There and Back Again: On the relation between Noise and Image Inversions in Diffusion Models
Authors: Łukasz Staniszewski
Łukasz Kuciński
Kamil Deja
Venue: ICLR 2026 Poster (2026)
Keywords: diffusion models
ddim inversion
image interpolation
Primary area: generative models
TL;DR: We show that DDIM inverted latents exhibit input image patterns, and provide simple fix

Abstract: Diffusion Models achieve state-of-the-art performance in generating new samples but lack a low-dimensional latent space that encodes the data into editable features. Inversion-based methods address this by reversing the denoising trajectory, transferring images to their approximated starting noise. In this work, we thoroughly analyze this procedure and focus on the relation between the initial noise, the generated samples, and their corresponding latent encodings obtained through the DDIM inversion. First, we show that latents exhibit structural patterns in the form of less diverse noise predicted for smooth image areas (e.g., plain sky). Through a series of analyses, we trace this issue to the first inversion steps, which fail to provide accurate and diverse noise. Consequently, the DDIM inversion space is notably less manipulative than the original noise. We show that prior inversion methods do not fully resolve this issue, but our simple fix, where we replace the first DDIM Inversion steps with a forward diffusion process, successfully decorrelates latent encodings and enables higher quality editions and interpolations.

Published as a conference paper at ICLR 2026
THERE AND BACK AGAIN: ON THE RELATION BETWEEN NOISE AND IMAGE INVERSIONS IN DIFFUSION MODELS
Lukasz Staniszewski Lukasz Kuciniski...55 Kamil Deja
1 Warsaw University of Technology 2IDEAS Research Institute University of Warsaw Institute of Mathematics, Polish Academy of Sciences SIDEA NCBR
ABSTRACT
Diffusion Models achieve state-of-the-art performance in generating new samples but lack a low-dimensional latent space that encodes the data into editable features. Inversion-based methods address this by reversing the denoising trajectory, trans- ferring images to their approximated starting noise. In this work, we thoroughly analyze this procedure and focus on the relation between the initial noise, the gen- erated samples, and their corresponding latent encodings obtained through the DDIM inversion. First, we show that latents exhibit structural patterns in the form of less diverse noise predicted for smooth image areas (e.g.. plain sky). Through a series of analyses, we trace this issue to the first inversion steps, which fail to provide accurate and diverse noise. Consequently, the DDIM inversion space is notably less manipulative than the original noise. We show that prior inversion methods do not fully resolve this issue, but simple fix, where replace the first DDIM Inversion steps with a forward diffusion process, successfully decorre- lates latent encodings and enables higher quality editions and interpolations. The code is available at hhttp::/giihubb.omm hwtpgihh......iiii....eeeeeeeeee
INTRODUCTION
Noise
DDIM Sampling
Diffusion- probabilistic models
(DMs), (Sohl-Dickstein al.) 2015).
yplanciin paa
have achieved state-of-the-art results
in many generative domains includ- ing image (Dhariwal & Nichol (021),
Phe sogion
Latent
speech (Popov et al., (2021), video (Ho eet al., (022). and music (Liu et al.; 2021) synthesis. Nevertheless, one of the sigmificant drawbacks that distinguishes diffusion-based approaches from other generative models like Variational Au- toencoders (Kingma & Welling 2014) is the lack of implicit latent space that encodes the images into low-dimensional, interpretable, editable representations.
DDIM Inversion
Figure 1: DDIM inversion produces latent encodings that exhibit less diverse noise in the smooth image areas than in the non-plain one. We attribute this problem to the errors of noise prediction in the first in- version steps.
To mitigate this issue, several works seek meaningful relations in the approximated starting noise used for generations. This method, known as inversion technique,
introduced by [Song lt al. (202)) with Denoising Diffusion Implicit Models (DDIM), and led to the proliferation of works (Garibi al.) al.|2022 [2244] Mokady al., 2023]] Huberman-Spiegelggaan
al., 2024 (amuel al.) 2025 Hong et al.] [ Parmar et al. 2023). ). The core idea is to use the noise predicted by the Diffu- sion Model and add to the image instead of subtracting it. Repeating this process effectively traces the backward diffusion trajectory, approximating the noise that could have generated the image. However, due to approximation errors and biases introduced by the trained model, discrepancies arise between the original noise and its reconstruction latent representation.
"Corresponding author: Tuks. stani i wzwwa' @gnai com

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Published as a conference paper at ICLR 2026
While recent works (Garibi et al., 2024 Mokady al. 2023 Parmar al. 2023 Huberman- Spiegelglas et al., 2024; et al. 2024) try to improve the inversion procedure from the perspec- tive of tasks such image reconstruction, editing, or interpolation, in this work, focus on the inversion process itself and analyze the errors DDIM inversion introduces. To that end, we analyze the relation between sampled noise, generated images, and their inverted latent encodings. First, we review existing studies and conduct additional analyses demonstrating that the reverse DDIM technique produces latent representations with pixel correlations that deviate significantly from Normal distribution. As presented in Figure [ we experimentally show that this deviation manifests as lower diversity in latents, particularly in regions corresponding to smooth image surfaces. We further attribute this discrepancy to the noise approximations in the first few inversion steps.
To highlight the consequences of the observed divergence, we show that the DDIM-inversion-basn latent space is less manipulative than the ground truth noise. This limitation is particularly no- ticeable in lower-quality image interpolations and less expressive edits, especially in smooth input image regions. Furthermore, demonstrate that prior inversion methods, although designed to improve image reconstruction, fail to preserve the Gaussian properties of the latents. Based on our analyses, we propose simple fix, replacing the first steps of the DDIM inversion process with forward diffusion. Finally, we show that such an approach successfully decorrelates the resulting latents, mitigating the observed limitations, and can be combined with state-of-the-e image edit- ing and style transfer engines to further improve their performance. Our main contributions can be summarized as follows:
We show that DDIM latents deviate from the Gaussian distribution, mostly because of less diverse noise predictions for the plain image surfaces during the first inversion steps.
We show that, consequently, the DDIM latents are less manipulative, leading to the lower quality of image interpolations and edits.
We demonstrate that prior inversion methods do not address this issue and propose simple and effective fix by substituting early inversion steps with forward diffusion.
2 BACKGROUND AND RELATED WORK
Denoising Diffusion Implicit Models. The training of DMs consists of forward and backward diffusion processes, where, in the context of Denoising Diffusion Probabilistic Models (DDPMs, Ho et al. (2020)), the former one with training image 20 and variance schedule {3. ) can be
expressed 2, vā vI u,Et, with a; 1 Br, ā. II Ogs and E; ~ (O,
In the backward process, the noise is gradually removed starting from a random noise ær ~ (0, fort T...1, with intermediate steps defined as:
It = Vai-i (x+
a₁ c (re, v)o
(1) (1t, c) +o+ V - ا of .6g
(I)
zo prediction
direction pointing to it
where (1) (Iz, c) is an output of a neural network (such as U-Net), and can be expressed as a com- bination of clean image (xo) prediction, a direction pointing to previous denoising step (x,), and stochastic factor d, where o, n/ //,3(1
1)((1 ā₂) and 2, NO Z). In the standard DDPM model, the parameter is set to = 1. However, changing it to process deterministic Denoising Diffusion Implicit Model (DDIM. Song et al. (20TT), a class of DMs we target in this work.
makes the whole
One of the advantages of DDIM is that by making the process deterministic, we can encode images back to the noise space. The inversion can be obtained by rewriting Eq. (I)
x VatI-11 (VI-a, Vai ā,)
(xt, c).
However, due circular dependency 6 (I22 c), Dhariwal & Nichol (021) propose ap-
proximate this equation by assuming the local linearity between directions (z;-1 + .x)) and (xr, + 1t so that the model's prediction in t-th inversion step can be approximated using #;-1 as an input, i.c.,
10 (2r, c) (0) (x)-11))
(3)
2

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While such approximation is often sufficient to obtain good reconstructions of images, it introduces the error dependent on the difference (I, - Tt-1), which can be detrimental for models that sample images with few diffusion steps or use the classifier-free free guidance (Ho & Salimans| [021] Mokady
et al.
2023) for better prompt adherence. As result, also noticed by recent works (Garibi et al.)
2024
Parmar al. 2023), latents resulting from DDIM inversion do not follow the definition of
Gaussian noise because of the existing correlations. In this work, we empirically study this phe- nomenon and explain its origin. We discuss the relations between the following three variables: Gaussian noise (Xr, an input to generate an image through a backward diffusion process), image sample (Xo, the outcome of the diffusion model generation process), and latent encoding ($r, the result of the DDIM inversion procedure as introduced in Eq.
Image-to-noise inversion techniques. The DDIM inversion, despite the noise approximation er- rors, forms the foundation for many applications, including inpainting (Zhang et al.) 2023a), inter-
polation (Dhariwal & Nichol 2021; Zheng et al. 2024), and edition (Su et al. 2022 Kim et al.
2022a
Hertz et al. [202]] Ceylan et al.]|2003 Deja et al.] (023). Several works (Mokady et al.
2023
Garibi et al. [024]] Sutberman-SSiegelle
et al. [024]] (amuel et al. |025, Hong et al. 2024
Miyake et al.
2023
Han et al. 2024
Cho et al. 2024: Dong et al. 2023] Zhhng et al. 2023b
Parmar et al.
2023 Tang et al. 2024 Wallace et al. [023 Pan et al. 2023 Wang et al, 2024
Brack et al.
2024; Lin et al. 2024; Ju et al. 2024) aim to reverse the denoising process in text-to-
image models, where prompt embeddings
strongly affect the final latent representation through Classifier-fret free- guidance (CFG) (Ho & Salimans 2021). Null-text inversion (Mokady et al., 2023) graiiir--rreeggeaeeeeeeee
extends the DDIM inversion with additional null null-embedding optimization, reducing the image construction error. Other techniques improve inversion for image editing through seeking embed- dings (Miyake al. 2023 Han al. 2024 Dong al. 2023) or leveraging DDIM latents (Cho (et al. (2024) for guidance. On the other hand, some works leverage additional numerical methods (Samuel et 2025 Pan et al. 2023 Garibi et al. (024) to minimize inversion error. In particular, Renoise (Garbi et al. (224)) iteratively improves the estimation of the next point along the diffusion trajectory by averaging multiple noise predictions, incorporating an additional patch-level regular- ization term that penalizes correlations between pixel pairs to ensure the editability of the latents. Huberman--Siegellgaa et al. (2024) followed by Brack et al. (2024) propose inversion methods for DDPMs, enabling the creation of various image edition results via inversion. Finally, to reduce the discrepancy between DDIM latents and Gaussian noises, Parmar et al. (2023) propose to addition- ally regularize final DDIM Inversion outputs for better image editing, Lin et al. (2024) introduce an alternative noise scheduler to improve inversion stability, while Hong et al. (2024) propose an exact inversion procedure for higher-order DPM-Solvers, solving the optimization problem at each step.
ANALYSIS
Model
Diffusion Space
Resolution
Training Dataset
Cond?
Arch
Image
Latent
3DM
Pixel
32x32
CIFAR-10
x
U-Net
In our experiments, we employ six dif- ferent diffusion models, which we com- pare in T For both generation and the DDIM sampler with, unless stated otherwise, T 100 steps. We provide more de- tails on the number of diffusion steps in Appendix N.I
ADM-64
Pixel
64x64
ImageNet
X
U.Net
ADM-2256
256x256
ImagoNes
U-Net
Latent
256x256
3x64x64
CelehA
X
U.Net
D:T
Lakeal
256x256
4x32x32
ImagoNat
DiT
IF
Pixel
64x64
LAION-A
UI-Net
inversion processes,
SDXL
Latent
1024x1024
4x128x128
U-Net
Table 1: Overview of diffusion models used for our ex- periments. We study both unconditioned and conditioned models, operating in pixel and latent spaces. More details on models are provided in Appendix J
3.1 LATENTS VS. NOISE
The inversion process provides the foundation for practical methods in many applications, with the underlying assumption that by encoding the image back with a denoising model, we can obtain the original noise that can be used for reconstruction. However, this assumption is not always fulfilled, which leads to the question:
Research Question 1: Are there any differences between sampled Gaussian noise and la- tents calculated through the DDIM inversion?
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Prior work and findings. This question relates to several observations from the existing literature, which highlight that outputs of the DDIM inver- sion differ from the standard Gaussian noise (Par-) mar et al.] 2023: Garibi et al.) 2024) and that the difference can be attributed to the approximation er- ror (Hong al. 2024; Wallace et al. 2023). While these works notice the divergence between noise and latent encodings, they do not validate them or study the source of this issue.
Model
Noise (XT)
Latent (Krp)
Sample (Xo)
ADM-32
0.039 a 063
0.382 o10
0.9644 022
ADM 64
0.039
0.126 008
0.925+.022
ADM-256
0.039
0.161 #.0L3
0.960+.006
0.039
0.498 ozs
0.936
LDM
0.039. 103
0.045 or
0.645
0.041 0o0
0.103 021
0.748 064
SDXL
0.036
0.155
0.637
Table 2: Mean of top-20 Pearson correla- tion coefficients inside 8 x 8 patches for random Gaussian noises, latent encod- ings, and generations. DDIM Latents are much more correlated than noises.
Experiments. First, we consolidate existing ob- servations on the presence of correlations in the la- tent encodings (RT) and validate them by running an initial experiment that compares latents to im- ages (Xo) and noises (xT) across diverse diffusion architectures. In Table 2 we calculate mean of top-20 Pearson correlation coefficients (their abso- lute values) inside C' x 8 x pixel patches, where C is the number of channels (pixel RGB colors or la- tent space dimensions for latent models). The results confirm that latent representations have significantly more correlated pixels than the noise. In Fig. 2 we show how the measured correlations visually mani- fest themselves ves in the latents. For pixel models such as Deepfloyd IF, we observe clear groups of corre- lated pixels as presented in Fig. 2h. For latent dif- fusion models, we can highlight the inversion error by plotting the difference between the latent and the noise, as presented in Fig. F... This property also holds for LDMs with a 4-channel latent space, with the use of PCA (Fig. (
AAz xy
(a) IF
(b) LDM
(c) DiT
Figure 2: Latent encodings exhibit im- age patterns. For small pixel-space models (a), we observe correlations directly in the inversion results. For larger models (c.g., LDMs), the same patterns can be observed in the absolute errors between the latent and noise (b). This observation also holds for LDM models operating on 4-channels, where we use PCA for visualization (c).
