Maximum Entropy Inverse Reinforcement Learning of Diffusion Models with Energy-Based Models

Maximum Entropy Inverse Reinforcement Learning for Diffusion Models using Energy-Based Models

The paper "Maximum Entropy Inverse Reinforcement Learning of Diffusion Models with Energy-Based Models" by Sangwoong Yoon et al. explores methodologies to improve the sample quality of diffusion generative models, particularly when the generation step count is constrained. The authors present a novel combination of Maximum Entropy Inverse Reinforcement Learning (IRL) and Energy-Based Models (EBMs), introducing an algorithm named Diffusion by Maximum Entropy IRL (DxMI). This paper's contribution provides a new perspective on diffusion models, standing at the intersection of generative modeling, reinforcement learning, and energy-based methods.

Overview

Diffusion models have achieved considerable success in generative tasks by transforming Gaussian noise into samples through iterative refinements. However, the generation process is computationally expensive due to its slow speed, often necessitating hundreds or thousands of steps. The slow generation speed arises from imitation-based training, which does not generalize well when deviating from the finely-tuned training trajectory.

To address this limitation, the authors propose rethinking the diffusion generation process through the lens of IRL, specifically focusing on the maximum entropy principle. In typical IRL, the reward function derived from expert demonstrations enables optimized policy training. Similarly, in DxMI, the diffusion model is trained using log probability densities estimated by an EBM, where the EBM serves as an implicit reward function.

Contributions

1. Formulation of DxMI: The key insight is to formulate the training of diffusion models as a minimax problem: \begin{align} \min{q}\max{\pi} \mathbb{E}{p} [\log p(x) - \log q(x)] - \mathbb{E}{\pi}[\log q(x)], \end{align} where (q(x)) is the EBM approximating the data density (p(x)), and (\pi(x)) is the diffusion model. This formulation effectively combines energy-based models and maximum entropy RL, ensuring stability and enhanced exploration.

2. Algorithm DxDP: Another major contribution of the paper is Diffusion by Dynamic Programming (DxDP), a novel algorithm to efficiently update diffusion models in DxMI. DxDP addresses the challenges of marginal entropy estimation and gradient propagation in discrete-time diffusion models. It reformulates diffusion training as an optimal control problem and employs dynamic programming to approximate value functions, thereby facilitating more stable and memory-efficient learning.
3. Experimental Validation: The empirical studies demonstrate that DxMI can fine-tune pre-trained diffusion models to achieve high-quality samples rapidly, using as few as 4 or 10 generation steps. Notably, DxMI also enables EBM training without MCMC sampling, thus stabilizing training dynamics and enhancing performance in anomaly detection tasks.

Strong Numerical Results

• CIFAR-10 and ImageNet: DxMI exhibits impressive performance on image generation tasks, outperforming other methods in terms of both FID (Fréchet Inception Distance) and precision-recall metrics, especially for fewer generation steps.
• MVTec-AD Anomaly Detection: When applied to the MVTec-AD dataset, DxMI achieves state-of-the-art performance in both anomaly detection and localization tasks.

Theoretical and Practical Implications

The integration of maximum entropy principles with diffusion models opens new avenues for robust generative modeling. The maximization of entropy ensures that the learned models explore the function space effectively, preventing overfitting to suboptimal strategies. Practically, DxMI's ability to enhance sample quality in fewer steps without significant computational overhead offers significant advantages in applications where real-time or resource-constrained generation is critical.

The use of value functions and dynamic programming in DxDP demonstrates the potential for RL techniques to stabilize and improve training dynamics in complex generative models. This innovative cross-pollination between RL and generative modeling suggests numerous future research directions, such as:

• Further Exploration of Optimal Control: Deepening the connection between diffusion models and optimal control through continuous-time formulations or alternative discretization approaches.
• Adapting to Different Data Modalities: Extending the methods to various data types such as text or audio, potentially integrating with other forms of expert-derived rewards.
• Combining with Human Feedback: Leveraging human-in-the-loop training paradigms to further refine and adapt diffusion models in real-world applications.

Conclusion

The proposed DxMI framework represents a significant advancement in the training of diffusion models, merging the strengths of maximum entropy IRL and EBMs. By addressing fundamental issues in sample quality and training efficiency, the paper sets a new precedent for generative modeling research. The compelling results and insights presented suggest that combining generative modeling with reinforcement learning can lead to robust, efficient, and high-quality generative models that excel across various applications.