Schedule Your Edit: A Simple yet Effective Diffusion Noise Schedule for Image Editing

We appreciate your thoughtful insights, and respond to the suggestions and concerns as follows:

Response to Q1

Difference compared with sigmoid schedule [1,2] ....; can the sigmoid schedule also solve the proposed singularity problem?

Thanks for providing this valuable work [1,2].

First, we present the mathematical formulation comparison between the sigmoid schedule [1,2] and our Logistic Schedule. Second, we clarify the diversity between these two schedules, focusing on the motivations of design. Finally, we explore the singularity issues within the sigmoid schedule.

1.Comparison of Formulation:

Logistic Schedule: $\bar{\alpha}_t = \text{Normalized}(\frac{1}{1 + e^{-k(t - t_0)}}.$

Sigmoid schedule: $\bar{\alpha}_t = \dfrac{-((t*(e- s)+s) / \tau).\text{sigmoid}() + v_e}{v_e - v_s}.$ where $s$ and $e$ represent start and end of the range of the $\text{sigmoid}$ function, and $v_s = (s/\tau).\text{sigmoid}(), v_e = (e/\tau).\text{sigmoid}()$.

2.Clarification of Differences:

Motivations:

• Logistic Schedule:
  • Motivation: Focus on singularity issues in DDIM forward (inversion), enhancing inversion stability and the noise space.
• Sigmoid Schedule:
  • Motivation: Focus on adaptive computation for scalable data generation, particularly for high-dimensional data, without addressing specific challenges of DDIM forward (inversion).
  • Lack of In-depth Analysis: Provided as a trick in the original work, it does not specifically address the singularity problem in DDIM inversion or offer a detailed analysis of DDPM or DDIM like the Logistic Schedule does.

3.Singularities Issues:

Moreover, the singularity issue also exists in the sigmoid schedule.

Due to the word limit in the rebuttal stage, we only provide the final analytical format of the derivatives of the sigmoid schedule below. The detailed proof has been incorporated in the revised manuscript.

Recap the definition of $\mathbf{x}_t$: $\mathbf{x}_t = \sqrt{\bar{\alpha}_t} \mathbf{x}_0 +\sqrt{1-\bar{\alpha}_t} \epsilon.$

To express the coefficient of $\epsilon$ in the derivative of $\mathbf{x}_t$ with respect to $t$, let's start with the given expression for $x_t$: $\mathbf{x}_t =a(t) \cdot \epsilon + b(t) \cdot \mathbf{x}_0,$ where $\epsilon$ represents the noise, and $\mathbf{x}_0$ is the original image. Moreover, since $\epsilon$ and \mathbf{x}_0\ are constants with respect to $t$, the differentiation yields:

$\frac{\mathrm{d}}{\mathrm{d}t} \mathbf{x}_t = \epsilon \cdot \frac{\mathrm{d}}{\mathrm{d}t} [a(t)] + \mathbf{x}_0 \cdot \frac{\mathrm{d}}{\mathrm{d}t} [b(t)].$

Here, we provide the coefficient of $\epsilon$ in the derivative of $\mathbf{x}_t$ with respect to $t$, $\dfrac{\mathrm{d}}{\mathrm{d}t} a(t)$, as below: $\frac{\mathrm{d}}{\mathrm{d}t} a(t) \ = \frac{(e - s) e^{-s - t(e - s)}}{2 \tau \sqrt{1 - \left( \frac{\frac{1}{1 + e^{\frac{s + t(e - s)}{\tau}}} - \frac{1}{1 + e^{\frac{t(e - s)}{\tau}}}}{\frac{1}{1 + e^{\frac{s}{\tau}}} - \frac{1}{1 + e^{\frac{t(e - s)}{\tau}}}} \right)^2 \left( e^{-s - t(e - s)} + 1 \right)^2}}.$

When $t\rightarrow 0$, we can have:

Dear Reviewer vCWG,

We greatly appreciate your helpful comments and your satisfaction with our responses! We will make comprehensive revisions to our work based on the above important discussions (e.g., comparison with sigmoid schedule, comparison with inversion techniques) in the final manuscript and highlight them.

Thanks again for your valuable suggestions and comments. We really enjoy communicating with you and appreciate your efforts.

We appreciate your valuable feedback. Before addressing your inquiries, we wish to clarify certain weaknesses highlighted in the review that we believe require further elucidation.

Response to W1

Limited improvements: Although there are improvements in the quantitative comparisons, the differences compared to other schedule methods require careful observation to notice ....

Indeed, in some tasks, especially in attributes editing, the improvement is mainly in the original content preservation.

These improvements, while subtle, are crucial for high-fidelity image editing tasks where minor artifacts and distortions can significantly impact the final result. For instance, in professional image editing applications like Photoshop, maintaining the integrity of small, yet critical parts of the image are essential.

We've zoomed in on the subtle differences and incorporated extra samples with significant improvements for a more intuitive comparison. These modifications have been synchronized in our manuscript to enhance readability. Once again, thanks for your detailed review.

Response to W2

Limited application scope: except image editing tasks, the effectiveness of Logistic Schedule in other types of tasks ...

Thanks for the valuable suggestion!

We agree that broader validation on other tasks can further demonstrate the applicability of our schedule design. The principles behind the Logistic Schedule, such as addressing singularities and improving noise stability, are indeed applicable to other tasks involving diffusion models.

