Autoimmune Sacroiliitis does not have a "cure", although some things can treat and help the symptoms. Some with Sacroiliitis have attained it due to injury. That has many more treatment options, and a much greater possibility of remission.
Sacroiliitis is an inflammation of one or both of the sacroiliac joints, which connect your lower spine and pelvis. With sacroiliitis, even the slightest movements of your spine can be extremely uncomfortable or even painful for you.
And yes, it can heal over time. It does take time as you basically have severe inflammation. So I'd only do exercises recommended by your doctor or physical therapist along with taking medications they prescribe.