Conclusion. Our initial experiments numerically validate observations from recent studies and demonstrate that latent representations computed using the DDIM inversion deviate from the ex- pected characteristics of independent Gaussian noise. Specifically, both visual analysis and quanti- tative evaluations reveal significant correlations between the neighboring pixels.
3.2 LOCATION OF LATENT ENCODINGS SPACE
To delve deeper, we first propose to empirically analyze the nature of this issue, posing a question:
Research Question 2: How do DDIM inversion latents differ from the Gaussian noise?
Experiments. To answer this question, we
Interpolation Step
ADM-64
DIT
1.00
first geometrically investigate the location of the latents with respect to the generation trajectory. We analyze the distance between the following steps (#z ) 1 of the backward diffusion pro- cess and intermediate points on the linear inter-
0.8
0.75
0.5
0.5
0.50
0.25
0.2
0.00
polation path between the noise and the DDIM latent. The results of this experiment are pre-
Ør 80
20 20
27
80
20
20
Denoising Step
sented in Fig. 3 where each pixel, with coor- dinates (t, A), is colored according to the l2 dis- tance between the intermediate trajectory step I, and the corresponding interpolation step. This distance can be expressed as [[(1 + zell2- For better clarity, we normalize the dis- tances column-wise.
Figure 3: lg-distances between intermediate denoising steps I; and points on the linear in- terpolation path from noise XT to the inverted latents ÅT. The consecutive intermediate gener- ation steps along the sampling trajectory conse- quently approach the latent.
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We observe that, while moving from the initial noise (x1) towards the final sample (Xo), the inter- mediate steps Iy approach the DDIM inversion latent (&r). while after the transition point around 50-70% (timesteps 50-30) of the generative trajectory. the distance to the latent becomes lower than the distance to the starting noise. This observation reveals that latents retain some characteris- tics of the original samples and contain information about the source generation.
Similar observation can be made on the basis of vi- sualizations in Fig. [ where we can distinguish the
Absolute Error Non-plain
Standard Deviation
Plain
Plain
Non-plain
coarse shape of the original objects in the latents.
Noise (det.)
In particular, while the pixels associated with the objects have high diversity. the areas related to the background are much smoother. This leads to the hypothesis that the most significant difference be- tween the initial noises and latent encodings the limited variance in the areas corresponding to the background of the generated images. To validate it, we compare the properties of the latents between plain and non-plain areas in the image. We deter- mine binary masks Mp by calculating the abso- lute difference between neighboring pixels. Pixels where this local variation falls below a fixed thresh- old (T = 0.025) across all channels are classified as plain regions, effectively isolating low-texture areas (see Appendix H for more details). This pro- cedure selects areas, such as sky, sea, plain backgrounds, or surfaces. In Table 3 we show that the error between the starting noise XT and the latent रT resulting from the DDIM inversion is higher for pixels corresponding to the plain areas. Across the models, this trend goes along with a decrease in the standard deviation of the latents' pixels related to those regions. suggests that DDIM inver- sion struggles with reversing the plain image areas, bringing them mean (0) and reducing their diversity. Additionally, in Appendix [P] we present that correlations and reduced latent diversity for plain image regions can be similarly observed within Flow Matching (Lipman et al. 2023) models.
ADM-32
0.49
0.43
U.34
0.46
ADM-64
0.22
0.15
0.49
0.64
ADM-256
0.29
0.33
0.66
IF
0.56
0.40
0.46
0.72
LDM
0.13
0.03
DIT
0.12
0.06
0.43
0.54
SDXL
0.30
0.26
0.87
0.96
Table 3: Average per-pixel absolute error
(between noise and latent) and standard deviation of the latents' pixels correspond- ing to the plain and non-plain image areas. The error for plain pixels, where latents are less diverse, is higher than for other regions.
Conclusion. Latent encodings resulting from the DDIM Inversion deviate from the Gaussian noise towards zero values. This is especially true for parts of the latents corresponding to the plain image surfaces. This observation reveals that inversion outputs retain some characteristics of the original input samples and contain information about the source generation.
3.3 ORIGIN OF THE DIVERGENCE
Given the observation from the previous section, now investigate the source of the correlations occurring in latent encodings. posing the question:
Research Question 3: What causes the spatial correlations observed in DDIM latents?
Experiments. We recall that the DDIM Inversion error can be attributed to the approximation of
the diffusion model's 's output at step t E 1. T with the output from step t -- 1 (see Eq. (3) Hence, we can define the inversion approximation error for step t as the difference between DM's output for the current and previous inversion timesteps / and - 1 as:
E(()
Fe (I2-1, (1) (2
(4)
E!
where & is the true model prediction at step 1, and El is the Dhariwal & Nichol 2021] approxi- mation using the previous step as an input. Based on the observations from the previous section, we propose to investigate how the approximation error (()) varies across pixels in plain and non-plain image areas throughout the inversion process. To that end, we average the approximation errors for 4000 images for each of the = 50 diffusion timesteps. To measure the error solely for the analyzed step we start the inversion procedure from the exact latent from step (t [t=1] 1) (cache from the sampling path). We split the latent pixels into plain and non non-plain areas based on the masks calculated for clean images. More details on this setup can be found in Appendix
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In Fig. 4a. present the visualization of calculated differences for each inversion step. There a sigmificant difference in prediction errors between plain and non-plain areas, especially in the initial steps of the inversion process. Notably, for pixels associated with plain image areas, the error predominantly accumulates within the first 10% of the inversion steps. Additionally, in Fig. 4b, we present that this error discrepancy is strongly connected to decrease in the diversity of diffusion models' predictions. More precisely, we calculate a ratio of the predictions' standard deviations between the sampling and inversion processes for the associated timesteps. We show that, for plain image regions, there is a significant decrease in the fraction of predictions' variance preserved during the first inversion steps. Those observations can be related to recent works (Lee et al.) [023 Lin et al.) 2024) analyzing why numerical solvers incur sig- nificant emrors during the earliest diffusion steps (as t + 0). Specifically, [eee et al.] (2023) trace the er- the 1/t curvature blow-up of the reverse-time ODE trajectory, whereas Lin et al. (2024) attribute the predominance of early DDIM inversion approxi- mations to a singularity arising from commonly used noise schedules. Our experiments extend those stud- ies by showing that the eπrоr can be mainly attributed the plain regions in the original images.
Plain pixels
Non-plain pixels
std( (edlg)//stdle let E
1.3
1e-4
(a) DDIM Inversion error
0.9
0.5
0.1
5
15
25
45
(b) % of variance recovered
100
90
80
5
15
25 35
45
Timestep
Figure 4: Discrepancy of the DDIM noise predictions for plain and non-plain image pixels. We show that, in the first inversion steps, the approximations are significantly (a) more erroneous and (b) less diverse for plain regions than for the rest of the image.
Conclusion. Early approximations during the DDIM Inversion procedure result in unequally dis- tributed errors across pixels related to the plain and non-plain image areas, which are the origin of the structural patterns and correlations in the latents.
CONSEQUENCES OF THE DIVERGENCE AND HOW TO MITIGATE THEM?
After identifying the differences between the noises and latents, and highlighting the origin of this phenomenon, we finally pose the last question:
Research Question 4: What are the practical consequences of the divergence between noises and inverse DDIM latents, and how can they be mitigated?
Our findings in Section 3.3 indicate that the initial inversion steps predominantly contribute to the divergence between DDIM latent variables and Gaussian noise, in the form of insufficiently diverse approximations of diffusion model predictions. Therefore, as a simple fix to this issue, we propose replace the first inversion steps with random noise, in forward diffusion process. The rationale behind this decision is twofold:
Substituting initial steps with Gaussian noise allows us recover the noise variance exactly when the DDIM inversion fails to do so.
Recent studies (Deja al. 2022 Liu et al. 2025 Li Chen 2024 Fesl et al. 2025) have
shown that final steps of the backward diffusion do not contribute additional generative information, instead functioning as data-agnostic denoising process. Therefore, the exact inversion of those steps is less important for accurate reconstruction.
The proposed inversion step therefore defined as follows (see Appendix F for pseudocode):
ift < t' [Varte-1+ (VI - Va, -Eg (I.-1,))
Varza VI Cie,
(forward diffusion)
21
(5)
ift> L'
(DDIM inversion)
Before moving to practical applications, we first evaluate the effectiveness of this approach using N 10000 images generated with T = 50 steps using DiT and IF models. For such generations, first noise them with a forward diffusion to the intermediate step t', followed by the DDIM inversion
for T t' steps, ending up with an approximation of the initial noise. In Table 4
we show that

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Published as a conference paper at ICLR 2026
BiT
prompt gencrations from:
oppaccal by
Piezl
Recoremmction Abunlat: Finer
KL. Do
Pool
Reconstaation Absolunc Einrr
KL.
Model
Region
Noise
Latent
Laten
forwadd (KT)
Con
X10ma
Cerr
x300-1
(beseline)
DDIM Lax:
w/Forwad 4
Nuna
DDMM lateni
1C2))
1..:5 (iin
1...2 ((55))))
0.16
001
601
0.00
0.07
0.05
0.10
0300
0.33
0.19
0.25
0.30
11.57
0.6
0.6
0.00
0.05
0.36
1021
1000
0.67
007
008
608.25
1015
0:30
0:05
0:12
IXT
IF
Nec plain
Neo-plain
Plain
Plain
18,00
1324
16.49
17:00
14.00 (+16 (4)
11:55 (112.9)
1534 7.0)
17.35 (+ 6.9%)
(618(-119%)
(3.7(2278) (-.16(-2-4))
(-2.7%)))
I... 10 (2096)
0.04
0.35
0.45
0.06
0.10
0.40
Table 4: Structures can be removed from DDIM latents by replacing inversion steps with forward diffusion. Using forward diffusion instead of the first 4% of inversion steps brings the resulting latents closer to Gaussian noise without& major degradation in the image reconstruction.
Table 5: PNG bit-rate (bits / pixel) after saving only the masked pixels. Higher compression (lower bpp) means less local variability in the pixel stream. Values in parentheses are the percentage change with respect the noise baseline.
Gaussian Noise (x')
DDIM Latent (F))
Latent (4% forward)
ADM-32
ADM-64
ADM-256
LDM
DIT
21.20
35.91
48.73
24.31
18.03
5.84
25.14
35.48
19:61
14.89
Recall f Precision t
0.2
0.5
0.8
0.2
0.5
0.8
0.2
0.5
0.8
0.2
0.5
0.8
0.2
0.5
0.8
0.78
0.93
0.46
0.81
0.52
0.57
0.67
0.41
0.78
0.5
0.8
0.5
0.8
0.2
0.5
0.8
0.2
0.5
0.8
0.8
0.59
0.45
0.36
0.50-
0.48
0.22
0.23
0.09
0.40
0.41
0.8
SLERP
Figure 5: The quality and diversity of images generated from interpolations of latents ÅT deteriorate along the path, as indicated by, accordingly, the FID peak and Recall decrease. In contrast, the quality of generations from noise XT interpolations remains stable. Our simple fix, which is replacing 4% of the first inversion steps with forward diffusion, alleviates this issue.
by replacing just 4% of the inversion steps, we can completely remove correlations in the latents, up to the level of random Gaussian noise. This replacement percentage allows trade-off between reconstruction fidelity and latent manipulability. We observe that this trade-off is highly favorable: replacing the first few steps (t' 4%) restores the Gaussian properties required for diverse editing, while maintaining a reconstruction error that remains within the perceptual noise floor (see Appendix N.2 for detailed analysis). To further evaluate this effect, in Table we measure the sizes of the different parts of images (plain vs non-plain) after saving them with PNG lossless compression. Compression most effective on parts related to plain images generated from DDIM latents, what inclines low diversity in their values. At the same time, replacing only 4% of inversion steps significantly reduces this issue. In the following sections, divergence between noise and DDIM latents has significant practical consequences, and show that our approach for removing correlations consistently mitigates them.
navigate the
further demonstrate that the
4.1 INTERPOLATION QUALITY
We start with the task of image interpolation, where the goal, for two given images, is to generate a sequence of semantically meaningful intermediary frames. Numerous methods (Dhariwal & Nichol
2021
Song et al. 2021 Samuel et al. 2023 Zheng et al.] 2024 Zhang et al.) 2024b) Bodin et al,
2025 employ Diffusion Models with DDIM inversion technique to obtain latent encodings from
input images, interpolate them, and regenerate back to images. (Song et al. (2021) propose to use the spherical linear interpolation (SLERP, Shoemake (1985). that, for two objects and y, with coef- ficient À E [0; 1]. is defined as (A) [1-A1 T + sin Ae, sin
sin 9 y, where = arccos ((x- ((x-y)/ w)/([[=|]]b]]]))
In our experiment, end, we sample N = 20k noises, use DDIM with = 50 diffusion steps to generate images, and invert those images back into their latents. Next, randomly assign pairs, which interpolate with SLERP for À E {0, 1 1 2 10k, generations starting from interpolations between random noises (in orange) preserve consistent
compare the quality of interpolations in the noise and latent spaces. To this
g. 3: 2. 3 1 and denoise. In Fig. 5 we show that, by calculating FID-
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lncul image source prompee
prompt generatte on
Veeu image Rourro prompt
Coussian rdiae
DOMM Inwesian Intert
DOMM bowe we farword
roon
stact
wi forword 6%
backgrandd
ect aouas
M
A$10g "an "an.ggus"" "as. Wotee
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Figure 6: Image editing by reversing the original image with source prompt and reconstruct- ing it with target one. DDIM Inversion produces less diverse image changes when the manip- ulation related to plain regions in source images, contrary to when using ground-truth Gaussian noise. Replacing the first inversion steps with forward diffusion leads to more editable latents.
quality along the entire path, meaning that all interpolated images fall into the real images manifold. In contrast, this property collapses for the setting with DDIM latents as inputs (in purple). In the fol- lowing rows, we show that worse interpolation results for latents stem from the decline in the variety of produced generations, as indicated by a lower recall (Kynkäänniemi et al., 2019). especially when getting closer to the middle of the interpolation path. Nevertheless, presented in Fig. [S] using our fix for the first 4% of steps mitigates this issue, enabling higher-quality interpolations with better diversity of the intermediate points. In Appendix [.1] present qualitatively that the proposed fix leads to more diverse interpolations, especially in the image background.
