Gradient-free Decoder Inversion in Latent Diffusion Models

Summary

The paper introduces a gradient-free method for LDM decoder inversion. Compared to traditional gradient-based methods, this method is computational and memory efficient which makes it suitable for large-scale tasks like video generation. They provide theoretical support for the method's convergence. Their empirical results show that their gradient-free method reduces computation time and memory usage in applications such as watermark classification using Stable Diffusion 2.1 and InstaFlow models. Using optimization strategies like the Adam optimizer and learning rate scheduling further boosts the efficiency.

Strengths

1- The authors introduce a new gradient-free method for decoder inversion, which is both faster and more memory-efficient that traditional gradient-based methods. 2- The paper provides a theoretical analysis of the proposed method, showing that it converges under reasonable conditions. 3- The method is shown to be effective in a practical application where precise decoder inversion is necessary, and their proposed method achieves comparable accuracy to gradient-based methods.

Weaknesses

1- The comparative experiments mainly focus on memory usage and runtime. There is limited evidence on how the accuracy of the inversion compares to gradient-based methods in various applications. Also, authors do not present images for qualitative comparison. 2- Experiments validating the convergence assumption are limited to specific hyperparameters for Stable Diffusion, LaVie, and InstaFlow. It is not clear if this behavior generalizes to other settings.

Questions

1- How robust is the assumption 𝐸∘𝐷 ≈ 𝐼 ? Can you provide empirical evidence for this assumption in the context of non-linear autoencoders? 2- Have you tested the proposed inversion method on video LDMs? 3- How does the accuracy of the proposed method compare to gradient-based methods in applications such as image editing? 4- How were these parameters chosen? Have you done an ablation study?

Rating

6

Confidence

3

Soundness

1

Presentation

2

Contribution

2

Limitations

Limitations have been briefly mentioned, yet there is not enough quantitative analysis for cases where the accuracy of gradient-based methods are significantly higher, and whether this affects applications in both image and video domain.

Summary

The paper proposes a gradient-free method for decoder inversion in latent diffusion models (LDMs), which significantly reduces computational complexity and memory usage compared to traditional gradient-based methods. The approach is theoretically proven to converge and is efficient in experiments with various LDMs, achieving comparable accuracy. This method is useful for applications like noise-space watermarking, demonstrating its practical utility in scenarios requiring efficient decoder inversion.

Strengths

* The paper is well-written, with clear and easy-to-follow explanations. * The proposed method replaces gradient operations with forward inference, significantly saving memory and improving computational efficiency. Theoretical analysis ensures the convergence of the method. * Extensive experimental results on various latent diffusion models (LDMs) demonstrate the superior efficiency and effectiveness of the proposed approach. * The method's practical utility is highlighted through its successful application in noise-space watermarking.

Weaknesses

* The theoretical convergence of the forward step method and KM iterations is provided. However, the experiments employ the Adam optimizer. It appears that the term $E(D(z^k)) - E(x)$ in Eq. (4) is treated as the gradient in Adam. More details to clarify this could help avoid potential misunderstandings. Moreover, an additional ablation study on the impact of using Adam and cosine learning rate decay may enhance the comprehensiveness of the findings. * The paper acknowledges that gradient-based methods can achieve higher accuracy in certain applications. A more in-depth discussion on the accuracy trade-off and scenarios where this method might fall short would provide a balanced perspective.

Questions

In Figures 2 and 4, there are some failure cases depicted. Could you provide more details on the success rate of the proposed method and how it compares to the gradient-based method? Additionally, a detailed analysis of these failure cases and potential reasons for the discrepancies would be very helpful.

Rating

6

Confidence

3

Soundness

4

Presentation

3

Contribution

3

Limitations

Yes

Summary

The paper introduces a zero-order (gradient-free) inversion optimization algorithm for encoder-decoder based generative models, particularly focusing on latent diffusion models (LDM). The objective of the optimization problem is to find the latent vector $z$ for a given image $x$ such that $x=D(z)$ where D is the decoder of the LDM. The proposed inversion algorithm updates the latent vector at the next iteration by relaxing the constraints of the objective function to find the z such that $E(x)=E(D(z))$ (E is th encoder) by iteratively taking the difference between the two push forward maps until it converges to a fix-point. The authors demonstrate their proposed method is motivated technically, they show their inversion algorithm converges to a fixed point under reasonable assumptions (section 3.4). This type of analysis is further expanded to momentum (section 3.4 demonstrates reasonable assumptions). Empirically, the authors show their method significantly decreases computational cost while maintaining similar performance to gradient-base inversion algorithms.

