Can vision improve over time on its own?

Usually not. Most visual defects, if the cause is a need for eyeglasses, will not improve spontaneously. This is always a hope of many and the reason why there are so many quack type things like eye exercises allegedly able to improve vision. There is some variability in the eye power over time and rarely vision may seem to improve in the elderly depending upon a number of factors, but this is uncommon.