A Veblen good is also one for which an increase (decrease) in price results in an increase (decrease) in the quantity consumed.
However, a Veblen good is not an inferior good . The increase in consumption when the price of the good increases is due to a perception that a higher price makes consuming the good more desirable in some way, perhaps conveying higher status.
It seems that when Giffen good gets cheaper, it triggers negative income effect (more remaining money) - this is how we get from goods price to income, therefore we can say it is inferior, i.e. income elasticity of demand is negative.