Schedule Your Edit: A Simple yet Effective Diffusion Noise Schedule for Image Editing
Authors: Haonan Lin
Yan Chen
Jiahao Wang
Wenbin An
Mengmeng Wang
Feng Tian
Yong Liu
Guang Dai
Jingdong Wang
QianYing Wang
Venue: NeurIPS 2024 poster (2024)
Keywords: image editing
diffusion model
Primary area: diffusion_based_models
TL;DR: The Logistic Schedule is designed for diffusion-based image editing, to eliminate singularities, improve inversion stability, and mitigate exposure bias, thereby enhancing content preservation and edit fidelity.

Abstract: Text-guided diffusion models have significantly advanced image editing, enabling high-quality and diverse modifications driven by text prompts. However, effective editing requires inverting the source image into a latent space, a process often hindered by prediction errors inherent in DDIM inversion. 
These errors accumulate during the diffusion process, resulting in inferior content preservation and edit fidelity, especially with conditional inputs. 
We address these challenges by investigating the primary contributors to error accumulation in DDIM inversion and identify the singularity problem in traditional noise schedules as a key issue. 
To resolve this, we introduce the *Logistic Schedule*, a novel noise schedule designed to eliminate singularities, improve inversion stability, and provide a better noise space for image editing. This schedule reduces noise prediction errors, enabling more faithful editing that preserves the original content of the source image. Our approach requires no additional retraining and is compatible with various existing editing methods. 
Experiments across eight editing tasks demonstrate the Logistic Schedule's superior performance in content preservation and edit fidelity compared to traditional noise schedules, highlighting its adaptability and effectiveness. 
The project page is available at https://lonelvino.github.io/SYE/.

Schedule Your Edit: A Simple yet Effective Diffusion
Noise Schedule for Image Editing
Haonan Lin'
Yan Chen'
Jiahao Wang'
Wenbin An
Mengmeng Wang25
Feng Tian'
Yong Liu4.
Guang Dai
Jingdong Wang
Qianying Wang'
School of Comp. Science & Technology, MOEKLINNS Lab, Xi'an Jiaotong University
2 College of Comp. Science & Technology, Zhejiang University of Technology
School of Auto. Science Engineering, MOEKLINNS Lab, Xi' an Jiaotong University
Institute of Cyber-Systems and Control, Zhejiang University
SGIT AI Lab, State Grid Corporation of China Baidu Inc
Lenovo Research
Abstract
Text-guided diffiusion models have significantly advanced image editing, enabling high-quality and diverse modifications driven by text prompts. However, effective editing requires inverting the source image into a latent space, a process often hindered by prediction errors inherent in DDIM inversion. These errors accumulate during the diffusion process, resulting in inferior content preservation and edit fidelity, especially with conditional inputs. We address these challenges by inves- tigating the primary contributors to error accumulation in DDIM inversion and identify the singularity problem in traditional noise schedules as key issue. To resolve this, we introduce the Logistic Schedule, a novel noise schedule designed eliminate singularities, improve inversion stability, and provide a better noise space for image editing. This schedule reduces noise prediction errors, enabling more faithful editing that preserves the original content of the source image. Our approach requires no additional retraining and is compatible with various existing editing methods. Experiments across eight editing tasks demonstrate the Logistic Schedule's superior performance in content preservation and edit fidelity com- pared to traditional noise schedules, highlighting adaptability and effectiveness. (Project page: https://lonelviiee .wwoooggittbbb. withub.io/SVE... io/SYE/
Introduction
Text-guided diffusion models have emerged as a leading technique in image generation, offering The noise latent space of these models can be leveraged to retain and modify images 32 66 68 enabling text- text-guided editing where source image is adjusted based on a target prompt. This requires first inverting the source image into a latent variable (e.g., via DDIM inversion), due to the absence of its predefined latent space 28
remarkable visual quality and diversity (2
50
39
While DDIM inversion proves effective for unconditional diffusion models 43
55
it results
in inferior content preservation and suboptimal edit fidelity when applied to conditional inputs [12 [7]. This phenomenon particularly evident in image editing, which requires incorporating
new conditionals into the generation process [6 59 33 611. DDIM converts the DDPM into
*Corrsspndiigg Author.
This work was completed during the internship at SGIT Lab, State Grid Corporation of China.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

---

(a) Attributes Content
(b) Object Addition
(c) Object Switch
with cleur up ara wntoow ovr mosth open
paasting of nasing
moneheria of Macbervizs shanlerric
Aky-hiic portics exter in maile of oiil
ssnal ce oihi Somastee and anlloingti nap (f) Non-Rigid (Pose) Editing
(d) Style Transferring
(e) Scene Tronsferring
vattreslar puteteg of aaa nilug saaviaard namg
e heaes ctar is feoe
a fager sonding stil seld der vild
ap of colvvir pointing o of
emm a fevepar pordse got lnsilng Soerr on feaco
ripasley mas wilh duumhh la aussinng skiwdestd
Image
Noise Schadule
Scaled
(Ours) Logistic Noise Schecule
Real Image
Neise Schedule
Scaled Linear
(Ours) Logistic
Scheouue
Real Image
Scoled Linear Noise Schecule
(Ours) Logistic Noise Schedule
Figure 1: Compared to linear noise schedule, Logistic Schedule 1 demonstrates high fidelity in attributes content editing (a, b) with EF-DDPM (21. preserves the high-level semantics of the source image while performing object translation (c) with pix2pix-zero [45) and style/scene transferring (d, e) with StyleDiffusion [63], and successfully conducts non-rigid alteration (f) via MasaCtrl [6]. Text prompts corresponding to each input image are presented beneath each sample,
with words introduced for image editing distinctly highlighted red.
deterministic process by approximating the Markov process non-Markov process based on a local linearization assumption [55]. This approximation introduces noise prediction errors that accumulate throughout the diffusion process, leading deviations in the inverted latent representation from its original distribution, as illustrated in Fig. left. Recently, inversion-bart emerged as a promising paradigm to address these issues by aligning the reconstruction path more closely with the DDIM inversion trajectory, thereby ensuring the preservation of the original content the edited images 41 15
editing methods have
25). However, these methods still heavily rely on the accuracy of the DDIM inversion. This leads to fundamental question: What if correct the DDIM inversion errors to naturally reduce the loss original content in the edited images?
Unlike previous picession-baee editing methods that focus on minimizing the distance between x and x (Fig. left), we investigate the primary reason for error accumulation in DDIM inversion.
Based on the fact that DDIM samplers can be derived by deterministic ODE processes 3 38 71]. our
analysis reveals that these traditional noise schedule designs result in a singularity problem (Fig. 2 right) when treating the DDIM inversion process solving a differentiable ODE. This results in unreliable noise predictions from the start, and as errors accumulate, the editing results degrade (Fig.[]. This insight motivates us to address the problem at its source: the noise schedule itself. To our knowledge, this is the first work focusing on designing noise schedules specifically for image editing,
providing an optimized solution without requiring complete model retraining [14] 20 23
29
26 34)
We present simple yet effective noise schedule. Logistic Schedule, designed to resolve the singularity problem of previous noise schedules and enhance inverted latents for image editing. The key ideas behind Logistic Schedule are twofold: (1) creating a well-defined noise schedule improve inversion stability, and (2) providing a better noise space that enables editing faithful to the source image. Specifically, Logistic Schedule eliminates singularities at the beginning of the inversion process, thereby reducing noise prediction errors in the inverted latents. It etaallss more stable data perturbation to preserve the original content of the source image in the edited image. Importantly, this design effective and compatible with other editing methods without requiring additional retraining.

---

coefficients of and X2 in dx,/ /dl
XT
XO
0U04
Linear Schedule
0.000
Tdeal Latent (non-exist)
0UR2
Source Image
-0.001
Reconstructed Image
0.000
Inverted Latent
200
500
2000
0.002
x
singularity
Tixee
(1)
0.000
Cosine Schedule
0,0000
Reverse Latent (wl source cond.)
0LI44
0.0005
0.002
Reverse Latent target cond.)
01000
Edited Image
singularity
Figure 2: Illustration of the DDIM inversion in image editing and its challenges. Left: starting from the source image Xo, the ideal latent x, approximated by the inverted latent x; using DDIM inversion. The perturbed noisy latent x; is then sampled in two branches-one for the source condition and one for the target condition- -niiiiion-yielding the reconstructed and edited images respectively, Right: the numerical computations of dx, for scaled linear and cosine noise schedules, highlighting the singularity at = that leads to potential inaccuracies in noise prediction during inversion.
We conducted experiments across eight distinct editing tasks using approximately 1600 images from F
diverse seenes. Fig. [illustrates that our Logistic Schedule effectively enhances editing results in terms of essential content preservation and edit fidelity compared commonly used noise schedules like the linear schedule. Moreover, our schedule can be seamlessly integrated with various existing diffusion- based editing techniques. demonstrating its versatility and effectiveness. Our main contributions are summarized as follows: (1) Theoretical Analysis: We analyze the failure of DDIM inversion in real- image editing step by step, identifying the singularity the noise schedule the key issue address. (2) Methodology: We introduce Logistic Schedule, novel diffusion noise schedule specifically tailored for real-image editing, which effectively reduces prediction errors during inversion. (3) Superiority: We showcase Logistic Schedule's 's adaptability by integrating it with various editing methods and demonstrate consistent superior performance across different editing tasks.
Background
This section will introduce diffusion models and their noise schedules, along with DDIM inversion, which are crucial for text-guided editing real images.
Diffusion Models. Denoising Diffusion Probabilistic Models (DDPM) 18 are designed to transform random noise vector Xy into series of intermediate samples x,, and eventually final image xy by progressively adding Gaussian noise E (00,)) I) according to a noise schedule By.
X -1 - V.EE-1
where [1.7] and T denotes the number of timesteps. The noise schedule determines the distribution of noise scales and is designed to ensure that the noise scale at each step is proportional to the remaining signal, which is usually fixed without additional learning. According to the properties of conditional Gaussian distributions, X, can be derived from real image Xo in the following closed form by reparameterizing a; B., a |1 0;:
X, Va
â,e.
(1)
Another commonly used sampling method is Denoising Diffusion Implicit Models (DDIM) (55) which formulate a denoising process to generate x, from sample x, via:
X, vI 0,50 (x,)
a:-1 of (1) (x,)
X, - Von-1
OTEE
Vai
direction pointing to
random noise
predicted No
3

---

where 6, (N,, D), 07 is the variance schedule, and Eg is a network trained to predict the noise added. When of T-
1-0r-1
ot_ for all I, the forward process becomes Markovian, and the generation 01-1
process becomes a DDPM. And in special case when s, = O for all 1, the forward process become deterministic given x and Xo, except for 1, and the generate process becomes a DDIM.
Inversion Image Editing. Although text-to-image diffusion models [50 52 19 have advanced feature spaces that support various downstream tasks 667 37 (3), applying them to real images muon-generated images) is challenging because these images lack a natural diffusion feature space. Editing real image first requires obtaining the latent variables Xy from the original image Xo and then performing the generation process under new conditions. To bridge this gap, DDIM inversion [55] is predominantly used due to its deterministic process, which can be represented by reversing the generation process in Eq. 2
with o, =
Va
1 co (x;-1-111).
Vai-1
a1
0:-1
However, existing editing methods that rely on vanilla DDIM inversion struggle to achieve both content preservation and edit fidelity when applied to real images M 4400 16]. Recently, inversion- based editing methods have improved the edited results by maintaining two simultaneous procedures: reconstruction and editing, as shown in Fig. left. These methods align the reconstruction path (x) more closely with the DDIM inversion trajectory (x"), ensuring better preservation of the original Despite their effectiveness, these methods still
content in the edited image [4 heavily rely on the accuracy of the inverted latents obtained from DDIM inversion. In contrast, we start from different perspective, focusing on improving the DDIM inversion accuracy to naturally enhance the edited results. In the following section, we begin with the transition from DDPM to DDIM, emphasizing the need for better noise schedule for the inversion process.
15
44
25
TO
3
On the Failure of DDIM Inversion
3.1 Warmup: Error Accumulation of DDIM
DDIM inversion for real images is unstable due to its reliance on local linearization assumption at each step, leading to error accumulation and content loss from the original image. Specifically, DDIM assumes that the denoising process in Eq. 2 is roughly invertible, meaning x; can be approximately recovered from X via:
X b,e(x;, 1)
X b,E(x;,,..)
x
a,
a,
where a, = va,,1//,, and b, -va, -1 aa,)/a, + VT 01-1 This approximation assumes r)x,,) x c(x",,-') and the inversion's 's accuracy depends on this assumption. However, ensuring accurate inversion under this assumption requires a sufficient number of discretization steps, which increases time costs and is impractical for many applications. With fewer timesteps higher noise levels, error accumulation becomes more pronounced, resulting in distorted reconstructions, as shown in Fig. leett. This occurs because once we deviate from the linearization assumption, the interpolation operation in Eq. 3 fails. The primary issue arises when estimating the "predicted xo in Eq. 2 at the initial step (t indicated by the red arrow in Fig. left), where simple expression for the posterior mean conditioned on X, no longer exists (55). Moreover, this problem is exacerbated in image editing, where the denoising process must incorporate new conditions into the image content. This increases the difficulty of noise predictions, leading to more severe artifacts and distortions.
3.2
The Devil Is in the Singularities
To get around this issue, our first insight is to reduce the prediction error at the beginning of the forward (inversion) process. But before we can figure out how to fix the error, we need to pinpoint the problem. We first provide the continuous generalization of DDPM, since sampling from diffusion models can be viewed alternatively as solving the corresponding ODE process [57 38]:
dx = f(x. 1) (1) - log pr (x) dr,
(4)

---

Comparison of Noise Schedules
Derivatives of Logistic Schedule
1.0
0.0015
-0.0005
0,0010
ccaled linear
0.5
cosine logistic
-0,0010
0.0005
0.0000
-0.0015
0
250
500
750
1000
0
500
1000
Time step (t)
Time step (t)
Figure 3: Left: trends of vT 0; (noise scales) for scaled linear, cosine, and logistic noise schedules. Right: dxr/dr for the logistic schedule, highlighting its smooth transition, which prevents singularities and maintains the integrity of the initial latent vector Xo.
where f(.,7) is a vector-valued function called the drift coefficient of x(r), and g(-) is scalar function known the diffusion coefficient of x(r). And the ODE form of DDIM is equivalent to special case of Eq. 4 as long as a, and A, are close enough (refer to details in Appendix A)).
By treating the DDIM inversion process as solving a differentiable ODE, we emphasize that precise and stable computation of dx, / at each timestep is crucial for accurate noise prediction, especially at the start of the inversion process. Fig. right highlights the pitfalls of widely-used scaled linear [8] and cosine 43 noise schedules through numerical computations of dx./dt.
Proposition 3.1 (Singularity in Inversion Process). During the inversion process, there exists singularity at i 0 for both the scaled linear and cosine schedule (Fig. right):
dxy
When =
sign(E) = sign(E))
di
1-0
This singularity significantly affects the starting point of the inversion process during image editing tasks. Properly modeling dx, /d ensures that the inversion closely aligns with the true continuous dynamics of the diffusion process, thereby reducing errors and enhancing the fidelity of the inverted latents, which is critical for high-qualin image editing. The proof can be found in Appendix
We argue that singularities in modeling dx, dd cause significant issues in inversion- text-guided image editing. Specifically, (1) the instability in the inversion process arises from the singularity of the derivatives at r = O, leading to inaccurate noise component estimates, making the starting point inconsistent with the data's 's true characteristies. The fast sampling in DDIM exacerbates error accumulation, where minor initial errors lead to substantial deviations in the final inverted latents. As result, reconstructed or edited images may display visual inconsistencies, distorted details, or unnatural artifacts, reducing the overall quality and fidelity. Furthermore, the singularity can also lead to (2) poor handling of complex data distributions in the real world. Discontinuities in derivatives result in the model receiving inconsistent and unreliable signals during the diffusion probabilistic modeling. This hinders the model's ability to capture intricate patterns and details, disrupting the consistency and integrity within an image 30
4 Better Noise Schedule Helps Inversion and Editing
4.1
Well-Defined Schedule Improve Inversion Stability
To address the issues highlighted in Proposition 3.1
we propose a new noise schedule in terms of ā
since å, represents the remaining signals in the latents during the diffusion process (Eq. [T]. Following the recommendations from iDDPM [43, the noise schedule should ensure that noise is added more slowly at the beginning to preserve image information in the middle of the diffusion process. We introduce our logistic noise schedule as follows:
(5)
I e k(t
where & and are hyperparameters that control the steepness and midpoint of the logistic function, respectively, In our experiments, we set & = 0.015 and int(0.67), discussed in Section 5.3.
5

