Wyoming makes divorce relatively easy, at least when it comes to the grounds on which you can file. It's a no-fault state, so you don't have the option of alleging that your spouse did something wrong and that this is why your marriage ended. You can only cite irreconcilable differences or that your spouse is incurably insane, and you don't have to live apart before you file.
In Wyoming, filing for divorce on the basis of irreconcilable differences does not require that you and your spouse live separately. You must simply tell the court in your complaint for divorce that your marriage is no longer working and that you're the aggrieved party -- the one who wants a divorce because of your differences. The only time periods involved are those for establishing residency – which is 60 days in Wyoming – and a waiting period of 20 days after you file your complaint before your divorce can be finalized.
Wyoming recognizes judicial separation. The grounds are the same as those for divorce, and the legal process is similar as well. When the court issues a separation decree, it may be open-ended – you can remain separated indefinitely without ever filing for divorce – or the judge might order a date at which you must make a decision whether to divorce or stay together.