Very sorry to hear about your situation - seems like your sex life has been marginal or worse for most of your relationship and that your fragile self esteem has been severely tested as a result.
I wish I could see a positive sign that your husband's sex drive would improve over time, but unless there is some underlying root physical or emotional issue than can be identified and fixed, I can't imagine how the situation will improve by itself over time.
The vast majority of posts on this matter sound almost identicle to yours in that the LD spouse rarely develops into a moderate desire indvidual. The LD spouse may make an effort for a few weeks to have a sex life but this is rarely sustained and the relationship reverts back to the never ending circle of frustration, anger and depression.
The only turn arounds seem to occur when the HD spouse threatens to leave and makes serious moves in this regard. This is a very risky proposition as there is a real danger that the LD spouse will not respond and you are left with either leaving or staying and loosing any leverage at all. I am not convinced that the situation improves over the long term if the LD spouse merely goes along with trying to have a sex life only to hold onto their spouse - over the longer term I wonder if the relationship slips back into its old ways.
I wish I could be more positive but I think you have a difficult decision ahead at a very early stage of your marriage. An active sex life is natural and important to most people and being robbed of this is a serious impediment to your sense of well being. From years of struggling in a relationship with a ND spouse, I can tell you that as a HD individual, surpressing your sexuality forever and living a happy life isn't really possible.
I wish you all the best of luck in a very difficult situation.