The title says it all. I am currently reading up on deep generative models, and frequently encounter the term "variational inference" as well as the term "variational approximation" to refer to what appear to be the same task--approximiating difficult-to-solve probability densities/distributions. Are these terms synonymous with one another, or is there some subtlety I am missing?

Reference that uses "variational approximation": http://www-scf.usc.edu/~zche/papers/icml2018.pdf

Variational inference appears much more often, it seems: https://arxiv.org/pdf/1807.05936.pdf, https://www.aclweb.org/anthology/P18-5003/

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    $\begingroup$ i'm not exactly an expert, but as far as i can tell, "variational inference" refers to the procedure by which the variational approximation of the posterior is obtained, and "variational approximation" is usually short for "the variational approximation of the posterior". $\endgroup$ – shimao Oct 4 '19 at 4:07

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