Instant double jump
An instant double jump, or IDJ for short, is the act of inputting a double jump immediately after a jump, ideally as low to the ground as possible.
Details
An instant double jump is a double jump performed immediately after inputting Jump. In most cases, this is done by buffering a double jump during a character's jumpsquat. If done correctly, the particles from the double jump should appear close to the ground.
Since the values that determine double jump height are different from regular jump height, the distance covered by an instant double jump is different from a short hop or full hop -- usually somewhere between the two.
The applications of this are numerous. For example, certain windows for late auto-canceling that are between the two jump heights can be achieved with an instant double jump or IDJ fast fall. In addition, certain aerials that can only be used once during a short hop can be used twice during an IDJ or followed up with additional aerials.