Strengths

To my knowledge, the proposed method is novel, effective, and straightforward to implement for any encoder-decoder based architectures. The proposed method demonstrates relatively similar performance with significantly less computational time in the experiments provided. The proposed algorithm is technically motivated, and the assumptions are verified computationally. The authors provided code for reproducibility.

Weaknesses

Certain aspects of the writing need attention. For example, ρ is not defined in Equation 3. Additionally, contribution bullet point 3 ends with "and," while the rest of the contributions end with a comma, suggesting missing information. The contribution section itself reads like a run-on sentence separated by bullet points. Figure 2: The scaling of the figure is confusing. It appears that NF is the ideal architecture because it has the lowest inversion error and the least computational runtime, which seems to argue against the proposed architecture LDM. The limitations of the optimization algorithm are not clearly articulated in comparison to other inversion algorithms. The proposed method requires x (the image or signal) to be given, whereas other inversion algorithms require a set of measurements y, and a forward operator. The results lack a visual verification to confirm the effectiveness of the proposed methodology. For instance, Section 5 replicates the experiments in [48], but does not reproduce the qualitative results to demonstrate the relationship between them.

Questions

1). Could the authors please provide qualitative results similar to experiments performed in [48]? 2). Could the author please comment on the scope of the inversion algorithm and what applications it is suitable for? 3). Encoder-Decoder models are not bijective, therefore $E(D(Z)$ is an approximation of an invertible map, so there will be some information loss when approximating image x. In certain subfields, this is described as ["Representation Error"](https://proceedings.mlr.press/v70/bora17a/bora17a.pdf). Could the authors please comment on how this phenomenon affects their analysis even though their method converges to a fixed point (possibly very close to z*), there will be some information loss due encoder-decoder structure of the model. 4). Could the authors explain the scaling of Figure 2? Please refer to the comment in the weakness sections.

Rating

3

Confidence

4

Soundness

2

Presentation

1

Contribution

2

Limitations

Please refer to the "weakness" portion of the review.

Summary

This work provides a method for gradient-free decoding for latent diffusion models that can reduce the amount of required GPU memory and lessen the computation time as opposed to gradient-based methods. The method focusses on providing better invertibility in ldms that is based on a theoretical assumption that guarantees the convergence of the forward step and the inertial KM iterations for the ground truth. They further showcase the proposed method for tree-ring watermark classification problem.

Strengths

1. They propose a new method for gradient-free decoding for the ldms that has some advantage over gradient-based methods. 2. The paper contains a detailed description of the method along with the reasonings behind the assumptions made. 3. Detailed set of experiments are present along with a thorough convergence analysis. 4. Well-written in terms of method description and experiments.

Weaknesses

1. The paper is hard to follow in the methodology description and has a lot of assumptions which are difficult to verify from the paper itself. For example, in lines 152 and 165, some assumptions are being made which are not backed by proofs. 2. Are the findings enough to support the validity of the said assumptions? A question I find hard to answer based on the described experiments. 3. The advantages of the given approach seems limited and not quite powerful. Being able to reduce some memory for decoding is not a big enough contribution in itself. 4. Limited novelty -- similarity with prior works like [14] mentioned in the paper. 5. Not enough quantitative experiments to establish the utility of the said method -- Comparing for memory consumption and runtime is not enough in my opinion. 6. Not enough applications provided to prove the merits of the proposed approach -- applying the current method on diverse set of applications like image generation, editing, interpolation, etc and comparing it with gradient-based methods and evaluating the results would help.

Questions

Please refer the weaknesses section.

Rating

4

Confidence

4

Soundness

2

Presentation

3

Contribution

2

Limitations

refer the weaknesses section.