EasyInv: Toward Fast and Better DDIM Inversion

Thank you for reviewing our paper. The novelty of our work is well recognized by the other two reviewers. However, we received the lowest score from Reviewer md9u. We appreciate your feedback and hope our explanations below address your concerns, leading to a score reconsideration.

1. Over-Simplification of the Kalman Gain and Questionable Noise Equivalence Assumption

Section 3.3 provides essential background on the Kalman filter, with Equations (12)--(14) summarizing standard formulations consistent with Section 7 of [a]. Notably, the cited reference explicitly states that for specific applications, the Kalman gain $K$ in Equation (14) can be simplified to a blending factor within $[0,1]$, a strategy directly adopted in our methodology. Furthermore, Equation (6) of KLDD [b] demonstrates that the Kalman gain can evolve into a time-varying constant at each timestep, aligning with our approach.

[a] Kalman and bayesian filters in python.

[b] Kldd: Kalman filter based linear deformable diffusion model in retinal image segmentation.

2. Misleading Analogy with PF-ODE Inversion

Regarding $\varepsilon^\ast$, while theoretically derived through score-matching optimization, it is important to clarify that this term is not simply a scaled score. Instead, as shown in Equation (15), it is scaled by $\bar{\beta}_t$. In practice, during SDv1.5 training, the model learns to predict the Gaussian noise added to original images [c]. Given its strong noise prediction capabilities, assuming $\varepsilon^\ast$ follows Gaussian characteristics is reasonable.

[c] High-resolution image synthesis with latent diffusion models.

3.Distribution between $z_t$ and $p_t$

Our formulation preserves the latent variable $z$'s distributional consistency. Equations (18)--(19) show that at the final inversion step ($\bar{t}=T$), $z_T$ emerges as a convex combination of $\eta z_T$ and $(1-\eta)z_{T-1}$. Since ${z_T}$ and ${z}_{T-1}$ are close to the sum of a series of $\varepsilon_i^\ast$ (Gaussian-distributed), their linear combination retains Gaussian properties. To validate this, we computed the KL divergence between inversed latent representations and random input noise in SDv1.5, yielding an average KL divergence of 210.69049 on 298 samples. For comparison, the average KL divergence across 298 randomly generated noise pairs was 247.50026. These results suggest our method effectively preserves latent space distribution.

4. Studies on Parameter $\eta$

To clarify our experimental choices, we conduct additional ablation studies on parameter $\eta$ using the same dataset as Table 3. Since $\eta = 1$ corresponds to standard DDIM inversion and $\eta = 0$ bypasses inversion, these cases were excluded. Our results show that $\eta = 0.5$ achieves the best performance.

5. Extra literature reviews

We appreciate the suggestion to broaden our literature review. The three cited methods—EDICT, BDIA, and O-BELM—are classified as exact inversion techniques.

• EDICT extends affine coupling mechanisms with alternating dual-state refinement through reciprocal updates between primary and auxiliary diffusion variables.

• BDIA enhances this approach with symmetric bidirectional state integration, ensuring provable invertibility but introducing trade-off parameters that may affect robustness across frameworks.

• O-BELM synthesizes concepts from both methods, employing a bidirectional explicit architecture while replacing heuristic hyperparameters with analytically derived coefficients optimized via local truncation error minimization, improving numerical stability.

While these methods highlight system reversibility, their empirical updates introduce trade-offs. We focus on fixed-point iteration but acknowledge that incorporating these methods could enhance our analysis. We will include them in the final version.

Dear Reviewer UW4y,

We would like to express our sincere gratitude to you. It is truly an honor and a stroke of luck to have a reviewer as dedicated and responsible as you. Your constructive suggestions have been invaluable to us. We are particularly touched by your understanding regarding our reimplementation of the Fixed-Point Iteration, given the lack of alternatives. Your insight that addressing Table 1 and Figure 3 could potentially raise our score is greatly appreciated. We are also impressed by your careful review, which effectively summarized our claims and supporting evidence.

We give our point-by-point response below.

1. Discrepancy Between Table 1 and Figure 3

The apparent discrepancy between Table 1 and Figure 3 arises from the different demonstration objectives of these experiments. While Table 1 quantifies ReNoise’s overall performance—showing that it performs reasonably well (albeit slightly inferior to our method), Figure 3 is designed to illustrate a critical limitation: ReNoise’s instability when processing real images with extensive white regions. In such scenarios, ReNoise tends to produce undesirable black artifacts. This visual evidence underscores the robustness and superior stability of our approach under challenging conditions.

We would like to emphasize that the above explanation will be explicitly incorporated into our final paper. We sincerely hope that our detailed explanation can effectively address your concerns and look forward to an increase in our score.

