I have several baths and bath floors where the grout between ceramic tiles has become dirty or moldy or both. The grout was sealed when it was put down, but is still porous and easily becomes dirty. I have tried the cleaning solutions available at Home Depot without much success, especially on the grout that was initially white.

Sometimes brout gets so bad that it can't be cleaned as good as new. You can abraid the grout with a grout saw or go all the way and remove the grout surface just enough so you can put down a new grout surface. I would recommend a two part epoxy grout that is stain proof.