---

10
Logistic Cosine Linear
logSNR
soded lineur
cosibe
logistic
250
500
750
1000
Time stop
Figure 4: Analysis of noise space for different schedules. Left: logSNR trends, where the logistic schedule maintains a more gradual decline. Right: inversion processes, with the logistic schedule preserving more details in the initial stage and minimizing low-frequency retention in the final stage.
Our logistic schedule is designed to have linear drop-off of at, in the middle of the diffusion process, with minimal changes near the extremes of = and = T, thus preventing abrupt changes in the noise level. Fig. left demonstrates the progression of vI for different schedules, in which linear and cosine schedules tend to add noise too quickly during the early stage of the inversion process. Crucially, our logistic noise schedule avoid the singularity of dx,/ r O. For simplicity expression, we set k 0.015 and to 30, resulting in the following:
When = 0, dx; dr 1-
1.486e -3 1.318e X0
The proof is provided in Appendix and the trend the derivatives of our logistic schedule is illustrated in Fig. Fig. right. By ensuring smooth and continuous transition in noise levels, the logistic schedule maintains the integrity of the initial latent vector Xo. This alignment with the diffusion process's continuous dynamics prevents undesired deviations, reduces errors, and leads more accurate and stable latent predictions, improving the inversion process's fidelity.
4.2 Exploring Noise Space of Logistic Schedule
We explore the properties of logistic noise schedule and its influence the noise space, specifically comparing the logSNR trends and inversion processes of different noise schedules.
Steady Information Perturbation. As depicted in Fig. (left), the linear and cosine schedules tend to drastically degrade image information at the initial stage of inversion, as evidenced by the rapid drop in logSNR. In contrast, our logistic schedule exhibits more linear decrease in logSNR before the final stage, ensuring steady data perturbation. This steadiness allows the logistic schedule to capture richer set of features and nuances from the original image, facilitating more detailed reproduction and higher fidelity in the edited images.
Comprchensive Pattern Capture. As shown in Fig. (right), we visualize the latents during the inversion (forward) process, using timesteps with the final step 981 instead of 999. In early stage, our Logistic Schedule preserves more original image information, reflecting the logSNR trend. Considering the later stage, linear and cosine schedules retain more low-frequency components due to higher endpoint SNRs, explaining why their noise maps don't 't fully cover the image. In contrast, Logistic Schedule ensures that the inverted latent closely resembles pure Gaussian noise, minimizing the retention of low-frequence components. This thorough process ensures that the inversion encodes a broader array of the original image's 's information, thereby enhancing the quality and fidelity of the edited images.
Experiments
In the section below, we evaluate our method both quantitatively and qualitatively on text-guided editing of real images. To validate the versatility and effectiveness of our proposed Logistic Schedule, we compare it with linear and concise schedules by employing different editing approaches across various editing tasks. Refer to Appendix B for detailed experimental results.

---

Attributes Editing Friendly
Object Switch
PixaPix-Zere
blond blond with headscary
fox walking
Carfled wulking
womon with block hoir = woman with black hatrr eyes clourd
a for stonding in the praze + a dog is monding in the grass
man with arange jacket man with black jacket
spiderman on tap sulricy -> a robat spuderman on top of salmway
Style/Scene Transferring with StyleDiffusion
Non-rigid (Pose) Editing
Masactri
elephonts walk acress field =p elephants walk across gontly rolling hills
sand sitting sond, raieing hend
aoox looking
Riger siming
nigoris standing
wimmnn blue drexy pizel art of a womun in blue dresv
on elephant is slanding in 200 an elephon running in 200
Linear
Cosine Schedule
Logistic Schedule
Linear Schedule
Cosine Schedule
Logistic Schedule
Real Image
Real Image
Schedule
Figure 5: Qualitative comparison of the Logistic Schedule with linear and cosine schedules across various image editing tasks. To preserve background content during ① attribute editing tasks (e.g., colors, and materials), we employ Edit Friendly DDPM [21; for tasks requiring background preservation such @ object translation, use Zero-shot Pix2Pix [45); for tasks involving 3 scene or style transfer, while maintaining object semantics, we utilize StyleDiffusion [63]; to validate spatial context preservation in & non-rigid editing tasks (e.g., motion, pose), consider MasaCtrl [6].
5.1 Experimental Settings
Implementation Details. We perform the inference of different editing and inversion methods under consistent conditions. We use Stable Diffusion v1.5 as the base model, with 100 timesteps, an inversion guidance scale of 3.5, and reverse guidance scale of 7.5. All experiments are conducted on a single Nvidia A 100 GPU. Quantitative results are averaged over 10 random runs. Additional implementation details are provided in Appendix D.2.
Datasets. Experiments are conducted on the PIEBench dataset 25
Recognizing the dataset's limited size and scenarios, extend it by incorporating face images from FFHQ [27] and AFHQ []] as well as indoor/outdoor common objects from MS-COCO [35]. This results in approximately 1600 images in total, across eight editing types (see Appendix(D.1.
Evaluation Metrics. As the editing process involves altering both the foreground and background of the images, follow Ju et al. in adopting three types of metrics: structure (DINO-I 7 58 51).

---

background preservation (PSNR, LPIPS 24 72,, MSE, SSIM (64). and image-image, text-image consistency (CLIP score 48 Detailed descriptions of each metric can be found in Appendix D.3
Table 1: Comparative table of diffusion noise schedules and their performance metrics. Bold values indicate the best results, while underlined values denote the second- results.
Schedule Structure
Background Preservation
CLIP Similarity (%)
Dist x10-3 1 PSNR LPIPS x10-3 MSE x10-4 SSIM x10-2 T Visual [
Textual [
Attributes Editing (with Edit Friendly DDPM)
Linear Cosine Logistic
35,66
20.70
134,88
113.61
77.60
79.82
23.06
26.57
22.38
110.52
80.01
80.15
81.35
22.39
17.37 34.6%
24.78
10.7%
81.80 26.0%
49.47
38.2%)
82.97 3.5%]
82.44
0.8%1
23.62 2.4%
Object Switch (with Zero-Shot Pix2Pix)
Linear Cosine Logistic
39.02
19.93
134.64
138.99
74.63
83.33
22.30
30.83
21.15
113.03
107.46
77.23
84.32
22,46
22.4 27%b
22.91
8%1
90.75 20%
82.05 24%)
79.32 3%T
84.52
0.1%
22.65 0.8%
Style/Scene Transferring (with StyleDiffusion)
Linear Cosine Logistic
38.06
21.17
93.70
111.01
81.85
77.65
25.39
28.44
22.70
75.75
78.93
83.74
79.23
23.92
18.64 34.4%.
24.81
9.3%
56.79
25.0%
48.96
38 38.0%]
85.84 2.5%M
80.81
1.2%
24.77 2.4%
Non-ridig Editing (with Masactri)
Linear Cosine
30.83
21.15
113.03
107.46
77.23
83.13
22.65
22.40
22.91
90.75
82.05
79.32
83.33
21.81
Logistic
15.87 29.2%)
24.66
7.7%?
75.18
17.2%
59.22 27.8%
81.11 2.3%V
84.32
0.1%
22.30 1.5%)
5.2 Qualitative and Quantitative Comparison
Qualitative Comparison. As shown in Fig. [] our Logistic Schedule demonstrates superior content preservation in each task. In tasks requiring fine-grained editing, such as attributes editing, the Logistic Schedule better preserves other attributes while making the desired changes. For tasks involving high- level semantics, such as object translation and style/scene transfer, the Logistic Schedule maintains the overall structure and pose more effectively. In tasks that involve low-level semantics like color and texture, such as pose and attributes editing, the Logistic Schedule shows better fidelity and consistency. For tasks that require background preservation, such as object translation and pose editing, the Logistic Schedule excels in maintaining the background integrity. Overall, the Logistic Schedule ensures higher edit fidelity across various tasks, whereas the linear and cosine schedules sometimes fail to maintain the desired quality and consistency.
Quantitative Comparison. Table shows that when employing the Logistic Schedule, all editing tasks exhibit improved retention of background and overall structure. While in some situations, the Logistic Schedule achieves slightly lower text alignment than the linear schedule, its preservation of background and structure is significantly superior.
5.3
Ablation Studies
In this section, we investigate the effects of different configurations of the Logistic Schedule and the adaptability of the Logistic Schedule with various inversion techniques and diffusion models. More experiments on hyperparameters (e.g., guidance scale, input scale) can be found in Appendix E The comparison with more design of the noise scheduler provided in Appendix E.4
5.3.1 Effects of Configuration of Logistic Schedule
We conduct experiments with different configurations of the Logistic Schedule in Eq. providing
further evidence for the noise space analysis (Section 4.2) The parameters of the Logistic Schedule (Eq. 5) specifically the steepness (k) and the midpoint (To) play a crucial role in balancing content preservation and edit fidelity. Table 2 provides the quantitative results of varying k and

---

100
(Ac fg)
001
00.006, 25)
00.008, 25)
00.011, 25)
0.1
(0.014, 25)
bike parked stop sign
motorbike is parked stop
(0.017, 25)
--0006
k--0011
2--10144
-0.07
(0,022 25)
logstir
(0,022, 25)
(0.025 25)
(0.022, 25)
man hold racket on oil painting hold racket tennis court
Figure 6: Impact of k on the logistic schedule. Left: change in ã, and logSNR with different values. Right: the effect of edited images.
1.0
(k, to)
t0 = 10 to = 25 to = 40
(0.014, 5)
Source Image
8 0.5
(0.014, 10)
(0.014, 15)
0.0
(0.014, 20)
(0.014, 25)
10
(0.014, 30)
logSNN
(0.014, 35)
gazebo
(0.014, 40)
+
10
(0.014, 45)
stone tower
20
Figure 7: Impact of to on the logistic schedule. Left: change in ã, and logSNR with different fo values. Right: each column represents edited results within three random seeds, under specific to-
Table Quantitative results of the Logistic Schedule across various hyperparameter settings. The best method is indicated in bold, and the worst method is shown in purple.
Structure Dist x10-3
Background Preservation
CLIP Similarity (%) Textual
Settings
PSNR
LPIPS x10-3 1 MSE x10 J SSIM x10-
Visual
k 0.015
17.37
24.78
81.80
49.47
82.97
82.44
23.62
to = int(0.)7)
k 0.008
16.27
26.45
75.62
43,20
85.28
84.07
20.47
& 0.011
16.64
25,80
77.90
48.83
84.15
83.76
21.46
& 0.017
22.79
22.33
99.98
57.32
81.52
82.10
23.25
& 0.029
27.82
21.05
103.45
64.36
78.48
80.66
23.81
to = int(0.477)
24.31
22.41
97.21
60.84
79.72
79.47
20.33
to = int(0.87)
29.47
21.64
95.58
63.89
75.14
77.05
22.68
Different k; Changing the steepness of logSNR. When & is larger, the logSNR values span larger range 6 left). However, the range is large, excessive steepness of logSNR results in excessive loss of original image information in edited images (Fig right). Interestingly, when small, the logSNR resembles that of linear and cosine schedules. but the logistic schedule better preserves the original image content without altering the overall structure. This further supports Proposition 3.J that the singularity in linear and cosine schedules tends destroy original image information, causing undesired changes.
Different Introducing shifts in logSNR. When to is close to 0, the lower bound of logSNR is higher, affecting editability by reducing diversity and fidelity, as shown in Fig. 7 Conversely, when close to T, the original information lost too quickly, degrading content preservation.
Balancing these parameters, we find that 0.015 and to int(0.67") strike the optimal trade-off between content preservation and edit fidelity, providing robust performance across various tasks.

---

5.3.2 Adapting Inversion Techniques and Diffusion Models
To validate the adaptability and robustness of the Logistic Schedule, we first apply it with Plug-and- Play [59] using Stable Diffusion v1.5 [50] as the baseline. We then design experiments with two other diffusion models. Stable Diffusion v2.1 I and Stable Diffusion XL [47] and incorporate three advanced inversion approaches: Null-Text Inversion [41], Negative Prompt Inversion (NPI) [40], and Direct Inversion [25]. As shown in Table 3 while more advanced stable diffusion models increase textual similarity, they degrade content preservation. Conversely, incorporating advanced inversion
approaches improves both content preservation and edit fidelity. Furthermore, Table 4 presents the
Table 3: Comparative performance metrics with different base models and inversion techniques.
Structure
Background Preservation
CLIP Similarity
Variants
Dist x10-3
PSNR T
LPIPS x10-3 J. MSE x10- 4 SSIM x10-2 1 Visual 1 Textual
PnP+SD-1.5
26.66
|22.46
111.27
77.74
80.02
81.24
21.74
Changing the Base Model
SD-2.1 SDXL
34.74
30.3%
19.94
11.2%%
152.25
36.8%
122.86 58.0%1
74.41 7.0%1
79.38 1.5%%
22.87
5.2%M
28.33 6.3%
21.57 4.0%g
122.14
9.8%1
89.02 14.5%
77.25 3.5%]
77.52
2.9%%
23.59
8.5%
Incorporating Advanced Inversion Approaches
Null-Text +NII
18.67 30.0%;
23.80 6.0%1
89.64
19.4%)
57.97 25.4%)
82.97 3.7%1
82,46 1,0%k
21.95
1.0%
24.82 6.9%
23.17
3.2%1
99.19
10.9%]
71.24 8.4%J
80.26
0.3%T
80.16
0.9%|
21.53 1.0%]
+ +Direct
16.06 39.8%]
25.73
14.6%
74.17
33.3%.
41.19 47.0%)
85.61 7.0%|
83.29 1.6%] 22.03 1.3%]
detailed comparison between the Logistic Schedule and the scaled linear schedule across different inversion techniques.
Table 4: Comparison of inversion techniques with the scaled linear schedule and our proposed
Logistic Schedule.
Structure Dist I
Background Preservation
CLIP Similarity
Variants
PSNR 1 LPIPS L
MSE 1 SSIM
Visual f
Textual f
Null-Text + Linear
21.00 18.67
23.00
95.00
63.00
81.50
81.00
21.30
Null-Text + Logistic
23.80
89.64
57.97
82.97
82.46
21.95
NPI Lincar NPI Logistic
28.00
22.40
105.00
78.00
78.50
78.50
20.90
24.82
23.17
99.19
71.24
80.26
80.16
21.53
Direct + Linear
19.00
24.90
78.00
45.00
83,50
82.90
21.90
Direct + Logistic
16.06
25.73
74.17
41.19
85.61
83.29
22.03
6 Conclusion
This paper presents the Logistic Schedule, a novel noise schedule that eliminates singularities and improves inversion stability for image editing. Our method enhances content preservation and edit fidelity without requiring additional retraining, making it plug-and-ple solution for existing workflows. Through in-depth analysis of the diffusion inversion process, we identify that current schedulers suffer from singularity issues at the start of inversion. The proposed Logistic Schedule provides a straightforward solution to this problem, offering superior performance and adaptability across various image editing tasks.
7 Acknowledgement
This work was supported by National Natural Science Foundation of China (62403429, 62293551 1, 62377038, 62177038, 62277042). Project China Knowledge Centre for Engineering Science and Technology, Project of Chinese academy of engineering "The Online and Offline Mixed Educational Service System for 'The Belt and Road' Training in MOOC China". LLENOVO-XITUU Intelligent Industry Joint Laboratory Project.
10

