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We present Generalized Contrastive Divergence (GCD), a novel objectivefunction for training an energy-based model (EBM) and a sampler simultaneously.GCD generalizes Contrastive Divergence (Hinton, 2002), a celebrated algorithmfor training EBM, by replacing Markov Chain Monte Carlo (MCMC) distributionwith a trainable sampler, such as a diffusion model. In GCD, the joint trainingof EBM and a diffusion model is formulated as a minimax problem, which reachesan equilibrium when both models converge to the data distribution. The minimaxlearning with GCD bears interesting equivalence to inverse reinforcementlearning, where the energy corresponds to a negative reward, the diffusionmodel is a policy, and the real data is expert demonstrations. We presentpreliminary yet promising results showing that joint training is beneficial forboth EBM and a diffusion model. GCD enables EBM training without MCMC whileimproving the sample quality of a diffusion model.

Generalized Contrastive Divergence: Joint Training of Energy-Based Model and Diffusion Model through Inverse Reinforcement Learning