To further demonstrate the effectiveness of our Logistic Schedule across a wider range of tasks, we have conducted additional experiments on text-to-image synthesis and image reconstruction.

Please kindly refer to Response to Q2 in "General Response to All Reviewers" for the detailed experimental results.

Response to Q1

Are there specific editing methods that are incompatible with the Logistic Schedule?

Great question!

We have experimented with the Logistic Schedule across various training-free methods, such as PnP, Pix2Pix-Zero, Masactrl (reported in the main content), DiffEdit, P2P, SEGA, and Blended Diffusion. Additionally, we tested it with various inversion techniques like NTI, NPI, EF-DDPM, and Direct-Inversion (please refer to General Response Answer 1). All these methods showed consistent improvements when integrated with the Logistic Schedule.

We also conducted inference with training-required methods, such as text-prompt tuning methods (e.g., Textual Inversion, DreamBooth) and condition-adapter methods (e.g., ControlNet, T2I-Adapter, IP-Adapter). Without any additional training, incorporating Logistic Schedule did not consistently improve performance.

Notably, training DreamBooth with the Logistic Schedule did bring improvements (please refer to Response to Q1 in "General Response to All Reviewers"), and we are actively investigating the effectiveness of our schedule in other training-required methods to validate broader compatibility

Response to Q2

How much do the parameters of the Logistic Schedule affect the results??

The parameters of the Logistic Schedule, specifically the steepness ($k$) and midpoint ($t_0$), play a crucial role in its performance.

In addition to the qualitative results displayed in Section 5.3.1, we also provide the quantitative results below (the best method is indicated in bold, the worst method is shown in $\color{purple}\text{purple}$):

These quantitative results reflect the visual results in the main content, that is:

• $k$ Changing Shape of $\text{logSNR}$:
  • Excessive $k$: Results in excessive loss of original image information in edited images.
  • Small $k$: Resembles $\text{logSNR}$ of linear and cosine schedules, but better preserves original image content without altering overall structure.
• $t_0$ Introducing Shifts in $\text{logSNR}$:
  • $t_0$ Close to $0$: Higher lower bound of $\text{logSNR}$, affecting editability by reducing diversity and fidelity.
  • $t_0$ Close to $t_0$: Original information is lost too quickly, degrading content preservation.

Considering the trade-off between content preservation and edit fidelity, we choose $k = 0.015$ and $t_0 = \text{int}(0.6T)$ as the default choice.

Is there a specific method for parameter optimization??

We recommend a grid search approach by incorporating CLIP-I and CLIP-T metrics to identify the optimal parameter settings for specific tasks and datasets.

We will include these quantitative analyses of the parameters of the Logistic Schedule in our manuscript. Thank you again for your valuable suggestions on our paper.

Dear Reviewer ihj2,

We sincerely appreciate the time and effort you invested in your comprehensive review and your valuable suggestions, especially regarding the investigation of Logistic Schedule in other types of tasks (General Response to All Reviewers -- 2.1 Text-to-Image Synthesis) and inversion without text input (General Response to All Reviewers -- 2.2 Image Reconstruction).

We have diligently revised our paper to incorporate these new experimental results. Once again, thank you for these valuable suggestions and valuable feedback, which have helped us further improve and enhance the quality of our work. We will thoroughly revise our paper based on your suggestion.

Thank you for your positive comments and helpful suggestions.

Response to W1

Additional comparisons with other noise schedules (except linear and cosine) or inversion techniques ....

We acknowledge the value of comparing our Logistic Schedule with other noise schedules and inversion techniques. Here we provide the additional comparisons:

1. Other schedulers:

   We've included experiments comparing the Logistic Schedule with other schedules under the DDIM paradigm, such as exponential, sigmoid, and hyperbolic tangent, etc.

   The quantitative results are displayed below. The best method is indicated in bold, the worst method is shown in $\color{purple}purple$, and the second-best method is $\underline{\text{underlined}}$.

   Moreover, the qualitative comparison is provided in Fig. 3 in the attached PDF.

2. Other Inversion techniques:

   Please refer to "Response to Q1" in the "General Response to All Reviewers" for detailed comparisons with additional inversion techniques.

Response to Q1

Can the Logistic Schedule be used in or combined with training-based methods to further improve the performance?

Thanks for your insightful suggestions. This is an area we are exploring in the following research.

Based on your advice, we conducted validations on training-based methods. Please refer to Response to Q2 -- 1.Text-to-Image Synthesis (Training-based methods) in the "General Response to All Reviewers" for the detailed comparison.

These results demonstrate that incorporating the Logistic Schedule into the training phase of diffusion models could help in learning more stable and accurate noise representations.

We will continue to extend our experiments with training-based methods.

We have included the above validations that were previously omitted in our manuscript. Thank you again for your valuable suggestions on our paper.

Dear Reviewer B36W:

Thank you again for your time and insightful comments! We have comprehensively revised our work according to your comments (please kindly refer to the rebuttal in the global comment and above). We hope we have addressed your concerns regarding the comparison with other schedule designs and compatibility with training-based methods.

Since the discussion is about to close, we would be grateful if you would kindly let us know of any other concerns and if we could further assist in clarifying any other issues.

Thanks a lot again, and with sincerest best wishes.

Authors

We appreciate your positive feedback and attention.

Response to Q1

Will the extended datasets be open-sourced?

Yes, certainly. We will open source the extended datasets and our experimental code, including the validations, to facilitate further analysis and research.