---

References
[1] Omri Avrahami, Ohad Fried, and Dani Lischinski. Blended latent diffusion. ACM Transactions on Graphics (TOG), 42(4):1-11, 2023.
[2] Omri Avrahami, Thomas Hayes, Oran Gafni, Sonal Gupta, Yaniv Taigman, Devi Parikh, Dani Lischinski, Ohad Fried, and Xi Yin. Spatext: Spatio-textual representation for controllable image generation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 18370-18388) 2023.
[3] Arpit Bansal, Eitan Borgnia, Hong-Min Chu, Jie Li, Hamid Kazemi, Furong Huang, Micah Goldblum, Jonas Geiping, and Tom Goldstein. Cold diffusion: Inverting arbitrary image transforms without noise. Advances in Neural Information Processing Systems, 36, 2024.
[4] Manuel Brack, Felix Friedrich, Dominik Hintersdorf, Lukas Struppek, Patrick Schramowski, and Kristian Kersting. Sega: Instructing -ottgg models using semantic guidance. Advances in Neural Information Processing Systems, 36, 2024.
[5] Tim Brooks, Aleksander Holynski, and Alexei A Efros. Instructpix2pix: Learning to follow image editing instructions. Proceedings of the IEEF/CVF Conference on Computer Vision and Pattern Recognition, pages 18392-18402, 2023.
[6] Mingdeng Cao, Xintao Wang, Zhongang Qi, Ying Shan, Xiaohu Qie, and Yinqiang Zheng. Masactrl: Tuning-free mutual self-attention control for consistent image synthesis and editing. In Proceedings of the IEEE/CVF International Conference Computer Vision, pages 22560- 22570, 2023.
[7] Mathilde Caron, Hugo Touvron, Ishan Misra, Hervé Jégou, Julien Mairal, Piotr Bojanowski, and Armand Joulin. Emerging properties in self-supervised vision transformers. In Proceedings of the IEFF/CVF international conference on computer vision, pages 9650-9660, 2021.
[8] Ricky TQ Chen, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud. Neural ordinary differential equations. Advances in neural information processing systems, 31, 2018.
[9] Ting Chen, Lala Li, Saurabh Saxena, Geoffrey Hinton, and David J Fleet. A generalist framework for panoptic segmentation of images and videos. Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 909-919, 2023.
[10] Hansam Cho, Jonghyun Lee, Seoung Bum Kim, Tae-Hyun Oh, and Yonghyun Jeong. Noise map guidance: Inversion with spatial context for real image editing. arXiv preprint arXiv:2402.04625, 2024.
(11) Yunjey Choi, Youngjung Uh, Jaejun Yoo, and Jung-Was Woo Ha. Stargan v2: Diverse image synthesis for multiple domains. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 8188-8197, 2020.
[12] Prafulla Dhariwal and Alexander Quinn Nichol. Diffusion models beat GANs image synthesis. In A. Beygelzimer, Y. Dauphin, P. Liang, J.d Wortman Vaughan, editors, Advances in Neural Information Processing Systems, 2021.
wttperrwwwiie.eeefrrrrrr. net/forum?
AAWuCzaV)
[13] Rinon Gal, Yuval Alaluf, Yuval Atzmon, Or Patashnik, Amit Haim Bermano, Gal Chechik, and Daniel Cohen-or. An image is worth one word: Personalizing text-to-image generation using textual inversion. The Eleventh International Conference on Learning Representations, 2023.
URL https::/oppenreviie
[14] Jiatao Gu, Shuangfei Zhai, Yizhe Zhang, Miguel Ángel Bautista, and Joshua M. Susskind. f-DM: A multi-stage diffusion model via progressive signal transformation. In The Eleventh International Conference on Learning Representutions, 2023. URL hattps://opeereeeee het//forum?xd-11BWWiILg.g

---

[15] Ligong Han, Song Wen, Qi Chen, Zhixing Zhang, Kunpeng Song, Mengwei Ren, Ruijiang Gao, Yuxiao Chen, Ding Liu, Qilong Zhangli, Anastasis Stathopoulos. Xiaoxiao He. Jindong Jiang. Zhaoyang Xia, Akash Srivastava, and Dimitris N. Metaxas. Proxedit: Improving tuning-free real image editing with proximal guidance. 2024 IEEE/CVE Winter Conference on Applications of Computer Vision (WACV), pages
2023. URLhttps::/app https////app.ssmttiicschhooooooo semanticscholar
org/Corpus : 259287564
[16] Amir Hertz, Ron Mokady, Jay Tenenbaum, Kfir Aberman, Yael Pritch, and Daniel Cohen-or. Prompt-to-prompt image editing with cross-attention control. In The Eleventh International Conference on Learning Representations, 2023. URL http://ppenreieeeeeeeeeerorrr
id=_CDixzkzeyb
[17] Jonathan Ho and Tim Salimans. Classifier-free difflusion guidance. In NeurlPS 2021 Workshop on Deep Generative Models and Downstream Applications, 2021. WRLLltttps//oppnrervee
pett/forumm3id=quBAAK YbI
[18] Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models, Advances in neural information processing systems, 33:6840-6851, 2020.
[19] Jonathan Ho, Chitwan Saharia, William Chan, David Fleet, Mohammad Norouzi, and Tim Salimans. Cascaded diffusion models for high fidelity image generation. Journal of Machine Learning Research, 23(47):1-33, 2022.
[20] Emiel Hoogeboom, Jonathan Heek, and Tim Salimans. simple diffusion: End-to-end diffusion for high resolution images. In International Conference on Machine Learning, pages 13213-
13232. PMLR, 2023.
[21] Inbar Huberman- Spiegelgla,, Vladimir Kulikov, and Tomer Michaeli. An edit friendly ddpm noise space: Inversion and manipulations. arXiv preprint arXiv:2304.061400 2023.
[22] Aapo Hyvärinen and Peter Dayan. Estimation of non-normalized statistical models by score matching. Journal of Machine Learning Research, 6(4). 2005.
[23] Allan Jabri, David J. Fleet, and Ting Chen. Scalable adaptive computation for iterative gener- ation. In Proceedings of the 40th International Conference on Machine Learning, ICML'23, page 21. JMLR.org, 2023.
[24] Justin Johnson, Alexandre Alahi, and Li Fei-Fei. Perceptual losses for real-time style transfer and super-resolution. Computer Vision-ECCV 2016: 14th European Conference, Amsterdam, The Netherlands, October 11-14, 2016, Proceedings, Part I1 14, pages 694-711. Springer, 2016.
[25] Xuan Ju, Ailing Zeng, Yuxuan Bian, Shaoteng Liu, and Qiang Xu. Pnp inversion: Boosting diffusion-based editing with 3 lines of code. In The Twelfth International Conference on Learning Representations, 2024.
[26] Tero Karras, Miia Aittala, Timo Aila, and Samuli Laine. Elucidating the design space of diffusion-based generative models. Advances in Neural Information Processing Systems, 35: 26565-26577, 2022.
[27] Vahid Kazemi and Josephine Sullivan. One millisecond face alignment with an ensemble of regression trees. In Proceedings of the IEEE conference on computer vision and paltern recognition, pages 1867-1874, 2014.
[28] Gwanghyun Kim, Taesung Kwon, and Jong Chul Ye. Diffusionclip: Text-guided diffusion models for robust image manipulation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2426-2435, 2022.
[29] Diederik Kingma, Tim Salimans, Ben Poole, and Jonathan Ho. Variational diffusion models. Advances in neural information processing systems, 34:21696-21707, 2021.
[30] Diederik P Kingma and Max Welling. Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114, 2013.
12

---

[31] Peter Eris Kloeden, Eckhard Platen, and Henri Schurz. Numerical solution of SDE through computer experiments. Springer Science & Business Media, 2012.
[32] Mingi Kwon, Jaeseok Jeong, and Youngjung Uh. Diffusion models already have a semantic latent space. In The Eleventh International Conference on Learning Representations, 2023.
URL
[33] Haonan Lin. Dreamsalon: A staged diffusion framework for preserving identity-context in editable face generation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Puttern Recognition, pages 8589-8598, 2024.
[34] Shanchuan Lin, Bingchen Liu, Jiashi Li, and Xiao Yang. Common diffusion noise schedules and sample steps are flawed. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pages 5404-5411, 2024.
[35] Tsung-Yi Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dollár, and C Lawrence Zitnick. Microsoft coco: Common objects in context. In Computer Vision-ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings, Part V 13, pages 740-755. Springer, 2014.
[36] Zhenzhen Liu, Jin Peng Zhou, Yufan Wang, and Kilian Q Weinberger. Unsupervised out- of-distribution detection with diffusion inpainting. In International Conference on Machine Learning, pages
PMLR, 2023.
[37] Justin Lovelace, Varsha Kishore, Chao Wan, Eliot Shekhtman, and Kilian Q Weinberger. Latent diffusion for language generation. Advances in Neural Information Processing Systems, 36, 2024.
[38] Cheng Lu, Yuhao Zhou, Fan Bao, Jianfei Chen, Chongxuan Li, and Jun Zhu. Dpm-solver: fast ode solver for diffusion probabilistic model sampling in around 10 steps. Advances in Neural Information Processing Systems, 35:5775-5787 2022.
[39] Chenlin Meng. Yutong He, Yang Song, Jiaming Song, Jiajun Wu, Yan Zhu, and Stefano Ermon. SDEdit: Guided image synthesis and editing with stochastic differential equations. In International Conference on Learning Representations, 2022. URL /tttps:/
net/forummid=aaBCjjjc
[40] Daiki Miyake, Akihiro lohara, Yuriko Saito, and Toshiyuki TANAKA. Negative-prompt inver- sion: Fast image inversion for editing with text-guided diffusion models. ArXiv, abs/2305.16807, 2023. /ttLsst/:://apt www.eeeemmcooooo.eeeee.
Parg/Corpuslll ID: 258947366
[41] Ron Mokady, Amir Hertz, Kfir Aberman, Yael Pritch, and Daniel Cohen-Or. Null-text inversion for editing real images using guided diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6038-6047 2023.
[42] Alex Nichol, Prafulla Dhariwal, Aditya Ramesh, Pranav Shyam, Pamela Mishkin, Bob McGrew, Ilya Sutskever, and Mark Chen. Glide: Towards photorealistic image generation and editing with text-guided diffusion models. In International Conference on Machine Learning, 2021.
URL https://api. bemanticschooar.. org/ Corpus 245335088
[43] Alexander Quinn Nichol and Prafulla Dhariwal. Improved denoising diffusion probabilistic models. In International conference on machine learning, pages 3162-8177 PMLR, 2021.
[44] Zhihong Pan, Riccardo Gherardi, Xiufeng Xie, and Stephen Huang. Effective real image editing with accelerated iterative diffusion inversion. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 15912-15921, 2023.
[45] Gaurav Parmar, Krishna Kumar Singh, Richard Zhang, Yijun Li, Jingwan Lu, and Jun- Yan Zhu. Zero-shot image-to-image translation. ACM SIGGRAPH 2023 Conference Proceedings, pages 1-11, 2023.
[46] Hamza Pehlivan, Yusuf Dalva, and Aysegul Dundar. Styleres: Transforming the residuals for real image editing with stylegan. In Proceedings of the IEEF/CVF Conference on Computer Vision and Pattern Recognition, pages 1828-1837 2023.
13

---

[47] Dustin Podell. Zion English, Kyle Lacey, Andreas Blattmann, Tim Dockhorn, Jonas Müller, Joe Penna, and Robin Rombach. SDXL: Improving latent diffusion models for high-resolution image synthesis. In The Twelfth International Conference on Learning Representations, 2024.
[48] Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al. Learning transferable visual models from natural language supervision. In International conference on machine learning, pages 8748-8763. PMLR, 2021.
[49] Aditya Ramesh, Prafulla Dhariwal, Alex Nichol, Casey Chu, and Mark Chen. Hierarchical text-conditional image generation with clip latents. arXiv preprint arXiv:2204.06125, 2022.
[50] Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. High- resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition (CVPR), pages 10684-10695, June 2022.
[51] Nataniel Ruiz, Yuanzhen Li, Varun Jampani, Yael Pritch, Michael Rubinstein, and Kfir Aberman. Dreambooth: Fine tuning text-to-image diffusion models for subject-driven generation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 22500-225 22000-2210,,, 10, 2023.
[52] Chitwan Saharia, William Chan, Saurabh Saxema, Lala Li, Jay Whang, Emily L Denton, Kamyar Ghasemipour, Raphael Gontijo Lopes, Burcu Karagol Ayan, Tim Salimans, et al. Photorealistic -exttt--mmae diffusion models with deep language understanding. Advances in 2022.
Neural Information Processing Systems,
[53] Axel Sauer, Tero Karras, Samuli Laine, Andreas Geiger, and Timo Aila. Stylegan-t: Unlocking the power of gans for fast large-scale text-to-image synthesis. In International conference on machine learning. pages 30105-301 18. PMLR, 2023.
[54] Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. In Yoshua Bengio and Yann LeCun, editors, 3rd International Conference on Learning Representations, ICLR 2015, Sun Diego CA, USA, May 7-9, 2015, Conference Track Proceedings, 2015, /ttp:t::/ http::://aax/v///e htt::/axxxvv.../aaaa
1556
[55] Jiaming Song, Chenlin Meng, and Stefano Ermon. Denoising diffusion implicit models. In International Conference on Learning Representations, 2021. URL https://
net/foorumidd-Stt1
[56] Yang Song and Stefano Ermon. Generative modeling by estimating gradients of the data distribution. Advances in neural information processing systems, 32, 2019.
[57] Yang Song, Jascha Narain Sohl-Dickstein, Dicderik P. Kingma, Abhishek Kumar, Stefano Er- mon, and Ben Poole. Score-based generative modeling through stochastic differential equations. ArXiv, 0as/2001..14455 2020. URL https://api wwwanticschollii..c.. 227209335
Ptrg/CorpusI
[58] Narek Tumanyan, Omer Bar-Tal, Shai Bagon, and Tali Dekel. Splicing vit features for semantic appearance transfer. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages (0748-10757) 2022.
[59] Narck Tumanyan, Michal Geyer. Shai Bagon, and Tali Dekel. Plug-and-play diffusion features for text-driven image-to-image translation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1921-1930, 2023.
[60] Bram Wallace, Akash Gokul, and Nikhil Naik. Edict: Exact diffusion inversion via coupled transformations. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 22532-22541, 2023.
[61] Jiahao Wang, Caixia Yan, Haonan Lin, and Weizhan Zhang. Oneactor: Consistent character generation via cluster-conditooned guidance. arXiv preprint arXiv:2404.10267 2024.
14

---

[62] Su Wang, Chitwan Saharia, Ceslee Montgomery, Jordi Pont- -uste, Shai Noy, Stefano Pellegrini, Yasumasa Onoe, Sarah Laszlo, David Fleet, Radu Soricut, al. Imagen editor and editbench: Advancing and evaluating text-guided image inpainting. In Proceedings of the IEEF/CVF conference on computer vision and pattern recognition, pages 18359-18369, 2023.
[63] Zhizhong Wang, Lei Zhao, and Wei Xing. Stylediffusion: Controllable disentangled style transfer via diffusion models. In Proceedings of the IEEE/CVF International Conference Computer Vision, pages 7677-7689, 2023.
[64] Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P Simoncelli. Image quality assessment: from error visibility to structural similarity. IEEE transactions on image processing, 13(4): 600-612, 2004.
[65] Tianyi Wei, Dongdong Chen, Wenbo Zhou, Jing Liao, Weiming Zhang, Lu Yuan, Gang Hua, and Nenghai Yu. E2style: Improve the efficiency and effectiveness of stylegan inversion. IEEE Transactions on Image Processing, 11:3667-3280 2022.
[66] Qiucheng Wu, Yujian Liu, Handong Zhao, Ajinkya Kale, Trung Bui, Tong Yu, Zhe Lin, Yang Zhang, and Shiyu Chang. Uncovering the disentanglement capability text-to-image diffusion models. In Proceedings of the ICEE/CVF Conference Computer Vision and Pattern Recognition, pages 1900-1910, 2023.
[67] Ruihan Yang and Stephan Mandt. Lossy image compression with conditional diffusion models. Advances in Neural Information Processing Systems, 36, 2024.
[68] Tao Yang. Yuwang Wang. Yan Lu, and Nanning Zheng. Disdiff: Unsupervised disentangle- ment of diffusion probabilistic models. In Thirty-seventth Conference on Neural Information Processing Systems, 2023. URL /tpLLttppe///peeeeiiiseeee/eeeee htt.://wwweeeeeeeeeeeeeoooooaaaa
[69] Cheng Zhang, Xuanbai Chen, Siqi Chai, Chen Henry Wu, Dmitry Lagun, Thabo Beeler, and Fernando De la Torre. Iti-gen: Inclusive text-to-image generation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 3969-3980, 2023.
[70] Kai Zhang, Lingbo Mo, Wenhu Chen, Huan Sun, and Yu Su. Magicbrush: A manually annotated dataset for instruction-guider image editing. Advances in Neural Information Processing Systems, 36, 2024.
[71] Qinsheng Zhang, Molei Tao, and Yongxin Chen. gDDIM: Generalized denoising diffusion implicit models. In The Eleventh International Conference on Learning Representations, 2023.
URL [RRp::tt////ooerriiiiee net net/forummi=-= 1hKE9qjvz-
[72] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unrea- sonable effectiveness of deep features as perceptual metric. In Proceedings of the IEEE conference computer vision and pattern recognition, pages 586-595, 2018.
[73] Yuechen Zhang, Jinbo Xing, Eric Lo, and Jiaya Jia. Real-world image variation by aligning diffusion inversion chain. Advances in Neural Information Processing Systems, 36, 2024.
[74] Peiye Zhuang, Oluwasanmi O Koyejo, and Alex Schwing. Enjoy your editing: Controllable (gan)s for image editing via latent space navigation. In International Conference on Learning Representations, 2021. URL https://openreviii wtt.:eorunnnii.eeee www.oruumnii--ooeottttooaa
15