4.2 DIVERSITY AND QUALITY OF IMAGE EDITION
Apart from image interpolations, text-to-image diffusion models with DDIM inversion are often used for text-based edition, where source image is first inverted and then reconstructed with different target prompt (Hertz et al.] 2022, Mokady et al. 2023) Garibi et al.) 2024 Huberman- Spiegelglas et al.) 2024). However, knowing that DDIM latents are less diverse in plain areas, we hypothesize that using them as a starting point might reduce the diversity and quality of the edited samples. To evaluate this, use DiT (Peebles & Xiel 2023) and IF (StabilityA] 2023)
as conditional DMs with T = 50 diffusion steps. For each model, we construct two sets of 1280 randomly selected (1) source prompts Ps, used during the generation and inversion, and (2) target prompts Pr, used for edition. Using source prompts Ps. we generate images Is from Gaussian noise XT and invert them back into the latents ÅT. Next, we regenerate images IT from the latents, changing the conditioning to the target prompts Pr. We compare the edits with ground truth targets IT generated from the original noise with Py. In Fig. 0
we present the drawback of leveraging latents as starting points for the denoising, where the structures for Is images' backgrounds limit editing performance in i target images.
In T we quantitatively measure this effect. First, we calculate the diversity of target generations (I) against source images (Is). We use DreamSim distance (Fu et al. 2023). LPIPS (Zhang et al.) 2018). SSIM (Wang et al. 2004), and co- sine similarity of DINO features (Darcet al. 2024) to measure the distance be- tween two sets of generations. The experi- ment shows that edits resulting from latent encodings ir are characterized by higher similarity (SSIM, DINO) and lower diver- sity (DreamSim, LPIPS) relative to starting images Is than the one resulting from noises IT. At the same time, in the bottom rows of Table 6 we show that the correlations occurring in the latent encodings induce lower performance in text-alignment to target prompts Pr. which we measure by calculating cosine similarity between text embeddings and resulting image embeddings, both ob- tained with the CLIP (Radford et al. 202I) encoder. Additionally, to better assess image editing quality, we directional CLIP similarity (Gal et al. 2022).
Property
Metric
Noise Xyy
DrT
Latent &y.
Noise Xop
Decpfloyd
Latent Sep
DreamSSm
1.71
0.67
Diversity against Is
IPIPS 1
0.59
0.56.612
0.38
0.33
SSIM
0.23-p11 13
0.26 14
0.34gan5
0.41 15
DINO 1
0.17
n.23
0.34
n.12
Text alignment
CLIP:T (P+)
CLIP- (PS)
0.681
0.465
0.150
0.662
B273
0.614
03333
Directional
0.570
0.541
0.776
0.676
Table 6:
Diversity of editions (generations from noise XT and latents åT, conditioned on tar- get prompt) in relation to source images Is and their alignment with source, target, and directional prompts. The arrows (f/L) indicate greater generation diversity and higher text alignment to the target prompt.
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DDIM Latent
Noise Xr
Latent (4% forward)
LPIPS
7 1-SSTM
1-CLIPA t
CLIPr,
Dir. CLIP
1
70.1
70.9
77.3
22.2
68
76
76.727.6
67.7
66.2
66.0 66.096.5
67.6
66.1
80.9
59.4
52.0 53.5
61.4
54.1
56.557.0
DI1
1F
D11
D11
DII 1F
D11
1F
(a) Image Diversity
(b) Text Alignment
Figure 7: Replacing first DDIM inversion steps with forward diffusion improves editions' pixel diversity (a) and prompt-alignment (b). For IF and DiT models, diversity of generations can be improved by leveraging the forward diffusion process in the first inversion steps, and denoising resulting latents with a different prompt. Additionally, we observe a boost in generations' alignment to the target prompts, indicated by the larger Directional CLIP Similarity, larger CLIP-T value for Pr, and the smaller one for Ps. We present details of the experiment in Appendix K
We further evaluate how replacing the first inversion steps with the forward diffusion affects the diversity and text alignment of generated outputs. As shown in Fig. 7.. swapping the first 4% of DDIM inversion steps with forward diffusion improves the diversity of images generated from latents almost to the level of the samples from original noise. At the same time, as presented in Fig. 7p. replacing the first inversion steps leads a significant decrease in generations' alignment to the source prompt (Ps) and an increase in similarity to the target one (Pr). This can also be observed in visualizations (Fig. Moreover, because of the random noise added as the initial inversion steps, as presented in Appendix 0.3 our approach enables stochastic image editing, producing diverse manipulations of the same image.
4.3 DO EXISTING INVERSION METHODS FIX THE CORRELATIONS?
So far, we have demonstrated the issues of the classical DDIM inversion method. In this section, investigate whether novel inversion methods introduced in prior work resolve the issue of selec- tively reduced diversity in latents. We employ the Stable Diffusion XL (Podell et al.) (2024) model and, using 2000 generations from COCO-30K prompts, measure the normality and editability of the resulting inversions, as well as image reconstruction performance. For fair comparison, we use the same number of NFEs. Results in Table indicate that methods based on predicted noise reg- ularization, such as Pix2Pix-Zero (Parmar et al., 2023) and ReNoise (Garibi et al. 2024). while slightly improving the latents' quality, do not offer significantly better editability, while being two times slower than DDIM. On the other hand, replacing DDIM approximation (Eq. 3 with reverse DPMSolver (Lu et al., 2022) leads to decorellated latents at the cost of high image reconstruction error. We show that our fix offers the best editability of latents with minimal reconstruction loss, all at the lowest computational cost. To be more precise, thanks to the fact that selected inversions steps replaced with the randomly sampled noise the least important in terms of accurate recon- struction, we can observe no increase in the reconstruction error when replacing 2% of forward steps (up to the 2nd decimal point of MAE), while for 4% of steps the additional error is around 1% of pixel deviations a value below the threshold usually employed by adversarial attacks as being not noticeable by human eye (Madry et al. 2017). This replacement percentage allows us navigate the off between reconstruction fidelity and latent manipulability.
Prior
Normality Corn. à
KL
MAE.
Image Reconstruction LPIPS
PSNR
Source
CLIP Aligmment Target
Direct, 1
[sfimage] J
time
Gousstan Noise
D.B8+
0.10
31 31.8811140
73.31en
80.0
DDIM
0.16g o
0.10&.05 05
27.58
54.99g11.30 36
69.58.10.1 10
7.17
Hi22Px-7ero
50
0.15 02
0.85
0,03
0.10+
27.35
34.86==1.19
60.73-20.122
70.80411787
22.07=1.44
RoNoisc (T=50, K=1)
0.14g
0.73
0.04
0,09
25.64
31.89
68.87
76.47 76.47
19.86
ReNoise (T=15, K=2)
0.14g 0
0.59
0.
24.81
35. 35.21gn14
69.68_1000
21.17
15.30_ t1
RoNaise (T-17, K-3)
51
0.13 02
0.47
0.066
0.13+.05
22.35
35.79
60.04.9.06
75.20
14.31
DPMSolvar1 (T=50)
0.09
0.50
0.06
0.300
22.55
70 70.26- 31.81211100
74. 74.76.
7.062.0
DPMSolven (T=25)
0.09
0.26
0.14+.07
24.76
31.69=11.35
71.2449.04
76.17+15.10
7.06g.co
Ours fforward 2%)
0.14. 02
0.71
0.03
0.10,
27.12
34.32 1222211.4
70.21 30:3
76.76.17.7
7,00, c.co
Ours (fowwrrd 4%)
48
0.09
0.38
0.04
0.14
25.68
33.62
72.17
78.91
6.861-11
Table 7: Evaluation of inversion methods across multiple metrics: latents normality, image reconstruction, prompt alignment, and speed. DDIM with the proposed fix offers a good trade- off between latent editability and image reconstruction, while increasing the inversion speed.

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Published as a conference paper at ICLR 2026
4.4 IMPROVING STATE-OF-THEE ART EDITING ENGINES WITH OUR FIX
Finally, we evaluate the possibility of combining our simple fix with existing methods designed for real image manipulation. We adapt StyleAligned (Hertz et al. 2024), the state-of-the-art method for transferring a style from a reference image to new generations, and MasaCtrl (Cao et al.) (023). a complex editing engine for text-based real image editing. these methods employ Naïve DDIM Inversion to find starting noise for input images, we can directly apply our simple fix to those tech- niques, without changing their generation procedure.
CLIP Prompt Alignment
Set Consistency (DINO)
Set Consistency (CSD)
Style Similarity (DINO)
Style Similarity (CSD)
Inversion Method
Naive DDIM
0.795
0.476
0.552
0.690 0.510
0.505
Ours (forward 4%)
0.795
0.471
0.554
0.697
Table 8: Style transfer from reference image with StyleAligned (Hertz et al. 2024) incorporat-
ing Naïve DDIM Inversion and version with our fix. Our fix improves similarity to imput style.
We evaluate style transfer by measuring generations' alignment the prompt, set consistency (pair- wise cosine similarities of DINO (Darcet et al. 2024) and CSD (Somepalli et al., 2025) embed- dings). and style consistency with the reference image (cosine similarities of DINO and CSD em- beddings). The Table 8 compares the performance of vanilla StyleAligned and the version with our fix in style transfer from StyleDrop (Sohn al., 2023) images. As presented, our approach improves the alignment with the target style. Additionally ly. in Fig. 8 we present qualitative comparison of both inversion algorithms when combined with StyleAligned (1) for style transfer and MasaCtrl (2) for real image editing. More examples can be found in Appendices 0.4 and 0.5
(1) Style transfer with StyleAligned "cow"
"butterfly"
"avocado"
"baby penguin"
"avocado"
DDIM Inversion
DDIM Inversion
style: painting
Reference style: "wttercolor"
Ours (forward 4%)
Ours (forward 4%)
(2) Image editing MasaCtrl
Input
DDIM Inv. Ours (4%)
Input
DDIM
(4%)
Input
DDIM
Ours (4%)
puppy aitting field of dandelions
weemingg Tiger
colorful porret wings spread
"at astronaut standing the water with- the clouds backiground
"o.. on the roef of night" cat dog
pointing of sifting loundry room shapherd dog poodle dog
Figure 8: DDIM Inversion with our fix, when merged to popular image manipulation engines, improves (1) style transfer with StyleAligned and (2) image editing with MasaCtrl. We use real images from, accordingly, StyleDrop (Sohn et al. 2023) and PlEBench (Ju al. 2024) benchmarks.
CONCLUSIONS
This work demonstrates that DDIM inversion errors cause latent representations to systematically deviate from Gaussian distribution, particularly in smooth regions of the source image. We trace this to high inversion error and insufficiently diverse noise during the early noising steps, and demon- strate that this divergence degrades the quality of image editing and interpolation. We propose sim- ple fix by replacing initial inversion steps with forward diffusion, which successfully decorrelates the latents and significantly improves sample quality in practical applications.
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ACKNOWLEDGMENTS
We thank (in random order) Wojciech Masarczyk, Bartosz Cywińskki, Katarzyna Zaleska, and Pawef Skiers for insightful feedback and discussions throughout the project. This work was funded by the National Science Centre, Poland, grant no TMO-2023/51BB/S6600000 puting resources were provided by the PL-Grid Infrastructure, grant no.: PLG/2025/018390 and PLG/2025/01 8424. This paper has been supported by the Horizon Europe Programme (HORIZON- EL4-2022HHUMANY under the project GA no. 101120237.
The com-
"ELIA: "ELIAS: European Lighthouse for Sustainability",
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A APPENDIX
CONTENTS
Limitations
19
LLM Usage
19
Broader impact
19
Compute resources
19
Approximation error in DDIM Inversion
20
Pseudocode for DDIM Inversion with Forward Diffusion
21
Most probable triangles
22
G. Methodology
22
2 Results
22
G.3
Example histograms
23
H
Plain surface thresholding
24
Calculating inversion error
25
J
Conditioning for Diffusion Models
26
Details on diversity and alignment of edition
26
Noise-to-image mapping
27
L.1 Smallest la mapping
27
L,2 Asymmetry of Noise-to-Image mapping
28
M On Noise-Image-Lateet relations during diffusion training
29
M. Spatial relations of noise and latents over training time
29
M.2 Image-to-noise distance mapping training time
29
M.3 Image alignment over training time
30
N Parameter impact analysis
33
N.I Number of inversion steps
33
N.2 Percentage of inversion steps replaced
35
Guidance scale
37
0
Qualitative examples
39
Image interpolation
39
0.2
Reconstructions of real images
40
Stochastic image editing
0.4
Real image editing with MasaCtr)
42
0.5
Style transfer with StyleAligned
44
atent correlations in Flow Matching models
46
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In the Appendix, we first outline the limitations (A) of our experiments, LLM usage during writing (B), discuss the broader impact (C) of this work, and list the computational resources (D) used. Fol- lowing, we describe, in detail, the DDIM approximation error (E), and the fix introduce (pseu- docode) in this work (F). Next, we describe our experiments: measuring the noise-image-latent triangles (G), methodology for identifying plain-regions pixels (H) in the image, and computing the inversion error (I). In (J), we demonstrate how we condition the models, and in (K), we present more details on image diversity and prompt alignment during editing. Next,
compare Gaussian noise and DDIM latents in their mappings to images (L) and track how these relationships evolve during DM training (M). In section (N) discuss the impact of different parameters' values: number of inversion steps used, number of inversion steps replaced with forward diffusion, and the impact of guidance scale. (O), we include additional qualitative results for image interpolation, reconstruc- tion, editing, and style transfer. Finally, in section (P), we present that the investigated issue with latents' correlations also exists in Flow Matching models.
