Disclaimer: I am in no way affiliated with any of the companies or products mentioned.
I've had closed comedones for approximately 8 years. They were the main source of my acne and were especially bad on my chin, side of chin, jawline, and areas around my mouth. I got them on my forehead, too. I have very oily skin and always assumed this was the source (which is kind of is).
I tried prescription medicines like tretinoin and retin a, salicylic acid creams and toners, and aha creams. Sometimes they worked okay but left my skin dry and irritated. Then, for awhile, I tried all natural products which left my skin more intact but did not help the CC's.
Last Christmas, as a 25-year old, my mother bought me a Clarisonic Alpha, which is the male version. It's basically the same as the female one but is advertised for men with beards and is a charcoal grey color. It came with an AHA cleanser that I was hesitant to use but ended up liking. My problem before was that I could get the comedones to surface into pimples but not prevent them. The clarisonic and the cleanser it comes with have done that. I just went to the beach for a week and only used it once: no cc's cropped up.
With that said, I have never had a CC just disappear. They have to come to the surface and be popped/extracted. I'm not talking about blackheads or the small bumps with rice grains in them (Clarisonic has helped them but not as much), but comedones that turn into full fledged whiteheads when they fully inflame and surface. They're like ticking timebombs just waiting under the skin. It took abut 3-4 months when I noticed I wasn't getting anymore clogs besides some small blackheads. I went from approximately 20 closed comedones under my skin to 0. My face is much clearer because there is no repeated cycle of erupted comedones and dark marks, which altogether took about a month to fully clear, in which another would erupt by then.
I just felt it necessary to share my method because I've had these for so damn long. I thought about suggesting the use of a soft brush instead of the clarisonic, but I read that the clarisonic not only exfoliates, it sends waves into the skin for deep cleansing. I'm not sure which has been more effective: the cleanser, clarisonic, or both, but having no closed comedones is amazing.
P.S. After re-reading my post, I want to add two things: diet seems to play no role in CC's, and exfoliation is key. My skin is so so oily, yet I have eradicated all CC's. I still get some small bumps and blackheads but those are almost invisible, easy to deal with, and harder to fully combat with the nature of my skin.