---

Appendix
Table of Contents
A Neural ODEs of DDIM
17
A.1 Preliminaries: Score Based Generative Modeling with SDES
17
A.2 Rewrite the DDIM Process as ODES
18
B
Proofs
20
B.
Proof Preliminaries
20
B.2
Derivation of Singularites Linear and Cosine Schedules
21
B.3
Derivatives of the Logistic Schedule
24
Related Works
24
Experimental Settings
25
Introduction Editing Types
25
D.2
Implementation Details
................................
26
D.3
Evaluation Metries
................................
26
E
Experimental Results
27
E.1
Quantitative Comparison Across Editing Types
27
E.2
Qualitative Comparison Across Editing Types
................................
28
Broader Application: Training- Based Methods
................................ 
29
Comparison With Other Noise Schedulers)
29
E.5
Reconstruction Ability of Different Noise Schedule
30
E,6
Effects of Guidance Scale
32
E.7
Effects of Iaput Scale
32
F
Liiitatons and Future Works
33
Broader Impacts
35
Ethics Statement
35
16

---

A Neural ODEs of DDIM
To support the analysis in Section on the failure of DDIM in inversion, we present the following connections to neural ODEs and DDIM.
A.1 Preliminaries: Score-Basee Generative Modeling with SDEs
We beginning with the process of constructing diffusion process using SDEs, extending DDPM to infinite noise scales for evolving data distributions from initial to prior distributions.
Perturbing Process with SDEs. DDPM [8] sets noise scales so that Xy approximates ((0, D), leveraging multiple noise scales for success. Song al. extended this infinite noise scales, evolving the data distribution via an SDE, The goal is to construct diffusion process {x(1)) r= where x(0) Po (data distribution) and x(7) Pr (prior distribution). The process is modeled by the SDE:
dx fxx, r)dr (
(6)
where w is the standard Wiener process with time flowing backwards from T to 0, f(.,r) is the drift coefficient, and g-)) is the diffusion coefficient.
Generating Samples by Reversing the SDE. Starting from x(7) pr and reversing the process, can obtain x(0)= po, given by the reverse-time SDE:
dx = [[(x,1) - g()) 2v log (x) dr + g())dw.
The score V, log (x) can be estimated by training score-based model samples using score matching [22 56].
Solving Reverse-Time SDE: Probability Flow ODE. Numerical solvers approximate trajecto- ries from SDEs. General-purpose methods like Euler-Maruy Maruyaaa and stochastic Runge- [I] discretize the stochastic dynamics. In addition to these, score-based models enable solving the reverse-time SDE via deterministic process, known as the probability flow ODE:
dx= f(x.1) 2 8()) log (x) dr
(8)
This ODE is determined from the SDE once scores are known. When the score function is approxi- mated by a neural network, it exemplifies a neural ODE 8
From Score- Based Models to DDPM: VE, VP SDEs The noise perturbations in SMLD 56 and
DDPM [88 are discretizations two SDEs: Variance Exploding (VE) SDE and Variance Preserving
(VP) SDE,
For SMLD with N noise scales, each perturbation kernel Par (x Xo) corresponds to the distribution of x; in this Markov chain:
X = X 0; of 07-12--1, i. .N..
(9)
where Z,-1 (O, and oo Markov chain (x, {x becomes a continuous stochastic process (x(1)) given by the SDE:
0. As N co, 1 becomes (1). z, becomes z(r), and the
dx d[) dw. dr
(10)
For DDPM, the perturbation kernels (Pa, (x x follow this Markov chain:
X; = VI-BBx--11 Bizi-1. 1= N.
(11)
As N - oo, this converges to the SDE:
dx = 1xx==-((1xxx B(1xddr vB())dw.
(12)
Thus, noise perturbations in SMLD and DDPM correspond to the SDEs and 12 respectively. Notably, the TO results in an exploding variance / - co, while the SDE 12 maintains fixed
variance of one, demonstrating the superiority of VP SDE for stable variance preservation.
17

---

A.2 Rewrite the DDIM Process ODEs
DDIM's Local Linearization Assumption: DDIM inversion for real images is unstable due its reliance on a local linearization assumption at each step, leading to error accumulation and content loss. DDIM assumes that the denoising process Eq. 2 roughly invertible:
X (,,(x,,1)
=
dr
+ VI - This assumes c(x;, 1) <(x () and inversion accuracy depends on this assumption. Moreover, estimating the "predicted Xo" the beginning (1 (1= 1) lacks a simple expression for the posterior mean conditioned on x,. This deviating from the linearization assumption causes the interpolation to break down from the start, resulting in server error accumulation problem.
where a, Vat-Ar/a, and b, = -1-
Relevance to Neural ODEs: Under this assumption, the DDIM iteration process (Eq. can be rewritten in format similar Euler integration for solving ODEs:
Xr-
Xy Vo,
dr
az
Eg
(xx).
(13)
V0
Reparameterizing (v1 aaaaavel Vα) with and (x/vœ) with in the continuous case, and
functions of 1, with or R20 - Rg0 continuous and increasing, (0) = 0. Eq. 13 can be seen as an Euler method over the ODE:
x(1)
(x =e!
do
(14)
+
which corresponds to the Eq. 10 of probability flow ODE. This suggests that with enough discretiza- can can be reversed, encoding to
of
tion steps and the optimal model eg the generation process Eq. 2 Xy and simulating the reverse the ODE in Eq. 14
Theorem A.1 (DDIM ODEs). While the ODEs are equivalent, the sampling procedures differ significantly. The Euler method for the probability flow ODE updates:
XI-AI
X,
+
1- -
1-
(1) Eg (x:),
(15)
Va
Var
at--s
Ct
a-
which is equivalent to Eq. 13 if; and ai- are close enough. However, achieving this closeness challenging with fewer time steps, and an inferior model can exacerbate the errors from this assumption. Moreover, the Variance Exploding SDE (VE SDE) has inherent flaws compared to the Variance Preserving SDE (VP SDE). VE SDEs lend to increase variance exponentially, leuding to instability and less accurate representations, whereas VP SDEs mainlain stable variance, ensuring a more consistent and reliable modeling process.
Modeling with di in Euler steps, as done in the probability flow ODE, ensures that the step size directly correlates with the temporal evolution, maintaining the integrity of the stochastic process and providing more faithful representation of the underlying data distribution over time. (55) state that the ODE of DDIM is a special case of the probability flow ODE (continuous-tima analog of DDPM).
Proof. We consider i as continuous, independent "time" variable and x and as functions of r. Let's reparameterize DDIM and VE-SDE using and o::
x(r) x(0) (t)e, e~ N(O,
for E [0, oo) and a continuous function or R20 - R20 where (00)
Define ar()) and x(1) for DDIM as:
x(1) x(1)
1- (())
va(1)
σ(t)
V
a(t)
This implies:
x(1)
x(1)
a(t) T+
(o2(1)+
+
18

---

From Equation noting a0)) = 1:
x(t) x(0)
1 a())
a(1) E,
va((1)
(O)(0)
which reparameterizes to:
x x(0) (1)E.
ODE form for DDIM: Simplify Equation 13to:
K(t Ar) = x(r) (orl - Ar) or() Eo (x(1)).
Dividing by -Ar and taking Ar O:
dR(1) do (r)
x(1)
(16)
dt dt
(v+2()+ +1)
matching Equation 14
ODE form for VE-SDE: Define (X) as the data distribution perturbed with (1) Gaussian noise. The probability flow for VE-SDE is given by:
d -K==-3(1'>V log p. (R)dt,
where g(t) =
(t)
The perturbed score function Vx (X) minimizes:
di
Vx log = arg min B4000--gt (c/or()))
where x x(() (t)e.
The equivalence between x()) and x(1) gives:
((()
x(i)
Vor
Vg log (X) Using Equation A.2 and the definition of g():
8(0)
dī(t) 1 (t)
(11) di,
dt 2 dt
rearranging terms:
dā(r)
do(()) (1)
x(1)
dt dt E
(o2(1)+1
which matches Equation 16 Both initial conditions are x(T) NO(,, (T))), showing that the ODEs are identical.
However, the above proof based on several assumptions as follows:
1. Equivalence Between x(() and x(1): The bijective mapping between the variables x(() and x(1) is crucial for transforming the DDIM formulation into the VE-SDE framework. If this equivalence does not hold perfectly, the transformation could introduce errors. Small discrepancies can accumulate over time, leading significant deviations the modeling process, resulting unreliable outcomes.
Gaussian and Constant Noise e: The noise e is assumed to be Gaussian N(O, /) and constant throughout the process, which simplifies the mathematical formulation and integration. However, in real-world scenarios, the noise might not be perfectly Gaussian or constant. Variations the noise affect the accuracy of the model's predictions, leading inconsistencies and unreliable results.
Continuity and Differentiability a<1)) and or):: The functions (1(1) and o()) are assumed to be continuous and differentiable. This ensures smooth transitions and allows for the derivation of the
19

---

differential equations. If (1) or (t) are not continuous or differentiable, the resulting differential equations may not accurately represent the underlying processes. This can lead instability and emoor in the model's ' behavior.
4. Optimal Model ( The model e is assumed to be optimal, meaning it perfectly minimizes the given loss function. In practice, achieving an optimal model is challenging. Suboptimal models can lead to inaccuracies in the predictions, and the error can propagate, reducing the reliability of the entire process.
5. Closeness of a, and dr-ár: It is assumed that a, and a,-ár close enough, which is necessary for the equivalence between the DDIM and VE-SDE formulations to hold. With fewer time steps, this assumption may not hold, leading to significant errors. Additionally, if the model is inferior, the emors arising from this assumption can be magnified, resulting in an unreliable process.
B Proofs
In this section, we first provide the detailed expressions of x, with respect to different noise schedules. Then provide the proof of the singularities problem in Proposition 3.1 By reparameterizing:
0r 1 1-Br- Br.
ai.
(17)
the forward process of DDPM can be expressed as:
x, vā,xo v1 8,E.
Apply the chain rule to /dr, we get:
dx,
dā + 2 v1 ā, d/
-1 da;
No di
(18)
di
2 Vār
B.1
Proof Preliminaries
B.1.1 Scaled Linear Schedule
The linear beta schedule is defined by:
Bend Bstart
B, Bstan +
T
where
0.0001 1000
0.1
B
T
T
and
0.02 1000
20
Bend
T
T
Thus,
0.1
20
0.1
0.1
19.9
B,
+1
T
T
+1
T
T
T
11)
In general form, the expression for B, is:
0.1 19.9
B. = T T(T 1)'
Incorporating Eq.
17 the ā, of scaled linear schedule is given by:
0.1 19.9 T
0
(19)
T(T -
20

---

B.1.2 Cosine Schedule
The cosine schedule is proposed in the iDDPM 43
where the definition of the schedule is given by:
f(1)
1/T+ 1+s 2
ã f(0)* f(r) = cos
(20)
where s a small offset to prevent B, from being too small near / Nichol and Dhariwal chose this setting since they found that having tiny amounts of noise at the beginning of the process made it hard for the network to predict accurately enough. Specifically, s is set as 0.008 such that vBg was slightly smaller than the pixel bin size 1/127.5.
Plugging f() into the expression, we get:
1/T+5
cos?
1
2
B.1.3 Sigmoid Schedule
The sigmoid schedule is introduced in Jabri et al., which is designed for scalable data generation, especially for high-dimensional data, without addressing the challenges of DDIM inversion. The formulation of the sigmoid schedule can be presented below:
(e=s)+s
sigmoid() + Ve
ā,
(21)
Vs
where and e are start and end sigmoid function's 's range, and v, (s/r) sigmoid(), Ve (e/r) sigmoid().
B.1.4 Logistic Schedule
Recall the expression of the logistic schedule Eq.
ã Normalized
+ e e((--))))
where & and are hyperparameters that control the steepness and midpoint of the logistic function, respectively.
B.2 Derivation of Singularities w.r.t. Linear and Cosine Schedules
Recall the Proposition 3.1
Proposition B.1 (Singularity in Inversion Process). During the inversion process, there exists singularity at t = for both the scaled linear and cosine schedule:
When = 0, dx,
sign(E) co sign(E).
dt
Next, we provide the derivatives for scaled linear and cosine in order, to support Proposition 3.1
B.2.1 Scaled Linear Schedule
For /x,/dr, where x, = Vā,No + VI ā,e, cannot use ā, TT
to find the 7(7-17
19.9.
feasible derivatives. Since the expression ā, = 11 0.1
T(7-1) represents a product of terms,
19.94
which makes difficult differentiate directly. Taking the derivative of product involves applying the product rule multiple times, which becomes impractical as the number of terms increases. Instead, we can use logarithms simplify the expression into sum, which is easier handle analytically. This approach allows us find an analytic approximation for ã, and subsequently for dx, /dr.
21

---

Proof. The logarithm of the product in Eq.
19 reads:
log(a,) = log
Σ
1
0.1 19
T
T(T
1=1
Given the small terms 0.1 T and 19.9.
T(T-1)' consider using first-order Taylor expansion for the
logarithm around The Taylor expansion of log(1 x) around 0s log(1 - x) = -x for small Substituting, we get:
lā) Σ
0.1 + T T(T- - 1)
19.9
Plugging Σ i
1(+1)) into the expression, we get:
0.1
19.9
0.1r
19.9
1(1+ 1)
log(ā,)
T
T(T -(T-1)
T
T(T - 1)
1=1
Let:
0.1r
19.9r(1+1)
f(1)
T
-T
We have:
0.1
19.9
0.1
19.9(2r 1)
f((1) T
(2r 1)
2T(T
T 2T(T
Plug ā, = f(t) into the chain rule of dē, dr
and substituting f(r) and (t), we have:
dē, =
(e (()))) = f f'(1)
dt dr
0.11 19.9/(1 10-9/(++)))
( (-0) 2T 1)
0.1 19.9(21 + 1)
exp
(T 2T
dē, dt
dx,
Substituting
back into the expression for
in Eq. 18
95249.85)
Ee
T0-D
2(7-1)
(0.17 + 19.9/ + 9.85)
dx,
(22)
dr
27
70-1
(T-
So, we have:
dx,
60e = sign(E).
When 0.
-
1-0
where denotes an unspecified directed infinity in the complex plane.
B.2.2
Cosine Schedule
Proof. Given the expression:
X, Vo,N0
V1 d,E.
where:
cos
1/T+s 1t5
2os
S.
I+5
22

---

By differentiating o, we have:
coss
t/
(-sin
sin
1/T+s
cos2
(1+8 -2
dæ,
I+y
[1++)
dr
cos
(1ts 4)
Simplifying the expression:
1/T+s 1+5
(- sin
1/T+x
dē,
cos
1+8
dr
cos2
-__
1+s
dē, dr
back into the expression for dx, dr
Substituting
in Eq.
18
dx, dr
1/T+5
1//++ π
1
Vaa
Xo v1 δ₁
2cos
1
sin
1 s
2
2T(1 + s) cos2
5
I+s
(23)
Considering the special cases:
When O, we have:
dx
tan x 2(1=5)
1.0 6 -0.5xx))
dr
T(1+s)
When / T, we have:
dxy
0
dr
B.2.3
Sigmoid Schedule
Proof.
Given definition of xy;
x, Vā,Na + v1 ā,G,
To express the coefficient of in the derivative of x, with respect to r, we start with the expression:
a b(t) Xo.
where represents the noise, and is the original image. Given that and Xo constants with respect to the differentiation yields:
d aa(1+ + Xo di
b(1.
(24)
Recall the definition of ã, in sigmoid schedule in Eq. 21 put it in the expression of a()), then the coefficient of e in Eq. 24 can be expressed as:
d a()) (e- (e-s)e-v-((-s))
xtrlm-x]
(es--(l--s) 1)2
dr
2T
Itc
1+c
When - O, we have the derivative diverges to infinity:
d lim (1)) oo,
-0 dr
23

