The Clean envelope generator is at heart two lag generators, similar to the well known Bissell Morph-Lag circuit: a slower one for the phrase and a faster one for the note. The gate signal drives both, but this gate signal is modulated in the phrase case by the velocity input, and in the note case by the output of the phrase case.

back-of-napkin block diagram
However, there are various other touches to improve response: to prevent long decay tails, the the last stage of the envelope signal first adds a little of the gate signal, then feeds through a “diode drop”: this acts to drop the signal down by .4V when the gate is removed. Also, the prhase lag has a slightly longer fall time than its rise time, so the “tongued note” effect should still be operating at fast attacks, to some extent.
Note that the Gate level as well as the Velocity level will have an effect on the levels. The module is set up for Gate at 5V and Vel of 0 to 5V, however it can handle smaller and larger values with dynamic effect: there is no flip-flop or state based circuitry. The module can be used as a poor kind of envelope follower.
Typical Use as Envelope Generator: Connect Gate signal to Gate In socket. Connect Velocity signal to Velocity In socket. Connect Output socket to subsequent module, such as VCA.
Use as Lag Generator: Feed an ADSR or AR EG CV into the Gate In socket, and the Out socket will have a small amount of that ADSR or AR mixed with a lagged version of the signal, with velocity control. You might use this lagged CV to control vibrato or to modulate a waveshaper.
Potential Other Uses: In theory, the same circuit could be used as an envelope follower and as an audio waveshaper, though this has not been tested. See the Release Notes.