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

Summary

This work proposes a maximum entropy inverse reinforcement learning (IRL) approach for improving the sample quality of diffusion generative models, especially when using a small number of generation steps.

Strengths

1. The paper presents a novel and principled approach for improving diffusion models by formulating the problem as maximum entropy IRL. This elegant formulation allows jointly optimizing a diffusion model and EBM to enhance sample quality, especially with fewer generation steps. 2. The proposed DxDP algorithm is a key technical innovation that makes optimizing the IRL objective tractable. By leveraging ideas from optimal control and dynamic programming, DxDP enables efficient diffusion model updates without back-propagation through time, which is a significant practical benefit. 3. Strong empirical results on both image generation and anomaly detection tasks demonstrate the approach's effectiveness. DxMI can generate high-quality samples with very few (4-10) steps and enables training EBMs without MCMC, such a diffusion step reduction is impressive to me.

Weaknesses

1. While the acclaimed acceleration of the diffusion model looks effective (and is also stated as a major advantage of this algorithm), the comparison to prior diffusion model acceleration methods is somewhat limited. A more comprehensive evaluation across different speed-quality tradeoffs and more discussion of DxMI's relative strengths and weaknesses compared to other approaches would be essential. 2. While the empirical results look good, the paper lacks theoretical analysis of the proposed methods, such as convergence rates for DxDP or any approximation guarantees relating the IRL objective to the original objective. Adding such analysis would help characterize this method's ups and downs.

Questions

1. Upon reviewing this work, I found that the energy-based objective (Eq. (2)) and training objectives (Eqs. (3), (4), (5)) share very strong similarities/motivations to the concepts employed in existing KL-regularized RL-based fine-tuning papers (e.g., [1-4]). In particular, Eq. (6) and Eq. (7) in [2] serve precisely as the KL-based training objectives and the energy-based model, which involves sampling from unnormalized distributions. While I think the similarities might be just in terms of high-level methodologies and principles, it still becomes crucial for the authors to provide a thorough discussion highlighting the technical and methodological distinctions between this approach and the prior works in order to well-position the proposed method. For discussing the methodological relations/differences, I also recommend the authors carefully check [1] as this paper is written in a principled way, such that it becomes a good reference for understanding the methodologies. 2. As mentioned, do you have any theoretical insight into the convergence properties of DxDP or approximation guarantees relating to the IRL and original objectives? Many IRL theories might be worth checking (references [1-4] also might be worth checking for this goal, probably). Even without providing rates/bounds, an intuitive discussion/remark on these points could further validate the approach. 3. Can the DxMI approach be extended to other families of generative models, e.g., bridge-matching diffusion models, which are very similar to standard denoising diffusion models? What are the key challenges or requirements for the generative model? 4. How do you expect this approach to scale to more complex datasets or higher-dimensional spaces? Will the sample efficiency gains be more or less pronounced? 5. In experiments, how sensitive are the results to hyperparameters of DxMI/DxDP, such as the coefficient on the entropy term? What strategies did you use to tune these? [1] https://arxiv.org/abs/2403.06279 [2] https://arxiv.org/abs/2402.16359 [3] https://arxiv.org/abs/2305.16381 [4] https://arxiv.org/abs/2405.19673

Rating

6

Confidence

4

Soundness

3

Presentation

3

Contribution

3

Limitations

The authors adequately addressed the limitations.

Summary

The authors propose learning a denoising diffusion model without using the denoising loss. Instead, they propose first training an energy based model and then treating the diffusion denoising sampler as an RL trajectory with the energy based model as the reward. To learn the energy based model, however they propose a generalized version of contrastive divergence which uses the current diffusion model as part of its objective function. Experiments are designed to validate this idea, starting from pretrained diffusion checkpoints.

Strengths

- The paper explores a creative combination of a variety of ideas all seeking to replace the simple denoising diffusion training objective. - The exposition is well written - The proposed approach involves learning both an energy based model and a diffusion model using DP where the number of steps can be small. The latter has value for fine-tuning diffusion models against other types of rewards.

Weaknesses

- The authors introduce an elaborate scheme to do away with the score function denoising objective, but their experiments rely on pre-trained checkpoints that use the score function training to get these results so the final results are based on stacking the new methods on top of the original diffusion training. - The objective in Eq (5) seems somewhat hard to be confident of, in the sense that given any $\pi$ and $p$, the optimal $q$ could diverge away from $p$ such that $KL(p||q) < KL(\pi|q) >> 0$ (while still being closer than q since the optimum value of the objective has to be negative). This could theoretically make it unstable as an iteration progresses, $\pi$ will track $q$ and then $q$ can take another step further away from both $p$ and $\pi$ while being optimal for Eq (5), which only requires that the relative distance to $p$ be less than that of $q$. As another point, when initializing with a $\pi$ that is close to $p$ (e.g. in the pretrained model case), the optimal $q$ does not look like it has to be close to either given the cancellation involved. - The key proposal in Algorithm 1 has a multiple highly unstable procedures mixed together within each iteration -- e.g. the energy update in Line 5 and the TD bootstrap objective in line 7.

