Are there generalizations of zero-inflated negative binomial and hurdle modeling that address continuous (i.e., non-count) variables?

I know that count variables whose distributions include a lot of zeros in them can be modeled with zero-inflated negative binomial models and also hurdle models, but I'm curious if there are similar kinds of models for continuous, non-negative outcome variables where the probability of departure from zero is itself modeled alongside simultaneous modeling of the non-zero magnitude. It occurred to me that it would be possible to discretize any continuous outcome variable and so convert it to a count variable, but I wonder if there are any models that explicitly address continuous variables of this sort. It goes without saying that such variables are only "continuous" beyond the transition from zero to non-zero values, but I'd be interested in any insights out there.