What about the individual cluster models -- can they represent dependencies of variables within a cluster? For instance, I'm thinking about the "salary prediction" example. Is the salary variable considered to be conditionally independent of all the other variables, given the cluster assignment? Or can it learn something like an additive model, where categorical variables are associated with higher or lower salaries within a cluster?

Or to use another example, can it learn correlations between two continuous variables, to solve things like linear regression?