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A LIMITATIONS
In this work, we analyzed the relation between the random noise, image generations and their latent encodings obtained through DDIM Inversion. While our studies focused on DDIM approximation error from (ong et al. (022I). there exist other solvers and inversion methods, as described in Sec- 2 bringing their own advantages and limitations. The error of DDIM inversion strongly depends on the number of steps with which it is performed. In particular, performing the process very gran- ularly, e.g., using
1000 steps, can result in strong suppression of the correlation. Nevertheless, the default number of steps we have chosen, i.e., 100, is, according to previous works (Hong et al.) 2024 Garibi et al., [024] Kim et al. (0022)), practical choice as a good balance between the recon- struction enror and the speed of the algorithm. In Appendix N.1 we present that the latents exhibit correlations when using 1000 sampling steps, and that the proposed fix can also help in such cases.
The observations from our analytical experiments (correlations in Table 2 interpolations in Fig. 5 generalize well to all tested diffusion models, but are less evident in the LDM model trained on the CelebA-HQ images. We attribute this exemption to the specificity of the dataset on which the model was trained - photos with centered human faces, usually with uniform backgrounds. We believe that, unlike models trained backgrounds is more stable and introduces little detail in subsequent steps, making the difference in approximation error for plain and non-plain areas less significant.
larger number of concepts, the process of generating faces with uniform
As mentioned in Section 2 the DDIM inversion error can be detrimental when using small number of steps. Even though the solution proposed in this work (involving forward diffusion in first inver- sion steps) drastically removes correlations in latents and, thus, improves image interpolation and editing, it does not improve the numerical inversion error resulting from using a small number of steps. In our experiments with 50 steps that are commonly used for editing, we show no significant drawbacks. However, in the extreme cases, using our fix in even a single step might result in the loss of information necessary for correct image reconstruction. hence it may then be less preferred than standard DDIM inversion. Appendix N.I. we present failure cases for the introduced solution.
B
LLM USAGE
Throughout the preparation of this manuscript, we employed a large language model (LLM) as a writing assistant. Its was focused improving the clarity and readability of the text, correcting grammar. and refining sentence structure. The authors carefully reviewed, edited, and take full responsibility for all content, ensuring the scientific integrity and accuracy of the final paper.
C BROADER IMPACT
As our work is mostly analytical, we do not provide new technologies that might have significant societal impact. However, our solution for improving the accuracy of DDIM inversion has potential implications that extend beyond technical advancements in diffusion models. As our fix enables more prompt-aligned image editing, it could be combined with various editing engines and misused advance image manipulation techniques. The enhanced interpolation quality could make synthetic content more convincing and harder to detect. The authors do not endorse using the method for deceptive or malicious purposes, and discourage any application that could erode trust or cause harm.
D COMPUTE RESOURCES
For the experiments, we used a scientific cluster consisting of 110 nodes with CrayOS operating system. Each node is powered by 288 CPU cores, stemming from NVIDIA Grace processors, each with 72 cores and a clock speed of 3.1 GHz. The nodes are equipped with substantial memory, featuring 480 GB of RAM per node. For GPU acceleration, each node in the cluster consists of NVIDIA GH200 96GB GPUs with 120 GB of RAM and 72 CPUs per GPU.
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Almost all the experiments perform are based on performing a sampling process using diffusion model from noise, performing DDIM inversion, and, possibly, image reconstruction from the latent, where each of these processes takes the same number of steps, hence the same number of GPU-hours on average. As our experiments differ in terms of number of sampling steps and images to generate, provide average GPU time per one sampling step per batch (with B denoting batch size) for each model as following: ADM-32 (B = 256): 0.054s, ADM-64 (B = 128y: 0.093s, ADM-256 (B3 64): 0.901s, LDM (B 128): 0.273s, DiT (B 128): 0.104s, IF (B 64): 0.609s. Note that some experiments, such as analyzing inversion approximation errors per step (Fig. 4 or sam- pling from noise interpolations (Fig. 5.. involves performing the procedures several times. Taking into consideration all the experiments described in the main text of this work, fully reproducing them takes roughly 110 GPU hours. However, considering the prototyping time, preliminary and failed experiments, as well as the fact that most of the experiments must be performed sequentially (e.g., inversion after image generation, image reconstruction after inversion), the overall execution time of the entire research project is multiple times longer.
E APPROXIMATION ERROR IN DDIM INVERSION
Denoising Diffusion Probabilistic Models (DDPMs, Ho et al. (2020) generate samples by reversing the forward diffusion process, modeled as Markov Chain, where clean image zo is progressively transformed to white Gaussian noise xr in T diffusion steps. A partially noised image Tt, which serves as intermediate object in this process, is expressed as 2; vārzo + vI- vāe where āe IT Os, Og 1 Be, C (N, I), and {B.)T- is variance schedule, controlling how much of the noise is contained in the image at the specific step t.
To enable sampling clean images from clean Gaussian noises, the neural network eg is trained to predict the noise added to a clean image To for a given intermediate image T,. Such a trained model is further utilized in the backward diffusion process by iteratively transferring more noisy image
(x²) to the less noisy one (x4-1) as
3.
01
(x2
c0 (x:)) + o+2,
(6)
Vot
VI
Ctt
with I0, being noise portion added back for denoising controlled by oz v [c(1 -(-1)/((-10))) az).
Song et al. (2021) reformulate the diffusion process as a non-Markovian, which leads to a speed- up of the sampling process. While previously obtaining less noisy image at He required all past denoising steps from T till (t- 1). this approach allows skipping some steps during sampling. More precisely, the backward diffusion process defined as a combination of predictions of image To.
next denoising step It, and random noise (with o = 1/ (1 at 11-1)/(1 ā.)) and 24 N I)):
Øt-1 =Vā--
X1
vI ai (2i4)
+ 11-au- āo-1 of (1) (xx) - ot
(7)
vāz
While setting 1] = 1 makes Eq. equivalent to Eq. (6). leading to a Markovian probabilistic diffusion model, setting 1 = removes the random component from the equation, making it a Denoising Diffusion Implicit Model (DDIM), which prominent ability is to perform a deterministic mapping from given noise (xT)) to image (zo0). One of the potential benefits of implicit models the possibility of reversing the backward diffusion process to transfer images back to the original noise.
Operating in such a space by modifying resulting inversions unlocks numerous image manipulation capabilities, i.a., image editing (Hertz et al. 2022
Mokady et al.) 2023
Huberman- Huberman-SSpcgelle Spiegelglas
et al.
2024
Parmar et al. [023] Rouu et al.; 2025 Miyake et al. 2023| Brack et al. [.[22 Tang
et al.
2024
Hong al.) 2024 Wallace al. 2203 (aamell et al. 2025 Garibi et al. 2024 Pan
et al.
2023
Dong et al. al.] 2023), image interpolation (Zheng et al. al. 2024 et al. [024b] Samuel
al. 2025)
2023
Dhariwal & Nichol 2021). or stroke-to-image synthesis (Meng al. [002 Rout al.]
The inversion process can be derived from Eq. (7). leading to the formula for transferring a
less noisy image Tt-1 to a more noisy one Zz:
Ft VoiSt-1 (V1 Oz Vou ot) 6 (axe)
(1)
(8)
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Unfortunately, perfect image-to-noise inversion is infeasible. Due to circular dependency 24 within Eq. (8) Dhariwal & Nichol (2021) propose to approximate this equation by assuming that the model's prediction in 1-th step for x, is locally equivalent to the decision for Iz-1 Eq (xx) & so (1) The inverted trajectory is determined in multiple steps. Hence, the error propagates further away from the image, leading to the latents that significantly deviate from the starting noise. This flaw is presented in Fig.
(t)
tt
(xr-))
Densising xy 25
(x))
co
X
2-
sy N10,)
Denoising Inversion
Inveraion
Images
Figure 9: The DDIM inversion error, derived from approximating DM's prediction for with the output for f4-1 (left), propagates with the next inversion steps, leading to a distribution of latents le that deviates significantly from the expected noise distribution x" (right).
PSEUDOCODE FOR DDIM INVERSION WITH FORWARD DIFFUSION
We present Algorithm T the pseudocode for the proposed solution to the decorrelation latent en- codings by replacing the first t' inversion steps with a forward diffusion process. In Appendices N.1 N.3 we analyze the sensitivity of this fix how performs for: different number of inversion steps 7 (Appendix I.I) different percentage of inversion steps replaced with forward diffusion f (Appendix N.2) and when classifier-fre guidance applied (Appendix)) N.3
Algorithm Finding decorrelated DDIM latent encoding Re
Require: image Xp: diffusion model eø; noise schedules {at)== (az ( number of inversion
steps T; forward-replacement timestep
Ensure: decorrelated latent encoding RT
I: sample (0,
2: Xt j Xo /1 1 i
forward diffusion
|
3: for 1trl+t1 I,..... do
4: 8t Var St-1 + (VI aj.
-vas) 66
(6)
(8t-1)
DDIM Inversion step
5: end for
6: return XT
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G MOST PROBABLE TRIANGLES
In Section 3.2, we analyze where the latent encodings are distributed in relation to the initial noise and generated samples. Here, we determine the most probable angles formed by noises XT, samples Xo. and latents & for each model.
G.1 METHODOLOGY
First, we determine the vectors going from each vertex to the other vertices of the noise-sample- latent (XT-Xo-XT) triangle. For sample Xo. we obtain vector leading noise XoxT XT
and to latent XO ËT Xo, and calculate the angle between them using cosine similarity as
XOXT
XO
Zxo = arccos
(9)
X
X
and convert resulting radians to degrees. Similarly, we obtain the angle next to the noise Zxr and latent ZRr.
Next, we determine histograms for each angle, approximating the probability density function for every angle -xxxx-P2xx-P225 P2&,,) binned up to the precision of one degree, see Fig. [T] Finally, for all angles triples candidates (where /xT + /xp + / = 180%), ), we calculate the probability of triangle the product of the probabilities and choose the triplet maximizing such joint probability:
argmax D/xT P//x p/8
(10)
(Lx1,2x0/280)
G.2 RESULTS
Results the experiment in Table 9 show that the angle located the image and noise vertices (accordingly Zxo and /xT) are always acute and, in almost every case, the angle by the latent vertex (L&T) obtuse. This property implies that, due to approximation errors in the reverse DDIM process, latents reside in proximity to, but with measurable offset, from the shortest-path trajectory between the noise distribution and the generated image.
Model
T
Zxo
ZxT
78T
ADM
44
120
100
29
28
123
32 32
1000
20
115
ADM
10
30
31
119
100
11
60
109
64 64
1000
6
79
95
ADM
10
24
50
106
100
24
73
83
256 256
1000
23
73
84
LDM
10
23
53
104
100
2
76
102
256 256
1000
1
83
96
DiT
10
27
47
106
100
4
66
110
256 256
1000
99
Table 9: Impact of the number diffusion steps on angles in the noise XT, image Xo, and latent 2T triangle. Regardless of the number of diffusion steps, latents appear between Gaussian noise and generations.
In Fig. 10 we provide example triangles for ADM-32 (a), ADM-256 (b), and LDD (c), which we calculate using N = 1000 images with T = 100 diffusion steps.
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Latent
Latent encoding
83
123
29
28
--2
24"
Image
Noise
Imsuge
Noise
(a) ADM-32 (CIFAR-10 10)
(b) ADM-256 (ImageNet)
Lateot encoding
102
76
Image
(c) LDM (CelebA)
Figure 10: Most probable triangles formed from random Gaussian noise (Xr), the images (Xo) generated, and latents (&T) recovered with DDIM Inversion procedure.
G.3 EXAMPLE HISTOGRAMS
In Fig. II we present histograms approximating probabiliy density functions for noise xT, image Xo. and DDIM latent êT angles.
Noise xT
Sample æo
56
64
71
6
16
26
Latent BT
101 111
121
Figure 11: Histograms approximating probability density functions of angles values for noise, sample, and latent vertices. Example calculated for DiT model using T' = 100 diffusion steps.
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H PLAIN SURFACE THRESHOLDING
During our experiments, we determine binary mask M to identify pixels corresponding to the plain areas in the images. We describe this process this section.
Let E RC be the input image. For each pixel value across every channel (c, h, w) in I, we compute the absolute difference to point in the the pixel in the next column Dw (c, h, w) = [Tc,h.w+11 h. We obtain DH E RCC and Dw E RC which pad with zeros (last row for DH and last column for Dw), making them of shape C x H x W. The difference matrix D, representing how point varies from its neighbors, is computed D (Dw Dn)/2.
Dv (c, h w) 1, h. and to
Finally, we determine a binary mask Mr per each channel by applying threshold r to D as
{ 1, if De(h, w) <T
Me(h, w)
(11)
0, otherwise
During the experiments, set 0.025.
The final mask M E (0, 1)W* can be derived by evaluating the logical AND across all channels for each pixel location
M(h, w) - II Mo(h,w).
(12)
After obtaining the final mask for plain pixels, which we denote as Mp. the according mask for non-plain image surfaces can be obtained by applying logical NOT to the mask as Mn = -Mp In Fig. [2] present example masks determined using methodology.
