A rocket moves under the conservation of linear momentum, where the gases formed inside it, exit through the nozzle, and in turn, the rocket moves forward. What I want to ask about is that: is it true that increasing the velocity of the issued gases would help in letting the gases be unseen by our eyes(or seen much unclearer) when looking at them flying in the atmosphere, as they are being issued in a diverging mode and not in a linear mode ?
In the atmosphere, the answer is mostly no, because the exhaust gases slow rapidly when they hit the surrounding air. Increasing the exhaust velocity by a modest factor will diffuse the plume only a very small amount, and increasing it by a large factor will probably put enough energy into the surrounding air to make it incandesce.
Outside of the atmosphere, the exhaust velocity is high enough to diffuse the plume quite rapidly; you can see the difference in any SpaceX launch video between the first-stage exhaust and second-stage. The chemistry is the same for both stages and the exhaust velocity only modestly higher for the second stage, but the plume from the second stage burn is much fainter. You can also see over the course of the first stage burn that the exhaust goes from a tightly confined bright yellow plume at low altitudes to a fainter, more diffuse and orangey pattern at high altitude.