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This paper proposes the divergence triangle as a framework for joint trainingof generator model, energy-based model and inference model. The divergencetriangle is a compact and symmetric (anti-symmetric) objective function thatseamlessly integrates variational learning, adversarial learning, wake-sleepalgorithm, and contrastive divergence in a unified probabilistic formulation.This unification makes the processes of sampling, inference, energy evaluationreadily available without the need for costly Markov chain Monte Carlo methods.Our experiments demonstrate that the divergence triangle is capable of learning(1) an energy-based model with well-formed energy landscape, (2) directsampling in the form of a generator network, and (3) feed-forward inferencethat faithfully reconstructs observed as well as synthesized data. Thedivergence triangle is a robust training method that can learn from incompletedata.

Divergence Triangle for Joint Training of Generator Model, Energy-based Model, and Inference Model