Image
mask
Image
Image
Plain mask
Image
Plain mask
Image
Plain mask
Image
Plain mask
Image
Plain mask
Image
Plain mask
Figure 12: Examples of samples together with their masks indicating plain (white). Im- ages generated using DiT model.
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I CALCULATING INVERSION ERROR
we study how the inversion error differs for pixels related to plain and non-plain samples' regions and investigate it across diffusion steps. In this section, we describe the method for determining the error.
In Section 3.3
First, generate N 4k images with T 50 diffusion steps with both ADM-64 and DiT models, saving intermediate noise predictions { 1t=00... during sampling. Next, we collect diffu- sion model outputs during the inversion process {8/ )=1...30 assuming all the previous steps were correct. While for t 1, E can be set to the diffusion model prediction from the first inver- sion step co (2a), for further steps, more advanced methodology is necessary. To this end, for each t' ='= 22...0. we map the images to latents with DDIM Inversion, replacing in t = 1...t'- 1 the predicted noise eg (Zz)) with the ground truth prediction & from denoising process, and collect the model output for the l' step as E, := ( For step 6, this methodology is equivalent starting the inversion process from + 1) denoising step and collecting the first diffusion model prediction.
In the next step, calculate the absolute error between outputs during inversion and ground truth predictions as &F = |E -. This way, we obtain the inversion approximation error for cach timestep.
Further, for the images in the dataset, we obtain binary masks MM and M, indicating, respectively, plain (p) and non-plain (n) pixels in the image, according the procedure described in Appendix (H] To ensure that the level of noise that DM predicts in each step does not bias the results, we divide the
absolute errors in each step by Iı-norm of model outputs, calculated separately for each diffusion step. For plain (p) pixels, it can be described as
EEP 1/1 Σ EEE o Mp),
(EF
(13)
and adequately for non-plain (n) pixels as
e.5m 1/11/11, Σ (EF o M,).
(14)
In Table 10, we present the error differences for plain and con-plain areas and how the first 10% of the diffusion steps contribute to the total inversion error. To calculate this error for plain regions in steps fu..... ter we sum errors for timesteps from a given interval as
EEp (1alta)
&
(15)
Model
Pixel area
Diffusion steps
ADM-64
DFT
Plain
15.11
5.67
...
100%
Non-plain
12.43
3.16
Plain
9.23
3.41
1,2...5
10%
Non-plain
6.80
1.42
Plain
5.87
2.23
6, 6...0
90%
Non-plain
5.63
1.74
Table 10: Total per-pixel inversion error (normalized) over different timestep ranges (ra.te) for plain and non-plain areas. Inversion approximation error is higher for pixels related to plain image areas, especially in the first 10% of inversion steps.
EE
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J CONDITIONING FOR DIFFUSION MODELS
For thorough analysis, we employ both unconditional (ADM-32, ADM-64, ADM-256) and con- ditional (DiT, IF, SDXL) diffusion models. For conditioning, we take prompts from the Recap- COCO-30K dataset (Li et al. 2025) for IF and Stable Diffusion XL and ImageNet class names for DIT. However, as noted by Mokady et (2023). Classifier-Free Guidance introduces additional errors to the DDIM inversion. To focus solely on the inversion approximation error, in the exper- iments from the main part of this work, we disable CFG by setting the guidance scale to 1. However, in Appendix N.3 we show that the proposed fix can also improve DDIM Inversion when CFG enabled (w 1).
K DETAILS ON DIVERSITY AND ALIGNMENT OF EDITION
In this section, we provide results for measuring the diversity (against source images Ig) and align- ment to conditioning prompts (source P's and target PT) of images generated from Gaussian noise XT, DDIM latents ÊT, or the latents produced by our fix (described in Algorithm I with modified prompts. We use distance-basee metrics (LPIPS (Zhang et al.) 2018). DreamSim (Fu et al.) 2023 similarity metrics (SSIM (Wang et al.] 2004). DINO (Darcet et al. (024)) to measure the diversity between source (input) images and target (edited) images, as well as the similarity between embed- dings produced by the CLIP (Radford et al. 2021) model to calculate the alignment between the results and prompts. The results in for introduced latent decorrelation procedure are obtained with varying percentages of the first DDIM inversion steps replaced with forward diffusion. In Table [I show that by selecting a small fraction of inversion steps replace with forward diffusion (from 2% up to 6%), the resulting latents are more editable.
Inversion steps replaced by forward diff. (%T)
Diversity against Ig
CLIP Alignment
DreamSim
LPIPS
SSIM |
DINO J
Ps |
Pr
Noise XT
0.709
0.591
0.228
0.174
0.465
0.681
DDIM Latent åT
0.677
0.564
0.261
0.223
0.480
0.662
1 (2%)
0.696
0.580
0.239
0.187
0.470
0.676
1... 2 (4%) 1 1...3 (6%)
0.701
0.587
0.227
0.179
0.469
0.677
0.705
0.594
0.216
0.173
0.468
0.678
1...5 5 (10%)
0.711
0.605
0.198
0.165
0.466
0.679
1. 1...50 50 (100%)
0.805
0.801
0.013
0.085
0.465
0.680
(a) Diffusion Transformer
Inversion steps replaced
Diversity against Ig
CLIP Alignment
by forward diff. (%T)
DreamSim
LPIPS
SSIM
DINO J
Ps l
Pr
Noise (100%)
0.665
0.380
0.339
0.344
0,273
0.649
DDIM Latent åT
0.609
0.328
0.406
0.416
0.353
0.614
1 (2%)
0.666
0.376
0.359
0.335
0.281
0.646
1...2 (4%)
0.660
0.369
0.359
0.351
0.287
0.649
1...3 (6%)
0.661
0.370
0.353
0.349
0.285
0.650
1. 5 (10%)
0.662
0.372
0.341
0.346
0.282
0.649
50 (100%)
0.733
0.521
0.004
0.272
0.274
0.649
(b) Deepfloyd IF
Table 11: Impact of first DDIM inversion errors on diversity and text-alignment of generations from resulting latent as an input. For both DiT (a) and IF (b) models, replacing the first inversion steps and denoising leads to more diverse generations against the source images Ts. Additionally, show using forward diffusion in first steps improves the alignment between generation and target prompts, which the generation process is conditioned by, as indicated by the larger CLIP-T value for Pr and the smaller one for Ps.
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L NOISE-TO-IMAGE MAPPING
We showcase additional study showing the differences that oceur between noise and latent codings, from the perspective of their mapping to the images. Several works investigate interesting properties between the initial random noise and generations that result from the training objective of DDPMs and score-based models. Kadkhodaie et al. (2024) show that due to inductive biases of de- noising models. different DDPMs trained on similar datasets converge almost identical solutions. This idea is further explored by ZZhang et al. (2024a), observing that even models with different architectures converge to the same score function and, hence, the same poise-to-imape mapping. Khrulkov & Oseledets) (2022) show that diffusion models' encoder map coincides with the optimal transport (OT) map when modeling simple distributions. However, other works (Kim & Milman Lavenant & Santambrogio 2022 contradict this finding.
2011
L.1 SMALLEST 12 MAPPING
Diffusion models converge to the same mapping between the Gaussian noise (XT) and the generated images (Xo) independently on the random seed, dataset parts (Kadkhodaie et al. (024)), or the model architecture (Zhang et al. 2024a). We further investigate this property from the noise-sample and latent-sample mapping perspective.
In our experimental setup, we start by generating N = 2000 images Xo from Gaussian noise XT with a DDIM sampler and invert the images to latents Åe with naive DDIM inversion. Next, we predict resulting images for the starting noise samples (XT -> xo) by iterating over all the N noises, and for each of them, we calculate
pixel distances to all the N generations. For given noise, we select the image to which such Ig-distance is the smallest. Similarly, we investigate image-to- noise (Xo + XT). image-to-latent (Xo - åT) and latent-to-image (&T + xo) mappings. We calculate the distance between two objects as norm of the matrix of differences between them (with C' x H x W being the dimensions of either pixel or latent space of diffusion model) as ||x v112 = E (Ia.jik 3.
In Table 12 investigate the accuracy of the procedure across varying numbers of diffusion steps T' for both image<>noise (a) and latent (b) assignments. We show that assigning initial noise generations (Xo + Xxr) through the distance method can be successfully done regardless of diffusion steps. For the reverse assignment, which is coise-to-image (XT - Xx) mapping, we can observe high accuracy with a low number of generation timesteps (T 10). but the results deteriorate quickly with the increase of this parameter. The reason for this is that greater values of T allow the generation of broader range of images, including the ones with large plain areas of low pixel variance. When it comes to mappings between images and latents resulting from DDIM Inversion, assignment both directions is infeasible for pixel diffusion, regardless T.
ADM-32
ADM-64
ADM-256
LDM
T
Xg + Xr
XT + Xo
Xg - XT
XT + Xa
Xu + Xy
XT + Xn
Xu - Xr
XT + Xu
Xo + Xr
30.3
91.0=2a
99.4gn.
100gao
100
39.2.0.2
100gna
100ga.
100
93. 7
100
98.9+1.2
50.421.9
100
59.0
100
23.2+4.
100
100
100
90.7=10.1
1000
1:10
99 39.82m.2
44.6an.
100
25.0+4.
100
100
100
96. 86.7444
4000
10.1
46.423.
90.5.0.3
43.3
(a) Assigning noise the corresponding generated image (xo + xT) and vice-versa (XT + xo).
ADM.32
ADM-64 64
ADM-256
LDM
DiT
T
Xg
&r
Rr
Xp
Xo +
Ro
Se + No
Xg
Kog
Ro -
X
No Ser
Xo
Xg - Ro
fop - No
10
66.4.1.
38.21a.
614417
100.0_a.
0.7.n2
30.814
100
1001no
99.810s
95.1
100
16.4_6.
33.4g07
8.6
57.5273
4.1.14
23.9.0
100
100200
99.5g17
90.7g10a
1000
3.6122
10.9127
1.7_13
41.718
23.9.a2
25.4144
100,a0
100109
100.0
96.6148
4000
2.8
41.9ga
1.9_14
43.5265
(b) Assigning images to the resulting latent encodings (&r - Xo) and vere-versa (Xo &r).
Table 12: Accuracy of the 1z-distance based assignment for both image<-noise (a) and lateet+ (b) mappings across varying number of diffusion steps T'. For pixel DMs, only the image-to-noiss (Xo + xT) mapping is feasible. For the latent space models, we correctly pre- dict assignments in all directions.
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For both noise x² and latents 47, their assignment to images in both directions be successfully done when the denoising is performed in the latent space, as shown for DiT and LDM models. We hypothesize that this fact is connected with the KL regularization term that imposes slight penalty towards a standard normal distribution Wo0, /) on the latent during training (Rombach et al. 2021
L.2 ASYMMETRY OF SOBE-TO--MAGE MAPPING
Results in Table 12a indicate that, even though the lg-distance is symmetrical, the mapping camnot be done in both directions. The reason behind this is that image and noise assignments are not the same due to the one-directional many-to-one relation, egg., there might be several noises pointing towards the same closest image.
We present examples of wrong noise-to- coise-to-image (XT -> Xo) assignments in Fig. 13A for ADM-64. In Fig. 133, we present the singular generations that lead to incorrect noise-to-ing toise-to-image classification (noise attractors), along with the number of noises for which they are the closest. Interestingly, in Fig. 13C, we sort all the generations used in the experiment by the variance of pixels and show 8 least variant images. We observe that the set of singular generations leading to misclassification partially overlaps with experiment with ADM-32 model.
generations. In Fig. [4 observe similar properties for ations tend be the closest (in l2-distance) for the majority of the noises in our experiments.
When assigning images the initial noises, there singular generations (with large plain areas) located close to the mean of the random Gaussian noise in the set of generated images. Such gener-
(A) Incorreet classficcatin examples
(B) Most attracting samples
Noise
Target Image
Closest Images 2nd
3rd
4th
(C) Sumples sorted by variance (from lowest)
Figure 13: Examples of incorrect assignments of initial noises to resulting images (A), two most noise-attracting images (B), and samples sorted in ascending order by variance pixels for ADM- 64 model trained the ImageNet dataset.
(A) Incorrect classification examples
(B) Most attracting samples
Noise
Target Image
Closest Images 2nd
3rd
4th
A
A
(C) Sumples sorted by variance
(From lowest)
ct
Figure 14: Examples of incorrect assignments of initial noises to resulting images (A), two most noise-attracting images (B), and samples sorted in ascending order by variance of pixels for ADM- 32 model trained the CIFAR R-10 dataset.
Those findings, connected with the reduced diversity of latents (Table 3) suggest that the DDIM latents, unlike noise, cannot be accurately assigned to samples, as the error brings them towards the mean, reducing their diversity and making them closest most of the images.
Conclusion.
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M ON NOISE-MAAGE-LATENT RELATIONS DURING DIFFUSION TRAINING
To further explore the relationships that exist between noises, generations, and latents, we study how the relationships between them change with the training of the diffusion model. We train two diffusion models from scratch and follow the setup from Nichol & Dhariwal (2021) for two unconditional ADMs for the ImageNet (64 64) and CIFAR- 10 (32 x 32) datasets. The CIFAR-10 model is trained for 700K steps, while the ImageNet model for 1.5M steps, both with a batch size of 128. Models employ a cosine scheduler with 4K diffusion steps.
M. SPATIAL RELATIONS OF NOISE AND LATENTS OVER TRAINING TIME
We conclude our latent localization experiments (Section 3.2) by showing that observations persistent across the diffusion model training process. We generate
2048 images with the final model, using implicit sampling with T 100 steps, and invert them the corresponding latents using checkpoints saved during the training. In Fig. [5] we show that both the angle adjacent to the noise ZxT and the distance between the latent and noise ||& xT quickly converge to the point that remains unchanged through the rest of the training, indicating that the relation between noises, latents, and samples defined at the very early stage of the training. Additionally, we observe that the noise reconstruction eπror in DDIM Inversion does not degrade with the training progress.
