  Energy-Based Models (EBMs) have been widely used for generative modeling.
Contrastive Divergence (CD), a prevailing training objective for EBMs, requires
sampling from the EBM with Markov Chain Monte Carlo methods (MCMCs), which
leads to an irreconcilable trade-off between the computational burden and the
validity of the CD. Running MCMCs till convergence is computationally
intensive. On the other hand, short-run MCMC brings in an extra non-negligible
parameter gradient term that is difficult to handle. In this paper, we provide
a general interpretation of CD, viewing it as a special instance of our
proposed Diffusion Contrastive Divergence (DCD) family. By replacing the
Langevin dynamic used in CD with other EBM-parameter-free diffusion processes,
we propose a more efficient divergence. We show that the proposed DCDs are both
more computationally efficient than the CD and are not limited to a
non-negligible gradient term. We conduct intensive experiments, including both
synthesis data modeling and high-dimensional image denoising and generation, to
show the advantages of the proposed DCDs. On the synthetic data learning and
image denoising experiments, our proposed DCD outperforms CD by a large margin.
In image generation experiments, the proposed DCD is capable of training an
energy-based model for generating the Celab-A $32\times 32$ dataset, which is
comparable to existing EBMs.
