It depends what you mean by "disease". Ultimately, the general things of growing old like weakness, thinner bones, poor circulation, etc. can be regarded as diseases. Even wrinkly skin is caused by the imperfections of new skin cells growing to replace old ones. Either everybody would live forever and there would be overpopulation and mass starvation, or there would be a natural point at which old people conveniently pop off (with a heart attack, for example) without any intervening disease.