While many use soap and water on their stones, I don't. As part of my job, I do finishing/refinishing of furniture and other wood and metal surfaces.
I learned about the dangers of soap remnants in an easy demonstration when we were learning about cleaning surfaces prior to finishing. Very mildly soapy water was put in a clean pane of glass, then rinsed well under warm water and allowed to dry while the rest of the demo went on.
The remaining stearates on the glass dotted it with their remains after drying. So I remembered one day when cleaning my diamond rods, and after I washed them and dried them, I tried cleaning them with lacquer thinner to see if I could remove any more dust or contaminants. A lot more steel dust came off, evidencing that the soap left its remains after rinsing. (As a sidebar, ever wonder just why you can smell soap on your hands after washing, on your hair after a shampoo, or on a towel? The stearates hold the fragrances, and when the stearates are left behind, they keep the fragrance as well.)
Sharing this piece of knowledge with the knife makers I see at out monthly gun show, the uniform response to my discovery was *duh*, and as usual, I felt like I was the last to know.
Now I do as Obsessed With Edges said, and clean them with a non scratching cleanser and a toothbrush. A couple of quick brushes and they are clean as a whistle. I allow them to air dry as a local knife maker here told me that he didn't dry his off as the diamonds would collect or cut off tiny pieces of lint that causes the diamond surface to be filled and cut less precisely.
I am not consumed with sharpening, but really like a sharp knife. With my job dulling my knives frequently, and my obsession with cooking, buy rods are used on about 3 - 4 knives a week, every week. More if I get a new knife I feel I need to reprofile. I am convinced that by keeping the surfaces clean they have lasted as well as they have. They are about 10 years old now, and while they aren't as aggressive as they once were, as pointed out above, that might not be such a bad thing.
Robert