A continuous latent representation is an internal encoding made from real-valued vectors rather than a fixed sequence of discrete symbols. An encoder learns to preserve information needed for reconstruction or another downstream task while discarding unnecessary detail.
Because values can vary smoothly, a generative model can move through the latent space and express gradual changes. In speech generation, this can avoid an extra autoregressive loop over several discrete codebooks and expose a different quality-compute trade-off.
The representation is not directly meaningful to a listener. A decoder must convert it back into audio, and the result depends on how well both the latent space and decoder preserve relevant speech characteristics.
ELI5
A continuous latent representation is a compact list of numbers that describes important features of something without storing it in its original form. Small changes to the numbers can produce small changes in the result.
For example, a speech model can create a hidden numeric description of a voice and then use a decoder to turn it into sound. The numbers are useful to the model even though people cannot listen to them directly.