Questions

In Algorithm 1, Line 5, are the $x$ and $x_T$ completely independent samples with no relation to each other? From the way its written, $x_T$ is sampled starting from independent noise $x_0$, and $x$ is a particular data sample for that iteration. Moreover, since for the pre-trained checkpoints, $\pi$ is likely close to $p$, the energy objective looks like it has minimal training signal.

Rating

7

Confidence

3

Soundness

3

Presentation

3

Contribution

3

Limitations

Yes

Summary

This paper seeks to improve diffusion models by employing inverse reinforcement learning methods of imitation rather than (more myopic) behavioral cloning methods, which prevalent existing diffusion models can be viewed as using. It trains an energy-based model using maximum entropy inverse reinforcement learning and proposes an optimal control problem for diffusion based on minimizing an upper bound of the contrastive KL divergence. The benefits of the approach are demonstrated with a focus on generating outputs with few diffusion iterations.

Strengths

The paper is motivated by the key connection between imitation and diffusion models, the characterization of existing methods corresponding to behavioral cloning approaches for imitations, and the potential for improved diffusion using more sophisticated inverse reinforcement learning imitation methods. This motivation is nicely described. The technical content of the paper is quite dense, but the authors present it clearly. Other work exists exploring this perspective of diffusion as imitation/optimal control, but the paper’s approach is nicely constructed to avoid MCMC and policy gradient optimization, which are often bottlenecks in existing methods. Experimental results show the benefits of this approach, including comparisons with a similar approach that is reliant on policy gradient (SFT-PG) and other recent diffusion model learning methods for generation and anomaly detection.

Weaknesses

Closely related work isn’t described in the introduction to better frame the contributions of this paper.

Questions

Is there potential for theoretical analysis or guarantees using this approach? Are there visual differences in the generated outputs of different models that could be highlighted in 5.2?

Rating

8

Confidence

3

Soundness

3

Presentation

4

Contribution

4

Limitations

Potential abuses using deep fakes are described, along with limitations.

Summary

The authors introduce a maximum entropy inverse reinforcement learning (IRL) approach for enhancing the sample quality of diffusion generative models, especially with limited generation time steps. Named Diffusion by Maximum Entropy IRL (DxMI), the approach involves joint training of a diffusion model and an energy-based model (EBM). The EBM provides the estimated log density as a reward signal for the diffusion model, which is trained to maximize both the reward from EBM and the entropy of generated samples. Additionally, the authors propose Diffusion by Dynamic Programming (DxDP), a novel reinforcement learning algorithm that optimizes diffusion model updates efficiently by transforming the problem into an optimal control formulation. Empirical studies demonstrate that diffusion models fine-tuned with DxMI can generate high-quality samples in as few as 4 to 10 steps and improve the stability of EBM training dynamics, enhancing anomaly detection performance.

Strengths

1. Innovation: The proposed DxMI methodology introduces the concept of maximum entropy IRL to the training of diffusion models, which is novel and potentially impactful in improving sample quality and inference time of diffusion model. 2. Clarity: The manuscript is well-written and logically structured, with clear explanations of the theoretical foundations and algorithms.

Weaknesses

1. Complexity of Implementation: The implementation of DxMI, particularly the joint training of diffusion models and EBMs, might be complex and require significant computational resources. The practical feasibility in various settings could be further elaborated. 2. Limited Scope of Experiments: The experiments, while promising, are somewhat limited in scope. More diverse and complex tasks could further validate the robustness and versatility of the proposed approach. 3. Comparative Analysis: While the proposed methods show improvements, a more detailed comparative analysis with state-of-the-art techniques, including training time and computational cost comparisons, would strengthen the paper.

Questions

1. Generalization to Complex Tasks: How do the authors envision the performance of DxMI in more complex generative tasks, such as high-resolution image generation or text-to-image synthesis? 2. Training Time Comparison: What is the average training time for models using DxMI compared to other generative model training techniques such as GANs or VAE-based approaches? 3. Scalability: How scalable is the proposed DxMI approach when applied to larger datasets or models with significantly more parameters? Are there any anticipated bottlenecks?

Rating

6

Confidence

3

Soundness

3

Presentation

3

Contribution

3

Limitations

The authors have clearly presented the limitations in the paper.

Reply

> Thus, our objective function always keep closer to than to, not invoking the instability questioned in the review comment. Thanks for the clarification, I understand the proposal better after re-reading the paper and have updated the initial review accordingly. While my comment related to the objective was not really trying to claim a formal counter example for demonstrating pathologies of the proposed objective, it would be quite impressive if you could convert your intuition in the above response into a formal argument backing the proposal.