---

B.3 Derivatives of the Logistic Schedule
Proof. The a, given by the Logistic Schedule is:
0 1 e-
By differentiating ä, we have:
dā dr dt
ke k(r-()))
(
(1 e-tk--tr))))
dā, back into the expression for
dx,
Substituting
in Eq.
18
dr dx,
dr
ke k1r (1 + e t0))
ds
2
Vā,
VT i4
Substitute back into the expression:
dx;
ke -kt-
Xo
(25)
dr 2(1 + 2
Ite kir-tpl
1te R(1-11
e k((-11))
e E
(26)
21 + ekte--oo)
When 0:
0.5
dx,
0.5ck
*0010
0.5kxoe kto
dr
ktu + 1.0
0.5 (ekt + 1.0)²
r-00
1.0
-0+11.0
Substitute the setting k = 0.015,
int(O.37) and T= = 100 into the expression, we have: dx;
1.486e 3 1.318e Xxo
dt
1-0
C Related Works
Text-guided Image Editing. Text-guided image editing significantly enhances the controllability and accessibility of visual manipulation by following human commands. With the advancement of large-scale training, diffusion models [49
[22
55 have shown remarkable capabilities in transforming
70 Some approaches train end-to-end models for image editing [5] (28). while others propose training- free methods that merge information from source and target images using masks for controllability []. breakthrough by Hertz et al. leveraged the attention maps within the UNet to climinate the need for manual masks, achieving promising results. This insight has been adopted and improved upon across multiple tasks by several works [59
images based on human-given instructions 13
62
However, most current image editing approaches still rely on predefined noise schedules without evaluating their effectiveness. In this paper, we propose a newly designed noise schedule for image editing that provides high content preservation and enhanced editability.
5
6
15 73
Inversion-based Image Editing. Editing real images requires first inverting image back to latent space of the diffusion model due to the lack of a native latent space for these real images [46 53 65 74,, process called image inversion. To address this, DDIM (55) introduced deterministic sampling process for diffusion, allowing the inversion of the sampling process to recover the latent

---

noise. However. the invertible properties of DDIM rely on its linearization assumption, which introduces deviations that drive the inverted latent away from its true distribution. As the Markov properties of the diffusion process come into play, these deviations gradually enlarge, resulting in suboptimal inverted latents that degrade reconstruction and editing quality. Recently, several
inversion-baseee -baoed methods have been proposed to mitigate this issue [41 60 40 25]. These methods
attempt to correct errors on the reconstruction path to the desired DDIM trajectory. ensuring that the original content in the source image is highly preserved and can be injected into the editing process for better content preservation. However, these methods still rely on the accuracy of DDIM inversion. This brings to the root of the issue: correcting the DDIM errors themselves.
Noise Schedule Adjustments. Previous work on noise scheduling focuses on training diffusion models from scratch to improve image quality optimize the variational lower bound (29 23 26 [1]
20
Hoogeboom et al. propose noise schedule adjustments and other strategies to effectively train
standard denoising diffusion models on high-resolution images without additional sampling modifiers. Lin et reveal that common diffusion noise schedules fail to enforce zero terminal SNR, causing discrepancies between training and inference. However, none focus on designing
off-the-shed noise schedule for image editing-a downstream task that does not require training from scratch and leverages existing models for sampling. This highlights the need for a simple but effective noise schedule tailored for downstream tasks like image editing.
D Experimental Settings
D.1 Introduction of Editing Types
Task Name
Source Prompt
Target Prompt
Attributes Content
a close up of a cat with yellow eyes
a close up of a cat with yellow eyes with its mouth open a smiling woman with blue eyes a silver figer sculpture is sitting in the grass
Attributes Color
a smiling woman with brown eyes a tiger is sitting in the grass
Attributes Material
Object Switch
bread on a table with tomatoes and a napkin
meat on a table with tomatoes and a napkin
Object Addition Non-Rigid Editing
a close up of a dog a tiger walking across a field in the wild a bench chair in front of moun- tains a man riding skateboard on ramp
a close up of dog with sunglasses a tiger standing still on a field in the wild
Scene Transferring
a bench chair in front of the sea
Style Transferring
watercolor painting of man rid- ing a skatcboard on a ramp
Table 5: Editing tasks with example source and target prompts. The change parts are noted in red.
We conducts eight editing tasks based on the real images to verify the effectiveness and versatility, along with the corresponding challenges for each task (Table
1. A Attributes Content Editing (Fig. 13): Modifies specific attributes, like changing a cat's expression. The challenge is ensuring high fidelity and preserving the original content without artifacts.
2. Attributes Color Editing (Fig. 14: Alters color attributes, like changing bird's color or eye color. The challenge is maintaining natural and coherent lighting and shading.
3. Attributes Material Editing (Fig. 15): Changes material properties, like transforming a tiger into a silver sculpture. The challenge is accurately rendering new materials while preserving shape and avoiding unrealistic artifacts.
4. Object Switch T6): Switches objects, like replacing bread with meat or transforming fox into a horse The challenge maintaining scene composition and seamlessly integrating new objects.
25

---

5. Object Addition 17): Adds new objects, like sunglasses to dog or more strawberries in a bowl. The challenge naturally integrating new objects, ensuring consistent lighting. shadows, and perspective.
6. Non-Rigid Editing (Fig. 18): Makes non-rigid modifications, like changing the pose of
tiger. The challenge is preserving anatomical correctness and natural appearance while making pose changes.
7. Scene Transferring (Fig. 19 Transfers scene context, like changing the background from mountains to the sea. The challenge is blending new backgrounds seamlessly with the foreground, maintaining consistent lightin, shadows, and color tones.
8. Style Transferring (Fig, 20): Transfers artistic style, like converting a photo into a water- color painting. The challenge is preserving essential details and content while accurately applying the new artistic style.
D.2 Implementation Details
All primary experiments are conducted using Stable Diffusion v1. with an image size of 512x512xx and a latent space of 64x64x4. For ablation studies (Section 5.3.2). SD v and SDXL are employed. Experiments run on single Nvidia A100 GPU with 100 timesteps. The inversion (forward) guidance scale is set to 3.5, and the generation (reverse) guidance scale is set to 7.5. For the logistic schedule, & is to 0.015, and to set to int(O.37), where the number of timesteps. Default hyperparameter settings are used unless otherwise specified. For each incorporated method, default hyperparameters are as follows:
Edit Friendly DDPM [2I]: Takip = 36, starting generation from timestep T Tskip-
StyleDiffusion 63 Uses SD v1.5 with 1000 inference timesteps and Tirans 301 for style
transfer.
MasaCtll 6 Starts mutual self-attention control step = and layer L 10.
Pix2Pix Zero 45 Applies noise regularization for 5 iterations at each timestep with weight of 20.
Null-Text Inversion 41 500 iterations for null-text optimization, with early stopping at
e le-
Negative Prompt Inversion [40]: Uses early stopping with threshold increasing linearly from le- by a factor of 2e through the sampling steps.
These settings ensure consistent evaluation framework across different experiments and methods.
D.3 Evaluation Metrics
In this work, seven metries are employed to evaluate the effectiveness of the Logistic Schedule, including three aspects introduced below.
Structure Distance: Structure Distance: To evaluate the structure distance between the source and edited images, we leverage DINO-1 which was proposed by DreamBooth (51) to emphasize unique properties of identities. For DINO-I, we calculate the cosine similarity between the ViT-B/16 DINO [7] embeddings of source and generated images. Additionally, we consider fine-tuning and editing time as metrics to evaluate the efficiency of the editing process. Since DINO is trained in self-supervised manner, it highlights general features rather than category- based distinctions, making suitable for capturing the structural integrity of images.
Background Preservation: To measure how the background is preserved during editing, we apply PSNR, LPIPS (24 [72) MSE, and SSIM (64] in the area outside of the annotated masks. These metries serve different roles in evaluating image quality and preservation:
http://wagggiittccccccoaallllllt ba-baae-1.0
26

---

PSNR (Peak hignal-to-Noise Ratio) measures the ratio between the maximum possible power of signal and the power of corrupting noise, reflecting the overall quality of the image:
MAX² MSE
PSNR = 10 log10
where MAX is the maximum possible pixel value of the image (e.g., 255 for an 8-bit image), and MSE is the Mean Squared Error.
LPIPS (Learned Perceptual Image Patch Similarity) evaluates perceptual similarity by comparing the differences in deep feature space using pretrained deep network (such as
VGG (54), ), capturing human visual perception better than pixel-wise metrics, by calculating the Euclidean distance between the feature representations of two images:
LPIPS = Lnr (x) 21(1)
where d denotes the feature map at layer of the pretrained network, and w, are the weights for each layer.
MSE (Mean Squared Error) calculates the average squared difference between original and edited image pixels, indicating the overall fidelity and error magnitude:
N MSE Σ (1(12
where N is the number of pixels in the image, / and I2 the original and edited images respectively, and indexes the pixels.
SSIM (Structural Similarity Index Measure) assesses image similarity by comparing lumi- nance, contrast, and structure, providing holistic view of image quality. The SSIM index between two images x and y calculated as:
(2HrHy + Ci) C2)
SSIM(x. y) (N² + 113 (i) < oz C2) C2)
where μx and Hy are the average pixel values of x and y, o and of are the variances of and y, Jxy is the covariance of and y, and Cj and C2 are constants to stabilize the division when the denominator close to zero.
Incorporating these metrics together can demonstrate background preservation more robustly since multiple metries offer a comprehensive evaluation from different perspectives.
Text-Image Consistency: CLIP Similarity 48 evaluates the text-image consistency between the edited images and the corresponding target editing text prompts. CLIP-I and CLJP-T assess visual similarity and text-image alignment, respectively. For CLIP-I, we calculate the CLIP visual similarity between the source and generated images. For CLIP-T, we calculate the CLIP text-image similarity between the generated images and the given text prompts. These metrics help ensure that the edited images accurately reflect the intended modifications described in the text prompts.
E
Experimental Results
E.1 Quantitative Comparison Across Editing Types
We provide the performance of Logistic Schedule following the editing methods configuration in Section 5 in 6 The results vary across different editing types. Attributes content editing shows high PSNR and CLIP visual similarity. We attribute this the relatively straightforward nature of modifying content attributes, which allows for high fidelity and coherence in the edited images compared to more complex edits. In the more challenging editing types, such as object addition (5th row) and non-rigid editing (e.g., pose, motion, 6th row), the model shows minimal changes, resulting in relatively better evaluation results essential content preservation metrics. The limited alterations required in these tasks help maintain the original structure and details, leading to higher PSNR and SSIM values. Object switch shows high CL.IP visual similarity. This can be attributed to the clear and distinct nature of object switching, which allows for more precise visual matching with the target
27

---

Hostmap Structure Distince
Hoarmap PSNR
Hestmap of LPIPS
17:0 2203
10.45
12.17
13:43
Iveman Qurlkan Scals
700
1.20
6:33
9:11 10:6
1231 18 21.11
Jenning Guikers Sout
07 1S 1577 20:23122 12 1267 11
142
15
5.1 6.00 W:7
10S3
15.35
99
1ntN 26-3
3 39
1A 57 16 1572
35,17
IO 1201
11
1E
MCS1
16
120
646
1774
1508
76
27.0
17.45 17 ST 16 1536
15.10 1677
12:09
Josnit
TCX
DXVT
1200
10:30
27,22
16.55
10.30
125) 11.00
3.0
6.
7.5
.00 12.5
164 200
25.0
3.0 50 7
10.0 12.5 150
230
26.0
5.0 7.5
10.0
12. .50 20.0
26.0
Rowee Grtdiioo Bade
Rewne Gaidane
Soal:
Rowme Carlanen Seals
Hestmop of MSE
Heatmap SSIM
Heatmap of CLIP-T
1074 a0s1
L12 72 00.33 57.21 6130 02:6
5055 58.00
73.0
22.57
20.35 C1.11 53 25
21722 21.20
21:11
72.5
9239
2011 95485 20:00
COU COLO G4L94
75.00 21 DE St 50 As 65 12.18
16 W
lnnean Crtlque Siaw
R3 12 2002
M
AL 2081 20.57
TILD
Joonia Grikkae
G1.99
(3L33 6G11
T3.00 71:00 muse 57 64.57 so $4. W 52
35
2x 22:1
25
pa
22.3
22
21.39
TiLl 7175
61.8 7877117
22.00
2116
22.02
09,05000
22.19
21.12 33
QLD
360
1011 5:329 20.30 000 601
M8 90 56.71
63 10 151.1 00.00
1800
20.33
22
2111 21:0 20.30
07.5
10.0 12.5 15D Boves Gualazee Stake
7.5
25.0
Roszao Challane Seale
Havira Gusllano Stae
Figure 8: Impact of different combinations of inversion and reverse guidance scales on various performance metrics. Results are averaged on Attributes Editing tasks using Prompt-to to-Prompt as the editing method [16), highlighting optimal scale settings for balanced performance across tasks.
Table 6: Performance of Logistic Schedule on different editing tasks in have ten independent runs with random seeds. Bold values indicate the best results, while underlined values denote the second-best results. 'Attr., 'Obj." and 'Trans.' denote 'Attributes', 'Objects', and 'Transferring' respectively.
Structure Dist x10-3 L
Background Preservation
CLIP Similarity (%)
Edit Task
PSNR LPIPS x10-3 J MSE x10-4 1 SSIM x10-2 T Visual
Textual
Attr. Content
26.58 15.74
70.69-2.1
51.04
84.48_3.0
89.30,3.2
22.05
Attr. Color
16.78.1.4
23.81
89.65-3.5
53.10=1.1
81.04_4.7
81.26,2.3
19.41=1.0
Attr. Material
18.67
25.73+0.9
74.17+3.4
41.19+1.6
81.61
78.0643.3
24.03=1.5
Obj. Switch
22.40+1.8
22.91+1.2
90.75+5.0
82.05+1.4
79.32+4.6
86.72+3.3
22.65
Obj. Add
11.11+1.1
25.40+1.5
63.05+3.2
40.52+1.0
85.32.4.6
76.33+3.3
23.09-0.9
Non-rigid
15.87
24.66
75.18-2.5
59.22.1.2
81.1124.8
81.26+3.6
22.30=1.1
Scene Trans.
17.6321.4
24.7941.
55.57
48.51
85.95
81.6341.6
22.11
Style Trans.
19.66.1.5
25.50
60.24_4.2
49.79
85.6026.0
80.2445.6
25.73
object compared to other editing tasks. Style transferring (8th row) shows the highest CLIP text similarity. This is likely because the task involves applying well-defined artistic styles that closely align with the textual descriptions, resulting in edits that match the intended style effectively. Scene and style transferring (7th and 8th row) show high LPIPS and SSIM. We attribute this to the nature of the task, which involves changing backgrounds styles while keeping the main subjects intact. This process maintains the overall scene coherence and structure consistency, resulting in enhanced perceptual quality and structural similarity.
E.2 Qualitative Comparison Across Editing Types
The logistic noise schedule consistently outperforms linear and cosine schedules across various editing tasks. It excels in preserving the original image content while making specified changes without artifacts (Fig. 13), maintaining natural and coherent lighting in color edits (Fig. 14), and accurately rendering new material properties (Fig. 15 For object switching and addition, it ensures
seamless integration with consistent lighting and spatial relationships (Figs. T6 [7). In non-rigid
editing, it preserves anatomical correctness and smooth transitions (Fig.
18 It also blends new
28