LX
|x'-
1x -R
L2 Distance
0.0
Angle
40
100
5:10
6-103
13-10
207
5 Training step
5-12"
13:10'
Training step
Figure 15: We investigate spatial relations between the noise xT, latents &T, and generated images Xo training process of diffusion model. We show that those relations are defined at the early stage of the training.
M.2 IMAGE-TO-NOISE DISTANCE MAPPING OVER TRAINING TIME
We analyze the image-noise mapping with 12 distanee from Appendix ovve diffusion model train- ing time. We sample N 2000 Gaussian noises and generate images from them using ADM models with T' = 100 diffusion steps, calculating the accuracy of assigning images to corresponding noises (and vice versa) using the smallest lg-distance. In Fig. 16 we can observe, for both models, that the distance between noises and their corresponding generations accurately defines the assignment of initial noises given the generated samples (xo - xT) from the beginning of the training till the end. At the same time, the accurate reverse assignment (xT -> xo) can only be observed at the beginning of the training when the trained model is not yet capable of generating properly formed images. Already in the beginning phase of model training, the quality of noise to image mapping rapidly drops and does not change until the end training.
Metric value [%6]
Metric [96]
80
20
09
ACCIK +x?
ACCIX -x*)
ACCINT x
100
5-181
6-121
13:10
5.13"
25:10
45-1P
65-189
Training step
Training step
(a) ADM-64
(b) ADM-32
Figure 16: Accuracy of assigning initial noise given the generated sample (Xo + xT) and sample given the initial noise (XT + xo) when training the diffusion model. We can observe that from the very beginning of training, we can assign initial noise with a simple L2 distance while the accuracy of the reverse assignment rapidly drops.
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M.3 IMAGE ALIGNMENT OVER TRAINING TIME
Inspired by the noise-image mapping experiment, we investigate how the generations resulting from the same noise visually change over DM training time. Thus, for each training step v {1 700K) for CIFAR-10 and {1... 1.5M} for ImageNet, we generate 2048 samples {x?,,, 12048 from the same fi=l
random noise xffeed (),, and compare them with generations obtained for the fully trained model. We present the visualization of this comparison in Fig. 17 using CKA, DINO, SSIM, and SVCCA as image-alignment metrics. We notice that image features rapidly converge the level that persists until the end of the training. This means that prolonged learning does not significantly alter how the data is assigned the Gaussian noise after the early stage of the training. It especially visible when considering the SVCCA metric, which measures the average correlation of top-10 correlated data features between two sets of samples. We can observe that this quantity is high and stable through training, showing that generating the most important image concepts from given noise will be affected by a longer learning process. For visual comparison, we plot the generations sampled from the model trained with different numbers of training steps in Fig. (right).
1.0
(A)
Image Alignment
0.8
0.8
0.4
CKA
SVCCA
(C)
SSIM
DINO
(A)
(B)
(C)
(D)
10a
5-10
9-10
13-10'
Train step
Figure 17: Similarity of the generations sampled from the same random noise at different stages of diffusion model's training to the final outputs for ADM-64 model. Only after a few epochs does the model already learn the mapping between Gaussian noise and generations. Pro- longed training improves the quality of samples, adding their content. This can be observed through different image alignment metrics (left) and visual in- spection (right).
features without changing
In Fig. 18 we visualize how the diffusion model learns the low-frequency features of the image already at the beginning of the training when comparing generations from the next training steps against the generations after finishing training for the ADM-32 model trained on the CIFAR-10 dataset. In Fig. [9 (ADM-64) and Fig. 20 (ADM-32), how generations evolve over training for the same Gaussian noise XT using DDIM sampler. Ini- tially, fow-frequency features emerge and remain relatively stable, while continued training improves generation quality by refining only the high-freque frequeer details.
show additional examples illustrating
Image Alignment
0.8
0.6
0.4
CKA
SVCCA
SSIM
DINO
0.2
0.5 10*
2.5
45.100
6.5-10"
Train step
Figure 18: Similarity the generations sampled from the same random noise at different stages of the diffusion model's training to the final outputs for ADM-32 (CIFAR-10). We plot CKA. SVCCA. SSIM, and DINO image alignment metrics and show that the diffusion model al- ready learns the mapping between Gaussian noise and generations at the beginning of the training.
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Training steps
20K
165K
S10K
454K
SB4K
723K
873K
1.02M
1.16M
1.30M
1.44M
1.50M
Figure 19: Examples of images sampled using DDIM scheduler from the same noise during the training process for the ADM-64 model trained on the ImageNet dataset.
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Training sleps -
176K
273K
371K
495K
595K
645K
700K
Figure 20: Examples of images sampled using DDIM scheduler from the same noise during the training process for the ADM-32 model trained on the CIFAR-10 dataset.
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N PARAMETER IMPACT ANALYSIS
N.1 NUMBER OF INVERSION STEPS
In this work, for the inversion process, we leverage the DDIM sampler with either T
50 or
T 100 sampling steps. This choice aligns with prior works (Hong et al. 2024 Garibi et al.) 2024 Kim et al.) 2022b) in image edition domain, where the authors used from 50 up to 200 inversion steps as proper balance between reconstruction quality and short algorithm runtime.
However, as described in Hong et al. 2024), the naive DDIM inversion procedure (Song et al. 2021) can be reinterpreted as solving the forward diffusion ordinary differential equation (ODE) in reverse order (along the time axis) with Euler method. With this reformulation, the inversion is correct under the assumption that, with dt being step size, noise predictions in & and + dt steps are almost exact, thus works only when performing with many iterations.
Since the presence of image structures in DDIM latents can depend on the number of steps with which the inversion is performed, in Table 13 we show for ADM-64, DiT, and IF models that the observations presented in this work generalize to cases where the number of inversion steps is several times greater (i.e., T = 1000, as performed during the training). Additionally, in Fig. [2 we show qualitatively by plotting the absolute enror between starting Gaussian noise and DDIM latents, that also for a large number of steps, the uniform areas on the image contribute more significantly overall inversion error.
For more thorough analysis, in Table 14 we evaluate how our fix decorraltes latents in situation where we use T 1000 inversion steps. As visible, replacing just 1 step of DDIM Inversion with forward diffusion significantly reduces correlation at minimal loss in image reconstruction.
Model DIT
Object
ADM-64
IF
Noise XT (baseline)
0.039+.00
0.039
0.039 0.00
DDIM Latent Sc-110
0.4164.03
0.297
0.783 01
DDIM Latent $T=25
0.242..02
0.203
0.698_.02
DDIM
Latent 80
0.177+.00
0.1444.02
0.608
DDIM
Latent 1r=110
0.133
0.106=:002
0.500=.02
DDIM
Latent RT=250
0.108
0.078
0.366
DDIM Latent 8T=500
0.100
0.069
0.294-_00
DDIM Latent S-p-
0.095
0.065
0.2419..0
Table 13: Latent encodings resulting from the DDIM Inversion exhibit correlations, even when
the procedure is performed with a lot of steps. By dividing latent encodings into 8 x 8 patches and calculating the mean of top-20 Pearson coefficients, we show that DDIM latents are correlated substantially higher than Gaussian noise, even when using T 1000 inversion steps.
Image 2o
|latent noisel
ADM-64
(T=1000)
DIT (T-1000)
IF (T=1000)
Figure 21: Approximation errors in DDIM inversion are significantly higher for plain image surfaces than for the rest of the image. Even when using T' = 1000 steps, we observe image structures in DDIM latents, notably for uniform image regions.
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Model
Prior
Corr. +
KL x10
Image Recon,
Noise (upper bound)
0.039 a 000
4.832
0.000
DDIM Latent
0.095
47.015
0.014
w/ our fix (4 ))
0.0554.00
5.125
0.033
ADM-64
w/ our fix (2% (2%)
0.055.2.00
5.363
0.024
(T=1000)
w/ our fix (1 %
0,055
5.679
0.019
w/ our fix (0.5%
0.055 .00
6.057
0.017
w/ our fix (0.2 %
0.055
6.662
0.015
w/ our fix (0.1 9%)
0.055..00
7.228
0.014
Noise (upper bound)
0.039 .00
4.832
0.000
DDIM Latent
0.065
17.931
0.009
w/ our fix %)
0.057
5.233
0.060
DiT (T=1000)
w/ our fix (2 3)
0.057=.00
5.071
0.041
w/ our fix (1 %)
0.057
5.850
0.029
w/ our fix (0.5%
0.058
7.029
0.021
w/ our fix (0.2 %
0.058
8.045
0.016
w/ our fix (0.1 %
0.058
8.409
0.014
Noisc (upper bound)
0.039
4.832
0.000
DDIM Latent
0.2194..02
63,962
0.044
our fix (4%)
0.055...00
5.024
0.037
IF (T=1000)
w/ our fix (2 ))
0.055
5.215
0.031
w/ our fix (1 %
0,055...0
5.706
0.027
w/ our fix (0.5%
0.055 000
6.117
0.026
w/ our fix (0.2% %
0.055
5.562
0.025
w/ our fix (0.1 %
0.0564.00
5.349
0.024
Table 14: Latent correlations, KI. divergence to random Gaussian noise, and image recon- struction error across models (ADM-64, DìT, IF) when using 1000 inversion steps. We show that using simple fix in just one step of inversion process significantly decorellates DDIM latents with minimal loss image reconstruction performance.
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N.2 PERCENTAGE OF INVERSION STEPS REPLACED
The fix to DDIM Inversion algorithm, proposed in this work, namely replacing neural network pre- dictions with random Gaussian Noise, implies the trade-off between preserving the original image information and improving the latents' editability. In this section, we present how the number of inversion steps substituted with forward step, impacts the image reconstruction error (MAE, LPIPS, and SSIM metrics) and latent editability (correlations and KL Divergence from (O; for: IF (Table 15). DIT (Table 16.. and SDXL (Table 17p models. We observe that replacing only the first 4% of inversion steps with forward diffusion improves latent normality to the level of Gaussian noise (100% of steps), while increases reconstruction error only slightly. Fig, 22 we show some failure cases when replacing 10% or 20% of the first steps can introduce significant changes to images.
# Steps Replaced (Percentage)
Image
Reconstruction
Latent Normality
MAE
LPIPS |
SSIM
Correlation
KL Div. x x10²
(0%)
0.073
0.030
0.878
0.643
60,449
(2%)
0.069
0.037
0.854
0.057
0.934
2 (4%)
0.071
0.038
0.845
0,050
0,352
3 (6%)
0.074
0.040
0.830
0,050
0,346
4 (8%)
0.078
0.043
0.813
0.049
0.341
5 (10%)
0.082
0.047
0.796
0.049
0.338
10 (20%)
0.099
0.066
0.713
0.049
0.344
20 (40%)
0.131
0.113
0.556
0.049
0.360
30 (60%)
0.169
0.179
0.394
0.049
0.367
40 (80%)
0.233
0.279
0.204
0.049
0.370
50 (100%)
0.487
0.437
0.009
0.049
0.374
Table 15: Impact percentage of inversion steps replaced with forward diffusion on recon- struction quality and latent normality for DeepFloyd IF.
Steps Replaced (Percentage)
Image Reconstruction
Latent Normality
MAE
LPIPS +
SSIM
Correlation 4.
KL. Div. x x102
(0%)
0.052
0.063
0.839
0.159
1,118
(2%)
0.070
0.097
0.741
0.038
0.011
(4%)
0.085
0.125
0.658
0.036
0.010
3 (6%)
0.097
0.151
0.594
0,036
0,023
4 (8%)
0.107
0.173
0.544
0.037
0,036
5 (10%)
0.116
0.195
0.505
0.037
0.041
10 (20%)
0.154
0.280
0.375
0.038
0,040
20 (40%)
0.231
0.437
0.235
0.037
0.020
30 (60%)
0.353
0.595
0.145
0.037
0.017
40 (80%)
0.521
0.710
0.071
0.037
0.017
50 (100%)
0.628
0.750
0.029
0.037
0.018
Table 16: Impact of percentage of inversion steps replaced with forward diff'usion on recon- struction quality and latent normality for Diffusion Transformer (DiT).
Steps Replaced (Percentage)
Image Reconstruction
Latent Normality
MAE
LPIPS +
SSIM
Correlation +
KT. Div. x 102
(0%)
0.027
0.099
0.814
0.166
0.800
(2%)
0.029
0.106
0.790
0.151
0.600
2 (4%)
0.035
0.137
0.716
0.120
0,300
3 (6%)
0.038
0.155
0.685
0.117
0,300
4 (8%)
0.041
0.171
0.663
0.116
0,300
5 (10%)
0.043
0.183
0.646
0.116
0.200
10 (20%)
0.051
0.230
0.588
0.115
0.200
20 (40%)
0.065
0.313
0.515
0.115
0,200
30 (60%)
0.082
0.389
0.460
0.115
0.200
40 (80%)
0.112
0.464
0.464
0.115
0.200
50 (100%)
0.159
0.541
0.541
0.115
0.200
Table 17: Impact of percentage of inversion steps replaced with forward diffuusio on recon- struction quality and latent normality for Stable Diffusion XL.
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Doise/Latens
Generaaion/Reconstruciion
Gaussian noise
DDIM Inversion
DDIM Inversion (w/ 2% forward)
DDIM Inversion (w/ 4% forward)
DDIM Inversion (w/ 6% forward)
DDIM Inversion (w/ 10% forward)
DDIM Inversion (w/ 20% forward)
Figure 22: Replacing first DDIM inversion steps with forward diffusion increases latents ed- itability at the cost of higher reconstruction error. By replacing from 2% up to 4% of steps, obtain reasonable image reconstructions while removing correlations from latents.