2. Evaluating the Latent Quality Versus the Image Domain

Our main contribution lies in performing fixed-point iteration in the latent space to improve computational efficiency during the denoising process. Since the ultimate objective is to achieve high-quality image generation via the final decoded images, we opted to emphasize the image-domain evaluation. While efforts have been made, we found it hard (or even irrational) to compare with ``ground-truth latent'' in the latent space for: 1. Lack of Suitable Metrics: We have been unable to identify a robust quantitative metric that can effectively measure the quality of latent representations.; 2. Irrelevance to Final Objective: Comparisons in the latent space do not directly reflect the ultimate goal of generating high-quality images. The latent space is merely an intermediate representation, and its fidelity does not necessarily correlate with the quality of the final decoded images.; 3. Efficiency Focus: Our primary motivation for operating in the latent space is to improve computational efficiency. The latent space serves as a means to an end, rather than an end in itself.

We hope you understand the limitations we face in providing direct comparisons in the latent space and appreciate our focus on achieving the best possible outcomes in the image domain.

3. Additional Ablation Studies on Parameter $\eta$

To further clarify our experimental choices, we present additional ablation studies on the parameter $\eta$, conducted on the same dataset as in Table 3 of our paper. Note that $\eta = 1$ would correspond to a standard DDIM inversion method and $\eta = 0$ would effectively bypass the inversion operation. Therefore, these boundary cases were excluded from the ablation experiments. Our findings indicate that $\eta = 0.5$ yields the best overall performance:

4. Clarification on Notation in Lines 201–207

We appreciate the reviewer’s suggestion regarding the notation used in lines 201–207. We agree that the current format is potentially confusing since these are not formal equations. In the revised version, we will switch to a clear itemized list (e.g., using (i) and (ii)) to improve clarity.

We appreciate the reviewer’s constructive feedback and suggestions for additional experimental validation. Due to space constraints, some of these analyses were deferred to future work; however, several of the suggested experiments have either been completed or are actively underway. We address the key points as follows:

1. Quantitative Analysis of Over-Smoothing

While our paper qualitatively discusses the over-denoising issue (e.g., the “peach” example in Fig. 3), we acknowledge that a more comprehensive quantitative analysis (e.g., using FID or user studies) would better elucidate its practical impact. We have initiated such studies and plan to incorporate these quantitative metrics in an extended version of our work.

2. Generalization Across Models

Our experiments currently focus on Stable Diffusion V1.5. We agree that evaluating our method on larger models (such as SD-XL) and alternative architectures (e.g., DALL-E 3) would strengthen the claims regarding generalizability. The qualitative experiments on SD-XL have been done, but not able to display here due to the restriction of OpenReview's rebuttal rule. We are actively extending rest experiments to include these models and will report the results in the final version.

3. Parameter Sensitivity Analysis

We conducted an ablation study on the parameter $\eta$, summarized in the table below, which guided our selection of $\eta = 0.5$ as it achieved the overall best performance. Note that $\eta = 1$ corresponds to a standard DDIM inversion method and $\eta = 0$ would essentially bypass the operation, so those cases were not included.

Regarding the empirical parameter $\tilde{t}$, our experiments with diffusion models having reduced parameter counts suggest that optimal performance is achieved when EasyInv is applied during the early denoising steps. We agree that further sensitivity analyses across different tasks and datasets would provide additional insights and are planned for our future revisions.

4. Validation Across Diverse Noise Levels

We recognize that our current experiments were conducted using a fixed noise configuration (T=50 steps). To further demonstrate the robustness of EasyInv, we plan to evaluate its performance under varying noise conditions (e.g., T=30 and T=100) and across different generation scenarios (e.g., low-step fast generation vs. high-step high-precision generation). These experiments will help clarify whether EasyInv maintains its efficiency and reconstruction quality when the inversion steps vary significantly.

5. Comparison with Established and Emerging Methods

We appreciate the suggestion to include direct comparisons with both classical inversion techniques (e.g., EDICT) and emerging approaches (e.g., Inversion-Free Image Editing). We excluded EDICT from our current comparisons because its original work lacked comprehensive evaluations against existing methods, which we felt diminished the persuasiveness of its results. Moreover, emerging techniques like inversion-free image editing rely on framework-specific implementations (e.g., rectified flow in SDv3/FLUX) that are currently incompatible with our framework. We plan to develop cross-framework adaptation layers and implement these reference methods in future work to provide a more comprehensive benchmarking of reconstruction fidelity, computational efficiency, and robustness.

Summary

We value the reviewer’s insights and are committed to enhancing the methodological rigor of our work through these additional experiments and comparative analyses. Many of these extensions are already underway, and we will incorporate the resulting findings in our revised and future publications.