Ki Pulse is an Additional Stat in Nioh. It affects the initial amount of Ki restored by a Ki Pulse.
You initiate a Ki Pulse by pressing R1 during the point in a combo where a blue essence swirls around your player. Executing it at the right time will result in restoring some of the Ki you have expended.
When you level up your Skill stat it improves your Ki Pulse. Normally, when you swing your weapon, your red Ki begins to fill up with light blue ki all the way from the left. When you hit an enemy however, part of your Ki will automatically be filled up with light blue. This allows you to get more of your Ki back when you have to Ki Pulse instantly. Essentially it pre fills the bar. Improving your Ki Pulse stat will increase the amount of pre fill, the amount of the red bar that is automatically filled with a chunk of light blue instantly, before it starts gradually filling up. It doesn't change the total cost of your moves at all. It allows you to recover faster.