I'll try to be more to the point than Karl Hallowell and a little more terse than Alen, but both answers should give you a picture already.
The exact answer to your question is, the rate of ascent (i. e., its velocity) increases as long as there is a net upward force acting on the balloon. This will only be the case for part of the balloon's journey.
However, that has to do only in part with its height. The balloon is accelerating upwards as long as it has positive buoyancy*, i. e. its velocity is rising as a function of time. At some point, the acceleration will be offset by the decceleration induced by the drag of the surrounding air and the velocity will remain constant for a while. Finally, the net buoyancy will decrease all the way down to zero, and drag will slow down the balloon until it stops.
Now, that last part actually is a function of the balloon's height, or, more precisely, a function of the density of the surrounding air (which decreases with height). The less dense the fluid displaced by a body, the lesser the buoyancy force exerted by the fluid. For a rigid container, that would be the whole story, for an expanding container (like a latex balloon), its increase in volume under lower ambient pressure counters that effect to some extent by displacing more of a now lighter fluid. As Karl has pointed out, this is an idealization, and a decrease occurs anyway.
Useful Wikipedia articles (as already given by Alen):
**note that I'm mixing gravity and buoyancy into "net buoyancy", which may be an oversimplification.*