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N.3 GUIDANCE SCALE
During experiments, we fix the guidance scale to w = 1 to ensure that our analysis focuses solely on the DDIM approximation error (Eq. (3). As described in Ju et al. (2024), prior works typically employ guidance scale between 1.0 (the most common choice) and 3.0 during inversion, as using > 3 often results in drastically worse image reconstructions.
In this section, we evaluate how the proposed fix improves upon Naïve DDIM Inversion when higher guidance scale w E {1, 2, 3, 4, 5) is applied both during inversion and reconstruction. In Table 18 we present result of this experiment with Stable Diffusion XL (Podell et al., (024). For scenarios with higher guidance scale, our simple fix, similarly to w 1, reduces correlations and improves editability when comparing with Naive DDIM Inversion. Additionally, we observe that, when guidance is applied, our fix improves image reconstruction error (measured with LPIPS). We hypothesize that amplifying the inversion emror in Naive DDIM with higher guidance scale leads to latents that are useless for image reconstruction. In such case, replacing the first steps with random Noise may lead to more preferable reconstructions. In Fig. 23 and Fig. 24 present qualitative comparison image reconstruction between Naïve DDIM Inversion and our approach.
Guidance Scale w
Latent
CLIP Alignment (Edit Prompt) f
Method
LPIPS
Corr. J
DDIM Inv.
0.100
0.166
0.695
1.0
ours (4%
0.137
0.120
0.722
A
+0.037
-0.046
+0.027
DDIM Inv.
0.199
0.170
0.779
2.0
ours (4%
0.179
0.120
0.807
A
-0.020
-0.050
+0.028
DDIM Inv.
0.390
0.171
0.764
3.0
w/ ours (4%)
0.267
0.121
0.815
A
-0.123
-0.050
+0.051
DDIM Inv.
0.525
0.172
0.725
4.0
w/ ours (4%)
0.372
0.121
0.800
A
-0.153
-0.051
+0.075
DDIM Inv.
0,582
0.174
0.687
5.0
w/ ours (4%)
0,452
0.121
0.770
A
-0.130
-0.053
+0.083
Table 18: Performance in image reconstruction (LPIPS), inverted latent normality (correla- tions), and text alignment to edit prompt for different values of guidance scale. We show that our forward step replacement (4%) improves DDIM Inversion algorithm.
Original Image
DDIM Inv.
Reconstruction: Ours (4%)
guidance scale: w=1.0
Figure 23: Examples of image reconstruction with Naïve DDIM Inversion and DDIM Inversion incorporating our fix (forward 4%) for guidance scale wo 1. Examples generated with Stable Diffusion XL.
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Original Image
DDIM Inv.
Reconstructions
Ours (4%)
guidance scale: w=2.0
Original Image
Reconstruction:
DDIM
Ours (4%)
guidance scale: w=3.0
Original Image
Reconstruction:
(4%) DDIM
guidance scale: w=4.0
Reconstruction: Original
Image
HATE
HATE
Ours (4%) DDIM
guidance scale: w=5.0
Figure 24: Comparison of image reconstruction examples with Naive DDIM Inversion and DDIM Inversion incorporating fix (forward 4%) across different values of guidance scale w E (2, 3, 4, 5). Examples generated with Stable Diffusion XL.
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O QUALITATIVE EXAMPLES
O.1 IMAGE INTERPOLATION
we presented that interpolating DDIM latents with SLERP (Shoemake 1985) leads to a decrease in image quality and diversity when compared to Gaussian noise. In Fig. 25 we qualita- tively compare our fix for removing correlations in latent encodings with naïve DDIM inversion in the task of image interpolation.
In Section 4
DDIM Inversion
DDIM Inversion (w/ forward 4%)
DDIM Inversion
DDIM Inversion (w/ forward 4%)
DDIM Inversion
DDIM Inversion (w/ forward 4%)
DDIM Inversion
DDIM Inversion (w/ forward 4%)
DDIM Inversion
DDIM Inversion (w/ forward 4%)
Figure 25: Qualitative comparison of images generated from interpolated latents produced with DDIM Inversion and our fix. Contrary to naïve DDIM inversion, the proposed solution enables generating high-quality objects with pixel-diverse backgrounds.
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O.2 RECONSTRUCTIONS OF REAL IMAGES
In Fig. 26 we present a qualitative comparison for reconstructions of real images from the Style- Drop (Sohn al. 2023) dataset. We observe that DDIM Inversion with our fix sometimes provides imperfect image reconstructions. However, those failures are also observable with vanilla DDIM In- version, indicating that they stem from DDIM approximation error itself, not from our replacement.
StyleDrop Image
Image Reconstruction: DDIM Inv. ours DDIM
StyleDrop Image
Image Reconstruction: DDIM Inv. w/ ours Naive DDIM Inv.
Figure 26: Examples of reconstructions of real images from the StyleDrop (Sohn et al. 2023) dataset with Naive DDIM Inversion and DDIM with our fix (forward diffusion in 4% of steps). Inversion process is run with T 50 steps and guidance scale 1.0. Reconstructions generated with Stable Diffusion XL.
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O.3 STOCHASTIC IMAGE EDITING
In this work, we propose a solution for decorrelating latent encodings resulting from DDIM inversion by replacing its first steps with the forward diffusion. As presented in Algorithm D the forward diffusion process involves sampling random Gaussian noise E ~ (0,, I) and interpolating it with the input image. Due the fact that, when we replace a small fraction of steps (2 4%), the change in image reconstruction error is insignificant, the use of different noises é (in practice, sampled with different seeds) allows stochastic image editing. i.e. generating different manipulations of the input image, feature not naturally available with DDIM inversion. In Fig. 27 we present examples of editing real images from the ImageNet-R-TTE dataset (which we annotate using GPT-4o) with IF model, showing various semantically correct modifications of the same image.
As preserving original image structure during editing is stated as a more difficult task for real images than the naturally generated by the diffusion model, we follow Hertz et al. (2022) by. first, denoising latent encodings with source prompt (the one used during inversion), and, after 6% of the steps, using target prompt conditioning. The examples presented in Fig, 27 indicate that our fix (1) enables stochastic editing of images and (2) enables image manipulations in plain image regions, contrary to editing with na've DDIM latents.
DDIM Inv. editing
Input image
Our editing (varying forward diffusion seed)
"fantasy-style palace with numerous towers and arches, all sculpted from golden sand under a bright-blue-sky colorful rainbow sky"
"miniature pizza made from clay, featuring colorful toppings like green peppers, red onions, and brown sausage pieces on bright red sauce base. the pizza is circular with a thick crust en-e- gray gradient-background with glass of drink"
"simple black colorful silhouette of bird thin, curved branch with few leaves, set against a plain white background, the bird faces to the right"
"a close-up photo of a hand holding a colorful origami hummingbird made from red and yellow paper, set-against plain plain-light drawings in the background"
Figure 27: Replacing first DDIM inversion steps with forward diffusion enables stochastic im- age editing, resulting in multiple semantically correct manipulations of the same input image. Contrary to DDIM Inversion, editing with latents produced by the solution introduced in this work enables image manipulations in uniform input image areas.
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0.4 REAL IMAGE EDITING WITH MASACTRL
In this section, we present examples for editing real images from the PIEBench dataset (Ju et al., 2024) when our inversion method is combined with the MasaCtrl (Cao et al. 2023) editing engine. In Figs. 28 to 30 we qualitatively compare with Naïve DDIM Inversion across several editing tasks: object replacement, attribute editing, and object removal. We present that replacing first 4% of inversion steps with forward diffusion lcads to more successful edits in prompt adherence, while not observing degradation in consistency to input images.
Input Image
Edit: MasaCtrl + DDIM Inv. Ours (4%)
Input Image
Edit: MasaCtrl + DDIM Inv. Ours (4%)
wearing pink tiger hat scarf
the roof at night" cat
cat
dog
"a cute little, with big bunny + pig eyes + ears
wearing colorful goggles" monkey man
chair "a... and lamp umbrella Figure 28: Object replacement on real images with MasaCtrl. Comparison for Naive DDIM Inversion and DDIM with our (forward diffusion 4% of steps). Model: Stable Diffusion 1.4.
"a fluffy with yellow eyes sitting floor" cat panda
Input Image
Edit: MasaCtrl + DDIM Inv. Ours (4%)
Input Image
Edit: MasaCtrl +
DDIM Inv. Ours (4%)
"a colorful parrot with its wings spread fold
"a cartoon painting of fox with in car" big eyes eyes
"painting of sitting a laundry room" shepherd dog poodle dog
"a cat looking up at something" long haired - short haired
"a man" serious smile happy Figure 29: Attribute editing on real images with MasaCtrl. Comparison for Naïve DDIM Inver- sion and DDIM with our fix (forward diffusion in 4% of steps). Model: Stable Diffusion 1.4.
beautiful white wolf" furry bald
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Input Image
Edit: MasaCtrl + DDIM Inv. Ours (4%)
Input Image
Edit: MasaCtrl + DDIM Inv. Ours (4%)
puppy sitting in field of dandelions'
a painting of d-dog the forest"
"a big ship in bottle the dark ocean"
"'a painting of orange chair
and-a lamp a living room"
"a cartoon of woman is painting pumpkin with a cat"
"a girl red dress standing in a field surrounded by battoons and trees"
"an astronaut standing on the water with- the moon clouds in the background"
"a poster of bus driving down a road with mountains and moon in the background"
Figure 30: Object removal on real images with MasaCtrl. Qualitative comparison for Naïve DDIM Inversion and DDIM with our fix (forward diffusion in 4% of steps). Examples generated with Stable Diffusion 1.4.
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O.5 STYLE TRANSFER WITH STYLEALIGNED
we present qualitative comparison of Naive DDIM Inversion and our approach when combined with StyleAligned (Hertz et al. 2024) for the task of Style Transfer. Examples have been generated with Stable Diffusion XL. using the same hyperparameters for both settings on the StyleDrop dataset (Sohn et al. 2023). We observe that replacing the first steps of DDIM Inversion with forward diffusion enables better prompt-adheen adheerncc for generations.
In Figs. 31 and 32
"baby penguin"
"robot"
"avocado"
"boat"
StyleAligned DDIM Inversion
Reference style: "watercolor painting"
StyleAligned w/ ours (forward 4%)
"bench"
"banana"
"baby penguin"
"moose"
SlyleAligned
Reference style: "watercolor painting"
StyleAligned (forward
"f1 race car"
"banana"
"christmas tree"
"robot"
StyleAligned DDIM Inversion
Reference style: 'oil painting"
StyleAligned DDIM ours (forward 4%)
"baby penguin"
"cow"
"butterfly"
"avocado"
StyleAligned
Reference style: "oil painting"
StyleAligned (forward
Figure 31: Examples of style transfers from real images from the StyleDrop (Sohn et al. 2023 dataset. Comparison for Naive DDIM Inversion and DDIM with our fix (4% of steps replaced).
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"coffee maker"
"f1 face car"
"baby penguin*
"butterfly"
StyleAligned
DDIM Inversion
Reference style: "glowing"
SlyleAligned DDIM w/ (forward 4%)
chhistmas tree"
"avocado"
"butterfly"
"baby penguin"
StyleAligned DDIM Inversion
Reference style: "glowing 3d rendering"
StyleAllinedd DDIM w/ ours (forward 4%)
"wood cabin"
"boat"
"christmas tree"
"baby penguin"
StyleAligned + DDIM Inversion
Reference style: "kid cranyon drawing"
StyleAligned ours (forward 4%)
Figure 32: Examples of style transfers from real images from the StyleDrop (Sohn et al. 2023 dataset. Comparison for Naive DDIM Inversion and DDIM with our fix (forward diffusion in 4% of steps). Examples generated with Stable Diffusion XL.
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P LATENT CORRELATIONS IN FLOW MATCHING MODELS
In this section, we analyze if, similarly to latents produced with DDIM inversion in Diffusion Mod- els, inversion procedure with Flow Matching models leads correlations.
The inversion procedure can be incorporated into Flow Matching (FM) models (Lipman et al. 2023
Liu et al. 2023). e.g., for image editing (Avrahami et al., 2025; Kulikov et al. 2025 Rout al. 2025 ). The generative process of FMs is defined as an ordinary differential equation (ODE) over time E [0, 1] with time-dependent velocity field V:
dep V(z, t)dt.
(16)
Commonly, this ODE, given an initial condition 21 (N( I), is solved numerically with Fuler method, leading to iterative sampling process E (T, T 1, ...., 1), defined as
-t-1 2z + (at-1 - ot) uz t),
(17)
with being neural network parametrizing the continuous velocity field leading to clean images 2o and or being a noise schedule.
The inverse step, described in Avrahami al. (202), can be expressed
= 21-1 + (o, o1-1) vo (z( t):
(18)
with an assumption that locally t) = v)) We refer to this formulation as ODE Inver- sion.
As the approximation relies on a similar assumption as in the case of DDIM (Eq. we ana- lyze if the ODE Inversion, similarly, induces correlation patterns in output latents. In Table T9 we report image reconstruction error, editing textual alignment (CLJP Similarity to edit prompt and Directional Similarity (Gal al. 2022)), and metries validating the latents' normality. We employ FLUX.1 (Labs] (024) model with T = 50 inversion and sampling steps. We present that the latents resulting from the ODE Inversion algorithm, similarly to the case of DDIM latents, exhibit corre- lations and visible deviation from the Gaussian distribution. Importantly, these deviations, when compared to using original noise, lead significant decrease in prompt alignment when starting the generation process with an editing prompt. Additionally, in Table [9] we compare original noise and ODE Inversion latent diversity for plain and non-plain input image pixel regions. Although not significantly visible as in DDIM latents, ODE Inversion outputs as well tend to be more erroneous for plain image pixels and less diverse in those areas.
