1. A computer-implemented method comprising: receiving, by a speech recognition model training system and from a first computing device, (i) a request for an update to a speaker-dependent speech recognition model associated with the first computing device, and (ii) recorded speech; generating, based on processing the recorded speech from the first computing device and by the speech recognition model training system, the update to the speaker-dependent speech recognition model associated with the first computing device; generating, based on processing the recorded speech from the first computing device and by the speech recognition model training system, an update for a speaker-independent speech recognition model associated with a second computing device; transmitting, based on receiving the request and by the speech recognition model training system, the update to the speaker-dependent speech recognition model to the first computing device; determining, by the speech recognition model training system, that a predetermined period of time has elapsed since the speaker-independent speech recognition model associated with the second computing device was last updated; and transmitting, based on determining that the predetermined period of time has elapsed since the speaker-independent speech recognition model associated with the second computing device was last updated and by the speech recognition model training system, the update to the speaker-independent speech recognition model to the second computing device.