---

backgrounds naturally in scene transfers (Fig. 19 and maintains essential details while applying new artistic styles (Fig. 20).
E.3 Broader Application: Training-Basse -Baed Methods
While the Logistic Schedule has shown broad applicability in various image editing tasks, we further explore its use in training-basee based methods, specifically in Text-to-Imase Image synthesis. For this, we conducted experiments by fine-tuning the UNet using DreamBooth [5T]. leveraging approximately 100 images for each configuration.
Table Performance comparison of DreamBooth fine-tuning using different noise schedules on the SD-1.5 model. The best results are in bold.
Setting
DINO (1)
CLIP-I (1)
CLIP-T (T)
PSNR (1)
PRES (T)
Real Images
0.823
0.902
N/A
26.86
0.653
DreamBooth (SD-1.5) + Linear
0.726
0.823
0.268
24.41
0.567
DreamBooth (SD-1.5) + Cosine
0.745
0.857
0.264
24.75
0.554
DreamBooth (SD-1.5) + Logistic
0.761
0.877
0.293
25.62
0,580
The related qualitative comparisons are shown Fig. These results demonstrate that training DreamBooth with the Logistic Schedule improves performance across key metrics such as DINO and CLIP-I similarity, as well as PSNR and PRES, outperforming both linear and cosine schedules.
Fine-tune Samples
Instruction Prompt
Fine-tune Samples
Instruction Prompt in green, wavy long olive-toned clear skin, red business suit with blue tie and glasses, standing in front of green and blue plants.
haired [V], fasturing diamond necklace and small earnings, wearing tioro. The image is in black and white, set against black backdrop
Linear
Linear
Cosine
Cosine
Logistic
Logistic
Figure 9: Qualitative comparisons fine-tuning DreamBooth using different noise schedules (Linear, Cosine, and Logistic). The top column presents the fine-tune samples, and the instruction prompts, and the below column displays the corresponding fine-tuned outputs. The Logistic Schedule produces superior outputs with improved fidelity and alignment to the prompts.
E.4 Comparison With Other Noise Schedulers
We conducted experiments comparing Logistic Schedule with other schedules under the DDIM paradigm, such as exponential, sigmoid, hyperbolic, and geometric schedules. Table X displays the quantitative results. The best-performing method is indicated in bold, the worst method is marked in purple, and the second- best method is underlined.
The results demonstrate that our Logistic Schedule achieves competitive performance across various metrics. Notably, it offers significant improvements content preservation and edit fidelity compared to other schedules. As shown in Fig. T0, the Logistic Schedule preserves the visual characteristics of the source image more faithfully during reconstruction and enables more precise control during editing.
29

---

Table 8: Comparison of different noise schedules. Metrics include Structure Distance (x 10-3)), PSNR
(higher is better), LPIPS (x (x10-3, lower better), MSE (x10 lower is better), SSIM 10 higher better), and CLIP Similarity for both visual and textual content.
Schedule
Dist L
PSNR
LPIPS L
MSE L
SSIM 1
Visual [
Textual
Linear
35.66
20.70
134.88
113.61
77.60
79.82
23.06
Cosine
26.57
22.38
110.52
80.01
80.15
81.35
22.39
Exponential
16.22
25.20
80.45
47.11
82.23
82.78
19.50
Hyperbolic
36.55
20.95
140.55
119.78
79.89
79.20
23.20
Geometric
18.12
24.10
92,45
62.13
82.05
82.20
20.45
Sigmoid
27.80
22.55
115.32
85.60
80.22
81.50
22.55
Logistic
17.37
24.78
81,80
49.47
82.97
82.44
23.62
Source
slinear
cosine
exponential hyperbolic
geometric
sigmoid
logistic
Reconstruct
Edit
digital art woman with curry nair
digital art woman with straight hair
Reconstruct
Source
slinear
cosine
exponential
hyperbolic
geometric
sigmoid
logistic
Edit
woman with arrow in her hand -3 woman with an arrow in her hand with fire in the background
Figure 10: Qualitative comparison between different noise schedules for both reconstruction and editing tasks.
E.5
Reconstruction Ability of Different Noise Schedule
Table 9: Comparison reconstruction quality using different noise schedules for DDIM inversion and Direct Inversion, showing the superior performance of the Logistic Schedule.
Structure
Background Preservation
Inversion
Schedule
Dist x10-3
PSNR 1 LPIPS x1n-3
MSE x10-4 1 SSIM x10-2 1
Linear
7.96
27.46
58.49
30.08
84.54
DDIM Inversion
Cosine
7.43
27.36
61.22
28.49
82.66
Logistic
7.04
25.78
71.87
37.59
80.07
Linear
2.78
29.58
36.36
20.23
85.28
Direct Inversion
Cosine
2.75
30.00
33.80
21.70
85.90
Logistic
31.30
31.16
12.27
88.94
To demonstrate the ability of the Logistic Schedule to better align inversion by eliminating the singularity at the start point, we evaluate the reconstruction results of DDIM Inversion (55] and Direct Inversion (55 using scaled linear, cosine, and our logistic schedule. During reconstruction, the condition is the source prompt, which also applied as condition during inversion. The comparison of reconstruction quality is shown in Table
30

---

Source Image
Source Prompt:
train traveling down the tracks
Target Prompt:
skyblue train traveling down the tracks
Denoising (Reversing) Guidance Scale
7.5
123
15
20
25
3.5
5
7.5
10
Inversion (Forward) Guidance Scale
Figure 11: Qualitative comparison of varying guidance scales during the inversion (forward) and denoising (reversing) processes of DDIM. The guidance scales for inversion are varied across the columns (1 to 10), and the guidance scales for denoising varied across the rows (3 to 25).
31

---

E.6 Effects of Guidance Scale
We investigate the impact of the guidance scale on the inversion (forward) and generation (reserve) processes of DDIM with the Logistic Schedule, consequently affecting the editing results. We illustrate the impact of varying guidance scales during the inversion and denoising processes of DDIM on performance metries in Fig[ with an example of how the edited images are affected shown in Fig [1 When keeping the inverse guidance scale constant, we observed that as the reverse guidance scales increased gradually, background preservation initially decreased. The inflection point occurred when the inverse guidance scale equaled the forward guidance scale. In contrast, CLIP similarity showed a consistently increasing trend until the reverse guidance scale exceeded 15. The quantitative heatmaps and qualitative results highlight a noticeable trade-off between essential content preservation and edit fidelity. Optimal incorporation of both scales ensures balance between structural preservation, perceptual quality, and text-image consistency, with a combination of 5.0 for inversion and 7.5 for reverse generally providing the best performance across most metries. This rrade-off arises because current editing methods struggle to differentiate between regions needing modification and those that do not, leading substantial alterations of the source image and conflicting with content preservation objectives.
E.7
Effects of Input Scale
Chen et al. proposed to modify noise scheduling by scaling the input No by a constant factor b via: Nā, + V1 C.C.
1.0
17.5
ipput scale: 0.85
120
Input scale: 0.8 *
17.0
Segetre
100
input scale
14.5
input soale:
16.0
20,0
20.5
24.5
21.0
31.5
210
20D 21.5 Tiat Seriberr (CLIP-T)
21.0
21D0
21.
24.0
Text Sentiantty (CLIP-T)
Tioe Sambury (CUIP-T
Tind Smilety (CLIP-T)
Figure 12: Impact of input scale on content preservation and edit fidelity. The optimal input scale balances the preservation of the original image structure (low structure distance, high SSIM) and the quality of the edits (high CLIP-T and CLIP-I).
As the scaling factor decreases, the original image's strength lessens and noise levels grow (9. As previous image editing works have not extensively investigated the effects of input scale, we investigate the effects of input scale in image editing in this work. We change the input scale from 0.5 to 1.4 with step size of 0.05, and illustrate the effects of the input scale on both content preservation and edit fidelity in Fig. 12 As observed, the input scale significantly impacts the balance between content preservation and edit fidelity. Higher input scales (closer to 1.4) better preserve the original image structure, as shown by lower structure distances and higher SSIM values but reduce edit fidelity (lower CLIP-T and CLIP-I scores). Conversely, lower input scales (closer to 0.5) enhance edit fidelity but degrade content preservation. 'he optimal input scale, found to be 0.8-0.95, achieves a balance between these objectives. This is because slightly higher noise levels improve editability while maintaining acceptable content preservation, providing satisfactory trade-off in image editing.
Table 10: Performance comparison of input scale normalization in object switch task using Zero-shot Pix2Pix, showing no improvement in content preservation edit fidelity.
Structure
Background Preservation
CLIP Similarity (%)
Input Scale
Dist x
PSNR LPIPS x10- 1 MSF x10-4 SSIM x10-2 V 1
Textual 1
w/o Normalizing b
22.40
22.91
90.75
82.05
79.32
86.72
22.65
w. Normalizing b
24.46
22.06
108.43
83.47
79.16
86.24
22.48
A strategy to improve training diffusion model from scratch is to normalize by its variance to ensure it has unit variance before feeding it to the denoising network. This prevents performance issues caused by variance changes in X, when Xo has the same mean and variance as e (26]. However, in our image editing work using off-the-shelf diffusion models, we find that normalization does not improve content preservation or edit fidelity, as shown in Table 10
32

---

Linear
Cosine Schedule
Logistic Schedule
Linear Schedule
Cosine Schedule
Logistic Schedule
Real Image
Real Image
Schedule
smiling woman with black hair smiling with black hair, eyes closed
a blond woman with blue eyes = blond woman with blue eyes, smiling
woman with long brown hair
pit bull puppy with hig ears a happy pit bull puppy with big ears
a woman with long brown hair, eyes closed
white dog lying grass a leopard dog lying on grass
long haired cat looking up something * short haired cat looking up at something
a tiger is sitting in the snow
woman with long curty hair = smiling woman with long curly hair
tiger is sitting in the snow with its mouth open
young boy playing water, laughing happily >> young boy is playing water, crying sadly
peaceful ocean wonden posts rough ocean with wooden posts
Comparison of linear, cosine, and logistic schedules in editing attributes content. The logistic schedule shows superior fidelity in preserving the original image content while accurately making the specified changes, without introducing artifacts or inconsistencies.
Figure 13:
Limitations and Future Works
This work endeavors to enhance inversion-based editing methods, focusing on improving noise schedule design during the inversion process. Even though this work reveals that modifying the noise schedule using off-the-shelf diffusion models can lead to editing improvements, there is still lack of research how other designs of noise schedules can lead to different effects. For example, is it possible to design dynamic adjustments of the noise schedule at each time step to achieve better results? Furthermore, the editing capabilities of the Logistic Schedule are inherently constrained by the limitations of inversion-basee determination of timesteps and layers for attention control, limiting its ability automatically adapt to diverse real-world objects with varying attributes.
methods. For example, MasaCtrl (6) editing requires manual
Even though extensive experiments prove the effectiveness of the Logistic Schedule, it is worth diving deeper into the schedule's performance in the generation task. Due to computational resource constraints, we have not conducted training on the diffusion model from scratch to validate the full potential of the Logistic Schedule. Future work will include training diffusion models using the Logistic Schedule to validate its generation ability.
Another potential future research direction lies in exploring whether a steadier decrease in logSNR during perturbation, described in Section 4 enhances editing quality. Additional experiments on both generation and editing are required to confirm if this trend extends to the generation process as well.
33

---

Cosine Schedule
Logistic Schedule
Cosine
Logistic Schedule
Real Image
Real Image
Schedule
smiling woman with brown eyes + smiling woman with blue eyes
a close up of a tiger close up of white tiger
black bird with yellow beak green bird with a yellow beak
a man standing on a snowboard = a man in black standing snowboard
close up a close up of a white cat
to each other = two men in indigo next to each other
close up of dog + close up of white dog
a parking meter a field = skyblue parking meter in a field
Figure 14:
Comparison of linear, cosine, and logistic schedules in editing color attributes. The logistic schedule excels in maintaining natural and coherent lighting and shading, resulting in more realistic and seamless color changes without introducing visual inconsistencies.
Linear Schedule
Cosine
Logistic Schedule
Linear
Cosine
Logistic Schedule
Real Image
Real Image
Schedule
Schedule
Schedule
tiger is sitting in the grass
a fox looking at the camera silver fox sculpture looking at the camera
silver tiger sculpture is sitting in the grass
bird on stool a silver bird sculpture on a stool
man wearing shirt + a man wearing a sweater
woman in black bikini top a wax statue of woman in a black bikini top
single rose in front of orange wall = single withered rose in front of an orange wall
Figure 15: Comparison of linear, cosine, and logistic schedules in changing material properties. The logistic schedule excels accurately rendering new material properties, such as reflections and textures while preserving the shape and form of the original objects, avoiding unrealistic artifacts, and ensuring natural appearance.
34

---

Linear
Cosine Schedule
Logistic Schedule
Linear Schedule
Cosine Schedule
Logistic Schedule
Real Image
Real Image
Schedule
tiger walking on snow wolf walking the snow
tiger sitting on at sunset = lion sitting rock at sunset
a. afoxx walks along a sidewalk = horse walks along sidewalk
red fox fox running across a green field = a red running across green field
a close up cat with yellow eyes + a close up of a fox with yellow eyes
close up of figer with its mouth open a close up of a lion with its mouth open
zebra standing on dirt field= leopard standing a dirt field
parking meter middle of a field stop sign in the middle of field
grazing in a field horse grazing in field
man riding wave surfboard * robot riding a wave on a surfboard
Figure 16: Comparison of linear, cosine, and logistic schedules in switching objects. The logistic schedule excels in maintaining the overall composition and context of the scene while seamlessly integrating the new objects with consistent lighting, shadows, and spatial relationships, ensuring natural and coherent appearance.
G Broader Impacts
Our work introduces a novel editing technique for manipulating real images using state-of-the-art text-to-image diffusion models. While this technology could potentially be exploited by malicious parties to create fake content and spread disinformation, this is common issue across all image editing techniques. Significant progress already being made identifying and preventing such malicious editing. Our research contributes to this effort by providing a detailed analysis of the inversion and editing processes in text-to-image diffusion models, thereby aiding in the development of more robust detection and prevention methods.
H Ethics Statement
Generative models for synthesizing images carry several ethical concerns, particularly when used by bad actors to generate disinformation or potentially displace creative workers through automation. These models, trained on large amounts of user data from the internet without explicit consent, may generate augmentations that resemble or copy such data. This issue not unique to our work but inherent to large-scale models like Stable Diffusion, which we employ in our data augmentation strategy. To mitigate this, we allow for the deletion of harmful or copyrighted concepts from the model's weights before augmentation, ensuring such material cannot be copied during the process.
35

---

Linear
Cosine Schedule
Logistic Schedule
Linear
Cosine Schedule
Logistic Schedule
Real Image
Real Image
Schedule
Schedule
a white dog laying on the floor white dog wearing sunglasses laying on the floor
blonde woman with long hair and smile blonde woman with long hair, a mustache and smile
beautiful garden beautiful garden with ballons
bike parked stop
bike parked next to stop sign baby besides
close up of man with curly hair = close up of with curly hair and black eyeshadows
woman with long blonde hair and blue eyes = woman wearing beanie with blonde halr and blue eyes
Rel
Tip
TO
woman about tennis on iron woman is hitting temnis ball
a white horse running white horse with a single horn running in the dirt
Figure 17: Comparison of linear, cosine, and logistic schedules in adding objects. The logistic schedule excels naturally integrating the new objects into the scene, ensuring consistent lighting, shadows, and perspective with the existing elements, resulting in realistic and seamless appearance.
Linear
Cosine Schedule
Logistic Schedule
Linear
Cosine
Logistic Schedule
Real Image
Real Image
Schedule
Schedule
Schedule
pigeon sitting ground a pigeon sitting on a ground, raising head
+
tiger running across filed in the wild + a tiger standing in a filed the wild
tiger sitling on a rock at sunset tiger is standing rock sunset
a white dog is laying on the floor > white dog walking the floor
an elephant standing in 200
a parking meter middle of a field three parking meters behind field
elephant is running in
Comparison of linear, cosine, and logistic schedules in making non-rigid modifications. The logistic schedule excels in preserving anatomical correctness and natural appearance while making significant pose changes, ensuring smooth transitions and avoiding unnatural distortions.
Figure 18:
36

---

Linear
Cosine Schedule
Logistic Schedule
Linear Schedule
Cosine Schedule
Logistic Schedule
Real Image
Real Image
Schedule
close up of car close un of a cat with green background
zebra standing dirt field a zebra standing on a beach near sea
an elephant standing in 200 =
a man riding a skateboard on ramp = riding skateboard flat ground
elephant standing in river
man sitring with trees in the background man sitting with city in the background
couple walking down dirt road an couple walking down snow covered road
Figure 19: Comparison of linear, cosine, and logistic schedules in transferring scenes. The logistic schedule excels in seamlessly blending the new background with the foreground objects, maintaining consistent lighting, shadows, and color tones, avoiding visible seams, and ensuring a natural and coherent appearance.
Linear
Cosine Schedule
Logistic Schedule
Linear Schedule
Cosine
Logistic Schedule
Real Image
Real Image
Schedule
Schedule
a close up of cat + digital painting close up of a
elephant standing in a artistic painting of elephant standing in 200
man holding tennis racket = a artistic painting of giraffe in front of a tree a artistic painting of man holding a tennis racket
giruffe in front of tree >
two men next to each other = abstract painting of two men next to each other
parking meter in a field = an oil painting of a parking meter a field
a man riding on a surfboard = oil painting of riding surfboard oil painting of elephants walking across field
elephants walking across a field =>
Figure 20: Comparison of linear, cosine, and logistic schedules in transferring styles. The logistic schedule excels in preserving essential details and content the original image while accurately applying the new artistic style, ensuring consistency across the entire image and avoiding artifacts, resulting in more natural and coherent style transfer.
37

