No, there is no cure. There is no treatment that can cure the disease in any of its forms, nor guarantee long-term recovery.
Depending upon how advanced the disease is at the time of diagnosis, some degree of heart function may be irreversibly lost. When diagnosed early, some forms of cardiomyopathy respond well to long-term medication use, or pacemaker or defibrillator implantation.
Research in the understanding of how heart muscle cells work is helping us work towards a potential cure for this disease.