What’s the cost of this infusion?

At 13th level, the kinetic knight gains the following ability:

At 13th level as a swift action, she can accept 2 points of burn to unleash a kinetic blast with the blade rush infusion.

I am now level 14, with Infusion specialization 4, which allows me to reduce the burn cost of an infusion by 4.

Does using this ability cost me 0 (2 from the ability + 2 from the normal blade rush – 4) or 2 burn that I have to take no matter what, then 2-4 =0 for the normal blade rush ?

At first it looks like a better pounce for free, but if it costs 2 burn everytime I want to use it, it will lose value pretty fast.