variational dude
OpenAI hires a bunch of variational dudes. • /r/MachineLearning
There's a wide class of generative models for which variational methods are the only known practical way to do inference. This includes basically any model with black-box ("neural") dependence relations, and many others as well, e.g., Bayesian nonparametrics for any significant dataset size. The point of variational methods is not to calculate partition functions (although you do get that as a side effect); the point is to fit sophisticated models that have complex latent structure. Which does yield improvements across pretty much any metric you'd care about.