---

Despite these concerns, these tools may also foster growth and improve accessibility in the creative industry.
38

---

NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: The main claims made in the abstract and introduction (Section accurately reflect the paper's contributions and scope.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or
NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
is fine to include aspirational goals as motivation as long as is clear that these goals are not attained by the paper.
2. Limitations
Question: Does the paper discuss the limitations the work performed by the authors?
Answer: [Yes]
Justification:
The limitations of the work discussed in Appendix
Guidelines:
The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create a separate "Limitations" section their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g.. independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution is low images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.
While the authors might fear that complete honesty about limitations might used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't 't acknowledged judgment and recognize that individual actions in favor of transparency play impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
the paper. The authors should use their best
3. Theory Assumptions and Proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: [Yes]
39

---

Justification:
Concerning Proposition 3.1 Appendix B provides its corresponding proofs,
with a short proof sketch to provide intuition.
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced the statement of any theorems.
The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide short proof sketch provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental Result Reproducibility
Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
Question:
Answer: [Yes]
Justification: Refer to Appendix D.I and D.2 for implementation details, the provided code in the supplementary materials ensures the reproducibility as well.
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is novel architecture, describing the architecture fully might suffice, or if the contribution a specific model and empirical evaluation, it may be necessary either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of large language model), releasing of a model checkpoint, or other means that appropriate to the research performed.
While NeurlPS does not require releasing code, the conference does require all submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) the contribution is primarily a new algorithm, the paper should make clear how reproduce that algorithm. (b) If the contribution is primarily new model architecture, the paper should describe the architecture clearly and fully.
(c) the contribution is a new model (e.g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce the model (e.g., with an open-source dataset instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome deseribe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should possible for other researchers to have some path to reproducing or verifying the results.
5. Open access to data and code
40

---

Does the paper provide open access to the data and code, with sufficient instruc- tions faithfully reproduce the main experimental results, as described in supplemental material?
Question:
Answer: [Yes]
Justification:
Refer to the provided code in the supplementary materials.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurIPS code and data submission guidelines (https://nips.co cc/
for more details.
While we encourage the release of code and data, we understand that this might not be possible, "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (c.g., for new open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines (https
//nips //ips.cc//pill wttp:ccppppcccceeeeeeeeee..c.ett httpa///guddeee/eeeeebiiissssss Coooeooomisssssseeeeeeee ssi.iiiiccyyyyyyy for more details.
The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended the paper) is recommended, but including URLs to data and code is permitted.
6. Experimental Setting/Details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary understand the results?
Answer: [Yes]
Justification: Table speciifess all the tasks included in this work. Appendix D.2 provides the employed hyperparameters.
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented in the core of the paper level of detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, as supplemental material.
7. Experiment Statistical Significance
Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Question:
Answer: [Yes]
Justification: Appendix E.I provides the statistical significance of the experiments.
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by error bars, confi- dence intervals, statistical significance tests, least for the experiments that support the main claims of the paper.
The factors of variability that the error bars are capturing should be clearly stated (for
example, train/test split, initialization, random drawing of some parameter, or overall with given experimental conditions).
41

---

The method for calculating the error bars should be explained (closed form formula, call a library function, bootstrap, etc.)
The assumptions made should be given (e.g., Normally distributed errors).
It should be clear whether the error bar is the standard deviation the standard error of the mean.
It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful figures symmetric error bars that would yield results that are out of range (e.g. negative rates).
show in tables or
If error bars are reported in tables or plots, The authors should explain the text how they were calculated and reference the corresponding figures tables in the text.
8. Experiments Compute Resources
For each experiment, does the paper provide sufficient information on the puter resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
Question:
Answer: [Yes]
Justification: Appendix D.2 provide sufficient information on the computer resources.
Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs as well estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary failed experiments that didn't I make it into the paper).
9. Code Of Ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurlPS Code of Ethics
Answer: [Yes]
Justification: The authors have reviewed and understand the NeurIPS Code of Ethics, and confirm that their research conforms to it in every respect.
Guidelines:
The answer NA means that the authors have reviewed the NeurIPS Code of Ethics.
If the authors answer No, they should explain the special circumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g., there a special consid- eration due to laws or regulations in their jurisdiction).
10. Broader Impacts
Question: Does the paper discuss both potential positive socictal impacts and negative societal impacts of the work performed?
Answer: [Yes]
Justification: Potential societal impacts of the work are discussed in Appendix G
Guidelines:
The answer NA means that there is no societal impact of the work performed.
If the authors answer NA or No, they should explain why their work has no societal impact why the paper does not address societal impact.
42

---

Examples of negative societal impacts include potential malicious unintended uses (e.g., disinformation, generating fake profiles, surveillance), faireess considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional unintentional) misuse of the technology.
If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML).
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data models that have high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
Justification:
The paper poses such risks.
Guidelines:
The answer NA means that the paper poses no such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere usage guidelines restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Are the creators or original owners of assets (e.g.. code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
Question:
Answer: [Yes]
The original papers of assets, and the corresponding versions are provided in Section 5) References and Appendix D.2
Justification:
Guidelines:
The answer NA means that the paper does use existing assets.
The authors should cite the original paper that produced the code package or dataset.
The authors should state which version of the asset is used and, if possible, include URL.
The name of the license (e.g., CC-BY 4.0) should be included for each asset.
For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.
43

---

If assets are released, the license, copyright information, and terms of use in the thcode. has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
package should be provided. For popular datasets, paperswi
latasets.paperssit
For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.
If this information not available online, the authors are encouraged to reach out to the asset's s creators.
13. New Assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [Yes]
Justification:
We will document the assets well when we officially release our code.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/moodl as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent obtained from people whose asset is used.
At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsoureing and Research with Human Subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well details about compensation (if any)?
Answer: [NA]
Justification:
The paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Including this information the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then as much detail as possible should be included in the main paper.
According to the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional Review Board (IRB) Approvals or Equivalent for Research with Human Subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or equivalent approval/review based the requirements of your country institution) were obtained?
Answer: [NA]
Justification: The paper does not describe potential risks incurred by study participants.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing research with human subjects.
Depending the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
44

---

We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors adhere the NeurIPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.
45


