Reviews: The Thermodynamic Variational Objective

The paper connects variational inference with thermodynamic integration, so that the data log-likelihood can be formulated as a 1D integration of the instantaneous ELBO in a unit interval. By applying a left Riemann sum, TVO, a novel lower bound for the marginal log likelihood, is derived in which the traditional variational ELBO is recovered when only one partition is used. The authors then design an importance-sampling-based gradient estimator to optimize the objective, and compare with other methods on both discrete and continuous deep generative models. Originality and Significance: the formulation of TVO is an interesting idea. Better optimization methods than the importance-sampling-based approach are worth further exploring.