SVI still uses sampling under the hood. Any probabalistic programming framework (such as pyro) uses random sampling, there's no other way to estimate the curve

SVI still uses sampling under the hood. Any probabalistic programming framework (such as pyro) uses random sampling, there's no other way to estimate the curves of a complex set of interacting probability distributions. Obviously there are some optimizations for simple distributions that are known (e.g. we know what the expected values of simple gaussians will be, and the PDF or CDF of a given sample).