Reviews:
[{"review_id": "ZpKHiORBLX", "reviewer": "Reviewer_j2Zw", "summary": "The authors introduce the Logistic Schedule, a novel noise schedule designed to resolve the singularity problem in traditional noise schedules, thereby enhancing inversion stability and reducing noise prediction errors. This new schedule enables more faithful editing that preserves the original content of the source image without requiring additional retraining. Experiments across eight editing tasks demonstrate the Logistic Schedule's superior performance in content preservation and edit fidelity, highlighting its adaptability and effectiveness.", "questions": "Refer to weaknesses. No more questions.", "limitations": "1. The authors mentioned they extend current datasets as their training dataset. Will this be open-sourced?", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1. The paper provides a thorough analysis of the primary contributors to error accumulation in DDIM inversion, offering a detailed explanation of how the Logistic Schedule resolves these issues.\n\n2. Extensive experiments across multiple datasets demonstrate the Logistic Schedule's effectiveness in improving content preservation and edit fidelity, showcasing its robustness and adaptability.\n\n3. The related code and models will be open-sourced.", "weaknesses": "1. The authors mentioned they extend current datasets as their training dataset. Will this be open-sourced?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate your positive feedback and attention.\n\n**Response to Q1**\n> ***Will the extended datasets be open-sourced?***\n\nYes, certainly. We will open source the extended datasets and our experimental code, including the validations, to facilitate further analysis and research.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "K3ATw6ASeJ", "reviewer": "Reviewer_B36W", "summary": "The paper proposes a noise schedule \"Logistic Schedule\" to solve the singularity problem in the traditional noise schedules for text-guided diffusion models for image editing. It aims to improve the stability of the DDIM inversion process, reducing noise prediction errors and enhancing content preservation and edit fidelity without additional retraining. It is validated on eight editing tasks and show performance in content preservation and edit fidelity compared to the original noise schedules.", "questions": "Can the Logistic Schedule be used in or combined with training-based methods to further improve the performance?", "limitations": "The authors have discussed the limitations of their work, along with potential negative societal impacts.", "rating": 6, "confidence": 3, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "The experiments cover a wide range of editing tasks which demonstrating the versatility of the Logistic Schedule.\nThe method does not require retraining existing models, which making it easily applicable to current workflows.\nIt is an easy solution to a well-defined problem.", "weaknesses": "The author mainly compared Logistic Schedule with linear and cosine schedules. Additional comparisons with other noise schedules or inversion techniques could be shown to further strengthen the point.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your positive comments and helpful suggestions. \n\n**Response to W1**\n> ***Additional comparisons with other noise schedules (except linear and cosine) or inversion techniques ....***\n\nWe acknowledge the value of comparing our Logistic Schedule with other noise schedules and inversion techniques. Here we provide the additional comparisons:\n\n1. **Other schedulers**:\n\n&nbsp;&nbsp;\nWe've included experiments comparing the Logistic Schedule with other schedules under the DDIM paradigm, such as exponential, sigmoid, and hyperbolic tangent, etc. \n\n&nbsp;&nbsp;\nThe 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 $\\underline{\\text{underlined}}$.\n\n| Schedule | Dist ($_{\\times 10^{-3}} \\downarrow$) | PSNR ($\\uparrow$) | LPIPS ($_{\\times 10^{-3}} \\downarrow$) | MSE ($_{\\times 10^{-4}} \\downarrow$) | SSIM ($_{\\times 10^{-2}} \\uparrow$) | Visual ($\\uparrow$)   | Textual ($\\uparrow$)  |\n| ------------ | ------------------------------------- | --------------------- | -------------------------------------- | ------------------------------------ | ----------------------------------- | --------------------- | --------------------- |\n| Linear   | 35.66 | $\\color{purple}20.70$ | 134.88 | 113.61 | $\\color{purple}77.60$ | 79.82   | 23.06   |\n| Cosine   | 26.57 | 22.38   | 110.52 | 80.01| 80.15 | 81.35   | 22.39   |\n| Exponential  | **16.22**   | **25.20**   | **80.45**| **47.11**  |  $\\underline{82.23} $ | **82.78**   | $\\color{purple}19.50$ |\n| Hyperbolic   | $\\color{purple}36.55$   | 20.95   | $\\color{purple}140.55$   | $\\color{purple}119.78$ | 79.89 | $\\color{purple}79.20$ |  $\\underline{23.20}$|\n| Geometric| 18.12 | 24.10   | 92.45  | 62.13| 82.05 | 82.20   | 20.45   |\n| Sigmoid  | 27.80 | 22.55   | 115.32 | 85.60| 80.22 | 81.50   | 22.55   |\n| **Logistic** | $\\underline{17.37} $ |  $\\underline{24.78} $ |  $\\underline{81.80} $ |  $\\underline{49.47} $ |  $\\underline{82.97} $ |  $\\underline{82.44} $ | **23.62**   |\n\n&nbsp;&nbsp;\nMoreover, **the qualitative comparison is provided in Fig. 3 in the attached PDF**.\n\n2. **Other Inversion techniques**:\n\n&nbsp;&nbsp;\nPlease refer to **\"Response to Q1\"** in the **\"General Response to All Reviewers\"** for detailed comparisons with additional inversion techniques.\n\n---\n\\\n**Response to Q1**\n> ***Can the Logistic Schedule be used in or combined with training-based methods to further improve the performance?***\n\nThanks for your insightful suggestions. This is an area we are exploring in the following research. \n\nBased 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. \n\nThese results demonstrate that **incorporating the Logistic Schedule** into the training phase of diffusion models could help in learning more stable and accurate noise representations. \n\nWe will continue to extend our experiments with training-based methods.\n\n\n---\n\\\n**We have included the above validations that were previously omitted in our manuscript. Thank you again for your valuable suggestions on our paper.**", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "nPVGPPEeDv", "reviewer": "Reviewer_ihj2", "summary": "This paper introduces a novel noise schedule called Logistic Schedule for text-guided image editing. The authors identify that traditional DDIM inversion methods suffer from accumulated prediction errors, leading to suboptimal content preservation and edit fidelity. To address this, this paper proposes the Logistic Schedule, which eliminates singularities, improves inversion stability, and provides a better noise space for image editing, resulting in higher content preservation and edit fidelity.", "questions": "1. Does the Logistic Schedule consistently improve performance across all existing editing methods? Are there specific editing methods that are incompatible with the Logistic Schedule?\n2. How much do the parameters of the Logistic Schedule affect the results? Is there a specific method for parameter optimization?\n3. Can you provide some inversion results without text input (w/o editing)？", "limitations": "See weaknesses.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The simple Logistic Schedule method effectively addresses the singularity issues in traditional noise schedules.\n2. The method is compatible with various existing editing techniques without the need for additional retraining, making it highly applicable.\n3. The proposed method is validated through experiments on eight different editing tasks using approximately 1600 images, demonstrating superior performance in content preservation and edit fidelity.\n4. The paper provides a thorough theoretical analysis of the failures in DDIM inversion, offering a well-founded solution.", "weaknesses": "1. **Limited  improvements**:  Although there are improvements in the quantitative comparisons, I am concerned that the generated results do not show significant improvement than other schedule methods. The differences require careful observation to notice.\n2. **Limited application scope**: While the method is broadly applicable, the current experimental validation focuses primarily on image editing tasks, leaving its effectiveness in other types of tasks.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "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.\n\n**Response to W1**\n> ***Limited improvements: Although there are improvements in the quantitative comparisons, the differences compared to other schedule methods require careful observation to notice ....***\n\nIndeed, in some tasks, especially in attributes editing, the improvement is mainly in the **original content preservation**.\n\nThese 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.\n\n**We've zoomed in on the subtle differences and incorporated extra samples with significant improvements for a more intuitive comparison. \nThese modifications have been synchronized in our manuscript to enhance readability. Once again, thanks for your detailed review.**\n\n\n&nbsp;&nbsp;\n\n**Response to W2**\n> ***Limited application scope: except image editing tasks, the effectiveness of Logistic Schedule in other types of tasks ...***\n\nThanks for the valuable suggestion! \n\nWe agree that broader validation on other tasks can further demonstrate the applicability of our schedule design. \nThe principles behind the Logistic Schedule, such as addressing singularities and improving noise stability, are indeed applicable to other tasks involving diffusion models.\n\nTo 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**. \n\nPlease kindly refer to **Response to Q2** in **\"General Response to All Reviewers\"** for the detailed experimental results.\n\n\n---\n&nbsp;&nbsp;\n\n**Response to Q1**\n> ***Are there specific editing methods that are incompatible with the Logistic Schedule?***\n\nGreat question!\n\nWe 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*. \nAdditionally, we tested it with various **inversion techniques** like *NTI, NPI, EF-DDPM*, and *Direct-Inversion* (please refer to **General Response Answer 1**). \nAll these methods showed consistent improvements when integrated with the Logistic Schedule.\n\nWe 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.\n\nNotably, **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\n\n&nbsp;&nbsp;\n\n**Response to Q2**\n> ***How much do the parameters of the Logistic Schedule affect the results??***\n\nThe parameters of the Logistic Schedule, specifically the **steepness** ($k$) and **midpoint** ($t_0$), play a crucial role in its performance. \n\n**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 $\\color{purple}\\text{purple}$):\n\n| Schedule   | Dist ($_{\\times 10^{-3}} \\downarrow$) | PSNR ($\\uparrow$) | LPIPS ($_{\\times 10^{-3}} \\downarrow$) | MSE ($_{\\times 10^{-4}} \\downarrow$) | SSIM ($_{\\times 10^{-2}} \\uparrow$) | Visual ($\\uparrow$) | Textual ($\\uparrow$) |\n| --------------- | ---------- | ---------- | ----------- | ---------- | ---------- | ----------- | ------------- |\n| **$k=0.015; t_0 = \\text{int}(0.6 T)$** | **17.37** | **24.78**  | 81.80  | 49.47| 82.97   | 82.44| 23.62 |\n| $k=0.08$   | **16.27** | **26.45**  | **75.62**  | **43.20**| **85.28** | **84.07**| 20.47 |\n| $k=0.11$   | 16.64 | 25.80  | 77.90  | 48.83| 84.15   | 83.76| 21.46 |\n| $k=0.17$   | 22.79 | 22.33  | 99.98  | 57.32| 81.52   | 82.10| 23.25 |\n| $k=0.20$   | 27.82 | $\\color{purple}21.05$  | $\\color{purple}103.45$| $\\color{purple}64.36$   | 78.48   | 80.66| **23.81** |\n| $t_0=\\text{int}(0.4 T)$ | 24.31 | 22.41  | 97.21  | 60.84| 79.72   | 79.47| $\\color{purple}20.33$  |\n| $t_0=\\text{int}(0.8 T)$ | $\\color{purple}29.47$| 21.64  | 95.58  | 63.89| $\\color{purple}75.14$  | $\\color{purple}77.05$ | 22.68 |\n\nThese quantitative results reflect the visual results in the main content, that is:\n- **$k$ Changing Shape of $\\text{logSNR}$**: \n    - **Excessive $k$**: Results in excessive loss of original image information in edited images.\n    - **Small $k$**: Resembles $\\text{logSNR}$ of linear and cosine schedules, but better preserves original image content without altering overall structure.\n- **$t_0$ Introducing Shifts in $\\text{logSNR}$**:\n  - **$t_0$ Close to $0$**: Higher lower bound of $\\text{logSNR}$, affecting editability by reducing diversity and fidelity.\n  - **$t_0$ Close to $t_0$**: Original information is lost too quickly, degrading content preservation.\n\nConsidering 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.\n\n> ***Is there a specific method for parameter optimization??***\n\nWe recommend a grid search approach by incorporating CLIP-I and CLIP-T metrics to identify the optimal parameter settings for specific tasks and datasets. \n\n**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.**", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "q4ycboNakA", "reviewer": "Reviewer_vCWG", "summary": "This paper focuses on improving the stability of DDIM inversion to produce a better noise space for image editing. They found that the key issue is the singularity schedule, and try to overcome this issue by adopting the logistic schedule rather than the linear schedule.", "questions": "Please refer to the weaknesses", "limitations": "The authors have discussed the limitations and broader impacts.", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1 This paper found that the singularity issue leads to error accumulation in DDIM inversion, leading to failed or unstable editing results. \n\n2. This paper proposes to adopt the logistic schedule to solve the singularity issue, which is simple but useful.\n\n3. This paper gives many theoretical analyses and visualization results, demonstrating its superiority.", "weaknesses": "1. The original denoising diffusion process has provided the sigmoid schedule, as shown in line 461 of (https://github.com/lucidrains/denoising-diffusion-pytorch/blob/main/denoising_diffusion_pytorch/denoising_diffusion_pytorch.py), which is similar to the proposed logistic schedule. The authors should clarify the diversity between these two schedules. Can the beta sigmoid schedule also solve the proposed singularity problem?\n\n2. The logistic scheduler aims to better preserve the content of the original image. Will the editing ability be decreased if much more original content is preserved? There seems to be a contradiction between the original content preservation and the editing ability for the target prompt.\n\n3. In Fig4, why does the noise map not cover the image for Linear and Cosine schedules?\n\n4. In Tab.2, the results of Null-text, NPI, and Direct should also be provided for better comparison.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate your thoughtful insights, and respond to the suggestions and concerns as follows:\n\n**Response to Q1**\n> ***Difference compared with sigmoid schedule [1,2] ....; can the sigmoid schedule also solve the proposed singularity problem?***\n\nThanks for providing this valuable work [1,2]. \n\nFirst, we present the **mathematical formulation comparison** between the *sigmoid schedule* [1,2] and our *Logistic Schedule*. \nSecond, we clarify the diversity between these two schedules, focusing on the **motivations of design**. \nFinally, we explore the **singularity issues** within the *sigmoid schedule*.\n\n**1.Comparison of Formulation**: \n\n*Logistic Schedule*:\n$$\\bar{\\alpha}_t = \\text{Normalized}(\\frac{1}{1 + e^{-k(t - t_0)}}.$$\n\n*Sigmoid schedule*:\n$$\\bar{\\alpha}_t = \\dfrac{-((t*(e- s)+s) / \\tau).\\text{sigmoid}() + v_e}{v_e - v_s}.$$\nwhere $s$ and $e$ represent `start` and `end` of the range of the $\\text{sigmoid}$ function, and $v_s = (s/\\tau).\\text{sigmoid}(), v_e = (e/\\tau).\\text{sigmoid}()$.\n\n**2.Clarification of Differences**:\n\n**Motivations**:\n- **Logistic Schedule**:\n  - Motivation: Focus on **singularity issues in DDIM forward (inversion)**, enhancing inversion stability and the noise space.\n- **Sigmoid Schedule**:\n  - Motivation: Focus on **adaptive computation for scalable data generation**, particularly for high-dimensional data, without addressing specific challenges of DDIM  forward (inversion).\n  - 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.\n\n**3.Singularities Issues**:\n\n**Moreover, the singularity issue also exists in the *sigmoid schedule***.\n\nDue to the word limit in the rebuttal stage, we only provide the final analytical format of the derivatives of the sigmoid schedule below. \nThe detailed proof has been incorporated in the revised manuscript.\n\nRecap the definition of $\\mathbf{x}_t$:\n$$\\mathbf{x}_t = \\sqrt{\\bar{\\alpha}_t} \\mathbf{x}_0 +\\sqrt{1-\\bar{\\alpha}_t} \\epsilon.$$\n\nTo express the coefficient of $\\epsilon$ in the derivative of $\\mathbf{x}_t$ with respect to $t$, let's start with the given expression for $x_t$:\n$$\\mathbf{x}_t =a(t) \\cdot \\epsilon + b(t) \\cdot  \\mathbf{x}_0,$$\nwhere $\\epsilon$ 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:\n\n$$\\frac{\\mathrm{d}}{\\mathrm{d}t}  \\mathbf{x}_t = \\epsilon \\cdot \\frac{\\mathrm{d}}{\\mathrm{d}t} [a(t)] +  \\mathbf{x}_0 \\cdot \\frac{\\mathrm{d}}{\\mathrm{d}t} [b(t)].$$\n\nHere, 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:\n$$\\frac{\\mathrm{d}}{\\mathrm{d}t} a(t) \\ = \\frac{(e - s) e^{-s - t(e - s)}}{2 \\tau \\sqrt{1 - \\left( \\frac{\\frac{1}{1 + e^{\\frac{s + t(e - s)}{\\tau}}} - \\frac{1}{1 + e^{\\frac{t(e - s)}{\\tau}}}}{\\frac{1}{1 + e^{\\frac{s}{\\tau}}} - \\frac{1}{1 + e^{\\frac{t(e - s)}{\\tau}}}} \\right)^2 \\left( e^{-s - t(e - s)} + 1 \\right)^2}}.$$\n\nWhen $t\\rightarrow 0$, we can have:\n\n$$\\text{ When } t \\rightarrow 0, \\left. \n\\frac{\\mathrm{d}}{\\mathrm{d}t} a(t) \\right|_{t\\rightarrow0} =  \\infty,$$\nwhich reflects the **Proposition 3.1 \"Singularity in Inversion Process\"** in L127-132 of the main content.\n\nFurthermore, we extended the **experimental comparison between the *sigmoid* and *Logistic* schedules**, please refer to Fig. 3 in the attached PDF and **Response to W1** with ***Reviewer B36W***.\n\n**Thank you again for your valuable suggestions on our work. We've incorporated this into our revised manuscript.**\n\n&nbsp;&nbsp;\n\n**Response to Q2**\n> ***Will the editing ability be decreased if much more original content is preserved?***\n\nIndeed, if we adjust $k$ to **preserve much content** at the early stage of inversion, the editability decreases. \n\nTo clarify, the trade-off between preservation and editing exists not only in our scheduler design but also in various image editing methods. \n\nImportantly, the key reason why the Logistic Schedule preserves original content better is **not by sacrificing editability** but **by addressing the singularity issue** present at the DDIM Inversion start point $t=0$.\n\nAs shown in results, the Logistic Schedule achieves better content preservation and maintains the capacity to perform effective edits as directed by text prompts. \n\nWe hope that our explanation clarifies your concerns.\n\n&nbsp;&nbsp;\n\n**Response to Q3**\n> ***In Fig4, why does the noise map not cover the image for Linear and Cosine schedules?***\n\nThanks for pointing this out.\n\nOne misunderstanding to clarify is that Fig4 showed the sampling with total timesteps set to 50 (a setting usually used during inference), so **the final step is 981 rather than 999**.\n\n(**large SNR at the endpoint*) Back to the question, this is because at the end of the DDIM forward process, the SNR of linear and cosine schedules is relatively higher than that of the Logistic Schedule (Fig. 4 (left)), resulting in the retention of low-frequency components at the end [3].\n\n&nbsp;&nbsp;\n\n**Response to Q4**\n> ***In Tab.2, the results of Null-text, NPI, and Direct should also be provided for better comparison.***\n\nWe agree, and thanks for the advice! Please kindly refer to **Response to Q1** in **\"General Response to All Reviewers\"** for these results. \n\n---\n\\\n**We have promptly integrated this revision into our manuscript to enhance the clarity. Once again, we extend our sincere appreciation for your insightful feedback.**\n\n---\n\\\n*[1] https://github.com/lucidrains/denoising-diffusion-pytorch/blob/main/denoising_diffusion_pytorch/denoising_diffusion_pytorch.py*\n\n*[2] \"Scalable Adaptive Computation for Iterative Generation.\" ICML. 2023.*\n\n*[3]  \"Common diffusion noise schedules and sample steps are flawed.\" WACV. 2024.*", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
## **General Response to All Reviewers**

We thank all reviewers for their insightful feedback. We appreciate that the reviewers found our paper theoretically and methodologically novel, with strengths such as 
- **thorough analysis** of DDIM inversion issues and **addressing singularity issues effectively** (***Reviewers j2Zw, B36W, ihj2, Btrz***), 
- **extensive experiments** across various tasks (***Reviewers j2Zw, B36W, ihj2, Btrz***), 
- the **simplicity and usefulness** of the *Logistic Schedule* (***Reviewers j2Zw, B36W, ihj2, Btrz***). 

We are also pleased to announce that the related code and dataset will be open-sourced.

---
\
There were a few shared questions about our paper, specifically regarding (1) **additional comparisons with inversion techniques**, (2) the **broader applicability** of the Logistic Schedule (such as training-based methods).

&nbsp; &nbsp; 

 ### **Question 1**
>  *Additional comparisons with inversion techniques.*

**Response to Q1**: 

&nbsp; &nbsp; 
In the Table 2 of the manuscript, we present the results of collaborating our Logistic Schedule with Various inversion techniques, including *Null-Text Inversion (NTI)* [1], *Negative Prompt Inversion (NPI)* [2], and *Direct Inversion* [3]. 

&nbsp; &nbsp;
Below, we present the comparison with using these inversion techniques with *scaled linear schedule* instead of our *Logistic Schedule*.

| **Variants**| **Structure Dist** $_{\times 10^{-3}} \downarrow$ | **PSNR** $\uparrow$ | **LPIPS** $_{\times 10^{-3}} \downarrow$ | **MSE** $_{\times 10^{-4}} \downarrow$ | **SSIM** $_{\times 10^{-2}} \uparrow$ | **Visual CLIP Similarity** $\uparrow$ | **Textual CLIP Similarity** $\uparrow$ |
| ------------------------------------- | ------------------------------------------------- | ------------------- | ---------------------------------------- | -------------------------------------- | ------------------------------------- | ------------------------------------- | -------------------------------------- |
| **NTI + Linear** | 21.00 | 23.00 | 95.00| 63.00 | 81.50| 81.00| 21.30 |
| **NTI + Logistic** | 18.67| 23.80| 89.64 | 57.97| 82.97  | 82.46  | 21.95|
| **NPI + Linear** | 28.00 | 22.40 | 105.00  | 78.00 | 78.50| 78.50| 20.90 |
| **NPI + Logistic** | 24.82 | 23.17 | 99.19| 71.24 | 80.26| 80.16| 21.53 |
| **Direct + Linear**| 19.00  | 24.90 | 78.00| 45.00 | 83.50| 82.90| 21.90 |
| **Direct + Logistic** | **16.06**| **25.73** | **74.17** | **41.19**  | **85.61** | **83.29** | **22.03**  |

&nbsp; &nbsp;
These results demonstrate consistent improvements on content preservation and edit fidelity with the Logistic Schedule.

&nbsp; &nbsp; 

### **Question 2**
> ***Broader Application**: While Logistic Schedule is broadly applicable in various image editing tasks, can this method be utilized in other types of tasks, including tasks requiring training?*

**Response to Q2**: 

&nbsp; &nbsp;
Below, we include utilize Logistic Schedule in two type of tasks, including (1) **Text-to-Image Synthesis** and (2) **Image Reconstruction**.

1. **Text-to-Image Synthesis  (Training-based methods):**

&nbsp; &nbsp;&nbsp; &nbsp; 
Due to the limited time of the rebuttal period, we conducted experiments on fine-tuning UNet using *Dreambooth* [4] with approximately 100 images.

&nbsp; &nbsp;&nbsp; &nbsp; 
The results are exhibited below, showing that training Dreambooth with the *Logistic Schedule* improves performance. 

| Setting | DINO $(\uparrow)$  | CLIP-I $(\uparrow)$ | CLIP-T $(\uparrow)$ | PSNR $(\uparrow)$  | PRES $(\uparrow)$  |
| --------------------------- | -------------------- | ------------------------ | ------------------------ | -------------------- | -------------------- |
| **Real Images**                            | 0.823 | 0.902  | N/A    | 26.86 | 0.653 |
| **DreamBooth (SD-15) + Linear**  | 0.726 | 0.823  | 0.268  | 24.41 | 0.567 |
| **DreamBooth (SD-15) + Cosine**  | 0.745 | 0.857  | 0.264  | 24.75 | 0.554 |
| **DreamBooth (SD-15) + Logistic** | **0.761** | **0.877**  | **0.293**  | **25.62** | **0.580** |
**The related qualitative comparisons are displayed in Fig. 2 in the attached PDF**.

2. **Image Reconstruction:**

&nbsp; &nbsp;&nbsp; &nbsp; 
Inversion results without any editing directives demonstrate the ability to preserve original content, *i.e.*, image reconstruction. 

&nbsp; &nbsp;&nbsp; &nbsp; 
**Quantitative results are provided in Table 6 in Appendix E.5. Additional qualitative results are included in Fig. 1 of the attached PDF**.

&nbsp; &nbsp; 

**To this end, we’ve added comparisons with other inversion techniques and expanded our experimental scope to include text-to-image synthesis and image reconstruction in the main content. We thank the reviewers for pointing these out.**

---

&nbsp; &nbsp; 

**Further Explanation:**

&nbsp; &nbsp;
The attached PDF showcases detailed qualitative results for the additional experiments, including the use of the Logistic Schedule with Dreambooth, comparisons of reconstruction and comparisons of more noise schedules. 

&nbsp; &nbsp;
We are actively investigating further applications of the Logistic Schedule in various tasks, including those involving training-based methods, in line with the reviewers' suggestions.

---

&nbsp; &nbsp;

*[1] "Null-text inversion for editing real images using guided diffusion models." CVPR. 2023.*

*[2] "Negative-prompt inversion: Fast image inversion for editing with text-guided diffusion models." arXiv preprint. 2023.*

*[3] "Pnp inversion: Boosting diffusion-based editing with 3 lines of code." ICLR. 2024.*

*[4] "Dreambooth: Fine tuning text-to-image diffusion models for subject-driven generation." CVPR. 2023.*

Meta-review: This submission first identifies the singularity issue in the noise schedule during DDIM inversion of diffusion models and proposes a novel logistic schedule. The effectiveness of the proposed method is well validated through extensive experiments and analysis.

The reviewers raised valuable concerns and left comments to improve the submission. The authors addressed the questions and additionally demonstrated the versatility of the proposed methods in the rebuttal. All the reviewers support the acceptance of this work.

There was a flag about the ethical concern, but the ethics reviewer checked and found no issue.
Decision: Accept (poster)