If there is an increase in saving, then assuming that income stays exactly the same, this will mean that there is a fall in spending as we are saving a higher proportion of our income - or in other words our marginal propensity to save has increased. If there is a fall in consumption due to people spending less of their income, then this could result in a fall in aggregate demand. If the economy is then producing at very little spare capacity, then a fall in aggregate demand could result in much less demand-pull inflation and hence an increase in savings will reduce inflation.
But can we think of some good evaluation points here?
A fall in savings may not necessarily decrease AD if other elements of AD are rising - for instance if higher saving is accompanied with higher government spending, then AD will not fall and hence we won't see a fall in demand pull inflation
Also, incomes may be rising and aren't constant - this means that savings and consumer spending could both be increasing at the same time, so AD is going up even though savings is also going up!
Finally, there may also be cost-push inflation taking place that will offset a fall in demand-pull inflation. The costs of production may be rising for suppliers - perhaps the cost of raw materials is rising such as oil - inflation from the rising costs of production will then offset falling demand pull inflation.