Techniques disclosed herein enable training and/or utilizing speaker dependent (SD) speech models which are personalizable to any user of a client device. Various implementations include personalizing a SD speech model for a target user by processing, using the SD speech model, a speaker embedding corresponding to the target user along with an instance of audio data. The SD speech model can be personalized for an additional target user by processing, using the SD speech model, an additional speaker embedding, corresponding to the additional target user, along with another instance of audio data. Additional or alternative implementations include training the SD speech model based on a speaker independent speech model using teacher student learning.