I believe this is really dependent on the particular movements you're looking to speed up. That said, two ways to increase your speed are to:
a.) Decrease the distance you're traveling! This was always very surprising to me. In my art, we side step, and I would find myself burning extra calories pumping extra energy into the movement to find that I had to put the breaks on harder to stop. The lesson I learned, the hard way and with significant practice, was to simply reduce the distance. If I was moving in an elliptical fashion, I might ask why I couldn't move in a straight line/cutting the hypotenuse.
b.) Simplify/factor your movement to the absolute tightest and smallest movement "within the realm of your safety."
Of course, this is all relative to the particular movements that you are training and you may already have arrived at the "prime factorization" of your expression. This is just to serve as a reminder that we should always challenge ourselves to critically examine our movements with questions like this.
~ Alan, Wing Chun Student