  We present a maximum entropy inverse reinforcement learning (IRL) approach
for improving the sample quality of diffusion generative models, especially
when the number of generation time steps is small. Similar to how IRL trains a
policy based on the reward function learned from expert demonstrations, we
train (or fine-tune) a diffusion model using the log probability density
estimated from training data. Since we employ an energy-based model (EBM) to
represent the log density, our approach boils down to the joint training of a
diffusion model and an EBM. Our IRL formulation, named Diffusion by Maximum
Entropy IRL (DxMI), is a minimax problem that reaches equilibrium when both
models converge to the data distribution. The entropy maximization plays a key
role in DxMI, facilitating the exploration of the diffusion model and ensuring
the convergence of the EBM. We also propose Diffusion by Dynamic Programming
(DxDP), a novel reinforcement learning algorithm for diffusion models, as a
subroutine in DxMI. DxDP makes the diffusion model update in DxMI efficient by
transforming the original problem into an optimal control formulation where
value functions replace back-propagation in time. Our empirical studies show
that diffusion models fine-tuned using DxMI can generate high-quality samples
in as few as 4 and 10 steps. Additionally, DxMI enables the training of an EBM
without MCMC, stabilizing EBM training dynamics and enhancing anomaly detection
performance.
