Being married to an addict is difficult. Making the decision to divorce one is just as hard. People might try to tell you that you can't just walk away from the person who has the problem. The truth is that you might have to walk away for your own health.
There are many behaviors that come with an addiction. Lying, adultery, stealing and behaving inappropriately are all possible. Sometimes, addiction comes with violent tendencies, which makes the situation even more dangerous. All of these can lead to the addict's spouse not being able to continue the relationship, especially when the person isn't willing to get help or doesn't acknowledge that there is a problem.
The divorce process is the same as any other divorce even if you are divorcing someone with an addiction of any sort. In some cases, these can still be resolved through mediation; however, there is a chance that the person might not be sober enough for this to occur. This means you would have to go through a trial.
An additional consideration that you must think of when you are in this position is that you have to figure out what is going to happen with the children. It might not be in their best interest to spend time alone with their other parent, especially if they are still deep in the throes of their addiction. You might have to try to push for supervised visits if it is safe for the child to continue a relationship with that parent.
You have to do what you feel is best for you and your kids. Be sure to explore all the available options before making any decisions.