along the bottom row to the shower pan that correlate with the discolored tiles.
While it may seem obvious regularly cleaning your bathroom floors is the most effective way to prevent tile discoloration.
After all the tile based discoloration has been successfully removed use a water soaked sponge or mop to get rid of any remaining traces of your solution.
Answer answer there are a number of variables involved in determining what is causing the discolored tiles and it will likely require some intrusive inspections to verify the cause and to determine how to remediate it.
Removing the stains without replacing the grout requires some effort but is less intensive.
I was inspired by the way you referenced installing pictures and did the same for myself.
Dirty stained grout can make an otherwise clean tiled area look filthy.
Step 5 prevent discoloration from reoccuring.
Cleaning your ceramic tiles.