I am no expert but I can speak to my own similar experience for what it's worth.
I had a significant diatom problem which was continuing 3 months after my tank had been fully cycled (90 gallon). I read that they usually burn themselves out a few weeks after the tank is cycled. So I switched from a Fluval 3.0 plant light to UNS Titan 1, which is a much brighter light with a more ideal spectrum, and the diatoms disappeared almost overnight. If you want to purchase a new light I would suggest checking around the forums and see what people recommend for popular lights. Though I do know that anubias doesn't need much light to thrive so it may not be worth it.
You may be able to get more advice from others if you post the following: how long has your tank been cycled for? Current ammonia, nitrite, nitrate readings, specifics of the light you have (incl. spectrograph)