Finally, in Fig. 33 we present qualitative examples for image reconstructions and latent correlation when ODE Inversion is performed. As visible, after decoding with FLUX's decoder, ODE Inversion latents exhibit correlations in locations that represent smooth pixel areas of images. Additionally, we plot the absolute error between original Gaussian Noise and ODE Inversion latents after applying PCA for dimensional reduction (as FLUX operates in 16-channel latent space).
Metric
Gaussian Noise
ODE Inv. Latent
Image
MAE
0.00
0.05
Reconstr.
LPIPS $
0.00
0.16
CLIP Text
Edit prompt 1
81.49
56.40
Alignment
Directional Sim. f
87.94
55.32
Correlation 4.
0.14
0.27
Normality
KI. Div. x10
4
0.20
3.80
Noise
Plain pixels
0.00
0.31
Error
Non-plain pixels
0.00
0.26
Plain pixels
0.98
0.94
Variance
Non-plain pixels
1.01
1.03
Table 19: Comparison between original Gaussian Noise and latents resulting from ODE Inver-
sion process with FLUX.1 model. We show that ODE inversions are more correlated than Gaussian and significantly deviate from normal distribution. This leads to worse text alignment during editing.
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ODE Inv.
Decoded:
INoise-Latentl (after PCA)
Image
Reconstruction
Noise
Inv. Latent
Figure 33: ODE Inversion in Flow-Matching models, similarly DDIM Inversion in Diffusion models, produces latent encodings with correlations. Reconstructions performed with FLUX.
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Reviews:
[{"review_id": "3Tl3j1ShMm", "reviewer": "Reviewer_W4R9", "summary": "This paper presents a systematic analysis of DDIM inversion in diffusion models, focusing on the discrepancy between the original Gaussian noise and the latent representation of DDIM inversion. The authors identify that inversion errors primarily accumulate in early steps and are particularly pronounced in plain image regions. Based on this observation, the paper proposes a simple method that replaces the first inversion steps with forward diffusion noise.", "questions": "- Have the authors tested whether similar inversion-induced correlation patterns appear in flow-matching models such as FLUX or Stable Diffusion 3?\n- Can the proposed method enhance performance when combined with various editing engines such as MasaCtrl or Pix2Pix-Zero? Demonstrating improvements across multiple editing scenarios would further strengthen the paper.\n- Tables 4 and 7 suggest that increasing the proportion of forward diffusion replacement decreases reconstruction fidelity, while improving editability. This appears to reflect an inherent trade-off between preserving the original image information and increasing the degree of manipulation. It would be valuable to analyze or formalize this trade-off explicitly.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "- The paper provides a thorough and insightful diagnosis of the underlying causes of latent distortions introduced during inversion.\n- The experiments are conducted across a diverse set of diffusion models, supporting the generality of the findings.\n- The proposed forward-diffusion replacement is conceptually simple, easy to integrate, and empirically improves both interpolation smoothness and the diversity of editing outcomes.", "weaknesses": "- The analysis focuses on diffusion-based models and does not provide evidence that similar problems occur in flow-matching models (e.g., FLUX, Stable Diffusion 3)\n- The paper evaluates mainly interpolation and text-guided editing, but does not explore other inversion-driven applications (e.g., local editing, style transfer).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "Boo3dkWZhh", "reviewer": "Reviewer_Q9MZ", "summary": "The authors examine DDIM inversion in diffusion models, a process of recovering an approximate noise map that reconstructs a user provided image. First, they study the statistical relation between pure normal gaussian noise, the corresponding sampled image, and the noise obtained via inversion of that same image. They show that the inverted noise maps differ from the standard gaussian distribution, having especially high neighboring pixel correlations in areas where the input image is smooth. Secondly, they claim that these statistical deviations lead to higher inversion error, and worse performance when used for of text-based editing and image interpolation. Finally, the authors claim that this error stems from low accuracy in the initial inversion timesteps and propose a simple fix of using random added noise instead, which improves the inverted noise statistics and its applicability to interpolation and editing.", "questions": "Please see weakness section. Addressing the raised concerns could affect my final rating for the paper.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "1.\tThe authors provide a nice observation regarding the statistics of inverted noise latents compared to the native noise space, and the repercussions regarding the usage of these latents for image manipulation and editing.\n2.\tThe authors provide a simple remedy to fix the inverted latent statistics, and as such their downstream editing potential, with minimal cost of reconstruction quality.\n3.\tThe authors provide thorough quantitative evaluation of the tasks presented (image interpolation and text-based image editing).", "weaknesses": "1.\tAdding random gaussian noise instead of inversion in the first steps. The authors claim that the last steps are not important for reconstruction quality, but the diffusion process acts as a coarse-to-fine spectral regressor throughout the whole process [1]. This means that the last steps should correspond to fine-grained details, such as textures. This can be observed, for example, in the results in figure 6 (top right) where the tower in the background is generated with small windows,  which did not exist in the original image.  An ablation on the effect of the added noise for different amounts of timesteps is recommended.\n\n2.\tHard to qualitatively evaluate the results for inversion reconstruction and text-based image editing. Only a few results are present in the main paper, and the results in the supplementary section are highly compressed, while no further image files were provided in the zip. I would recommend adding more results to the paper, especially for the editing experiments, since current metrics cannot fully replace human assessment.\n\n[1] Rissanen et al. 2023. Generative Modelling With Inverse Heat Dissipation", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "IQEYgTovib", "reviewer": "Reviewer_Mq2S", "summary": "This paper sheds light on a known phenomena—the discrepancy between a real Gaussian noise and the inversion noise obtained through DDIM inversion—and provides a simple fix to mitigate it. When performing DDIM inversion on an image, the resulting noise is generally not Gaussian. The authors point out that this is particularly true in regions of the image that are flat (i.e. textureless). Through a set of experiments, they pinpoint the reason of this discrepancy to lie in the very first few steps of inversion. To solve this, the paper proposes to replace the first few steps of inversion by a forward noising step. This is generally done for only ~4% of the denoising path. \n\nExperiments ablate the threshold to which one should do forward noising, and validate that this fix indeed improves inversion quality for editing tasks.", "questions": "**DDIM Inversion Formula**\n\nThere appear to be different formulations of DDIM inversion in the literature. On one hand, Null-text inversion (https://arxiv.org/pdf/2211.09794, Sec 3.1) and Dhariwal & Nichol (https://arxiv.org/abs/2102.09672) both call the denoising network on $x_{t-1}$ with timestep $t-1$, i.e. $\\epsilon^{(t)}\\_{\\theta}(x_{t}, c) \\simeq \\epsilon^{(t-1)}\\_{\\theta}(x_{t-1}, c)$. On the other hand, the authors in Eq. (3) seem to follow ReNoise (https://arxiv.org/pdf/2403.14602, Sec 3.1) and keep the same timestep but change $x_{t}$ to $x_{t-1}$, i.e. $\\epsilon^{(t)}\\_{\\theta}(x_{t}, c) \\simeq \\epsilon^{(t)}\\_{\\theta}(x_{t-1}, c)$. In my understanding, the former formulation (calling the network on $x_{t-1}$ with its corresponding timestep $t-1$) represents the correct reverse ODE. This leads to the following questions:\n\n- Which version exactly did the authors implement in the experiments?\n- Have the authors noted any difference in the conclusions using the other version? \n- In particular, this choice changes the definition of the approximation error $\\xi(t)$ in Eq. (4). How does that change the results and conclusions?\n\nNote that in Appendix E, the authors use the latter formulation (non-matching timesteps) in the text, but the illustration in Fig. 8 seems to show the former formulation (matching timesteps). I believe this could be further clarified to improve the reproducibility of the experiments.\n\n**Image Editing and Reconstruction**\n\nOverall, I am not very convinced by the validation provided to measure the quality of image editing applications.\n\n- In Fig. 7, the explanation suggests the method is superior to standard DDIM inversion because it performs similarly to original Gaussian noise in both image diversity and prompt alignment. However, this comparison may not fully validate the editing task. While using real Gaussian noise $x_T$ with a target prompt will expectedly yield a high-quality, prompt-aligned image, it offers no guarantee of fidelity to the source image. Successful editing requires preserving significant portions of the original image while making targeted modifications. Therefore, performance closer to real Gaussian noise does not, by itself, validate superior editing performance.\n- A similar remark applies to Table 7 and Sec 4.3: CLIP text alignment alone is insufficient to assess image editing quality, as it does not measure the preservation of unedited regions. I would suggest considering metrics specifically designed for editing, such as **directional CLIP similarity** (StyleGAN-NADA, https://arxiv.org/abs/2108.00946) or **AugCLIP** (https://arxiv.org/abs/2410.11374), for a more comprehensive assessment.\n- Image editing performance often differs between generated and real images. I may have missed it, but are there any editing results with real images? If not, adding a few such examples would significantly strengthen the assessment of the method's practical utility.\n\n**Result with Large Latent Diffusion Models**\n\nLarge text-to-image diffusion models like Stable Diffusion are very common in the field, yet not fully assessed in this paper.\n\n- Considering the widespread use of Stable Diffusion models (SD2.1, SDXL, SD3), I was wondering why the authors did not include analysis with these models in the first part of the paper (beyond the results with SDXL in Sec. 4.3)?\n- Did the authors observe any correlation between the quality of standard DDIM inversion and the size of the model's training dataset? One might expect that models trained on larger datasets are less prone to inversion errors, and that the proposed fix would have less impact in these cases. I would be happy to get the authors' perspective on this.\n\n**Other questions and notes**\n\n- What model was used in Figure 1, Figure 6 and Figure 13?\n- The CFG scale can significantly impact experiment outcomes. The authors mention in Appendix G that they use a CFG scale $w=1$ for conditional diffusion models. Does this apply only to the image editing part, or to all experiments in the first part of the paper as well?\n- In Sec 4.3, I believe it could be more explicitly mentioned that the results in Table 7 are based on a comparison with an equal number of function evaluations (NFEs).\n- Appendix H shows interesting differences in the shape of the most probable triangles between models. Do the authors have an explanation for what might be causing these vastly different triangle shapes?\n- In Fig. 3, perhaps a different color scheme or the addition of level set lines could help better visualize the intended point. If I understand correctly, the bottom-left corner (distance between $x_T$ and $x_T$) should be 0. However, its color appears similar to the top-right corner, which would suggest that the image latent $x_0$ is almost the same as the inverted noise $\\hat{x}_T$. This seems counter-intuitive, and a clarification would be helpful.\n- Appendix N shows an interesting experiment using the $L_2$ distance. In general, it is understood that the noise is not necessarily close to the image in an $L_2$ sense, but rather that they are correlated. Out of simple curiosity, does the mapping become feasible if a Pearson correlation metric is used instead?\n- Lastly, I noted a minor citation issue: the reference to Samuel et al. appears to be missing the year, showing up as \"Samuel et al.\" in the text instead of \"Samuel et al. 2025\".\n\nI thank the authors for their time and look forward to any clarifications they can provide.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "The paper provides a structured analysis of the problem, which can be valuable to the community. While many of its conclusions are already well-established within the field (DDIM inversion is not a Gaussian noise etc.), the experiments presented in the methods section offer tangible evidence that reaffirms these claims. Furthermore, the paper proposes a simple solution that appears to effectively mitigate the identified issues. Overall, the presentation is clear and easy to follow.", "weaknesses": "My main concern with the paper lies in its contributions. The method is organized into three subsections, in which the authors address the following questions:\n\n- Sec 3.1: Are there any difference between the original noise and the DDIM inversion noise? (Answer: Yes)\n- Sec 3.2: How does it differ? (Answer: Loss of variance mostly in plain regions)\n- Sec 3.3: Why? (Answer: Because it happens in the first few steps)\n\nIn my opinion, the first two sections primarily reiterate observations and facts that are already well known to the community, albeit supplemented with additional visualizations and plots that support these claims. The authors themselves mention prior work studying the same problem at the beginning of Sec 3.1. The third section has the potential to be more interesting; however, its conclusion appears to be based mainly on empirical observation, and the authors do not provide a convincing explanation for the observed phenomenon, which would have been the most compelling aspect of the analysis. Lastly, the proposed fix, while somewhat effective, appears ad hoc and lacks a principled justification.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "373L9tSU4z", "reviewer": "Reviewer_H3z8", "summary": "This paper analyzes DDIM inversion, specifically the non-gaussian properties of the final latent $\\mathbf{\\hat{x}}_T$ which has been mentioned multiple times in previous literature but not explored throughoutly like the authors have done in this work. The authors show that the inverted latents quantitatively exhibit spatial correlations with the original image, especially in smooth (plain) iage regions, attributing it to the approximation errors in the early inversion steps. They propose a simple fix of replacing the first few steps with the original forward diffusion process. Their fix restores the gaussian properties of the final inverted latents, improving editability and text alignment when using DDIM inversion.\n\nOverall, although this work has limited applicability (see weaknesses), this work is technically solid with extensive experiments that dive deep into the emprical findings that have been brushed off in previous works. Limited applicability do not outweigh its contributions in the form of empirical analyses.", "questions": "- in appendix G, the authors mention: \"Classifier-Free Guidance introduces additional errors to the DDIM inversion, so to focus solely on the inversion approximation error, we disable CFG by setting the guidance scale to w = 1. To the extent of my knowledge, this is the main reason multiple \"image-to-noise inversion techniques\" have been explored in literature. Although setting w > 1 does drastically alter the given image, I wonder if applying the proposed fix also provide a meaningful improvement in terms of fidelity or text alignment.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The main strenghts of this paper is in its arrangement and analysis of previous work. The authors go through great lengths in analyzing the claims of previous work that have mentioned this non-gaussian property of the final latent in DDIM inversion, and structures it well with their own quantitative experiments, corroborating past claims with evidence.\n- Their quantitative experiments bring a clear insight that the early inversion steps were the root cause of the issue, emphasized more in what the authors call smooth (plain) image regions. Their proposed fix is simple and easy to implement, with convincing quantitative/qualitative improvements compared to the vanilla method of simply changing the target prompt starting from $\\mathbf{\\hat{x}}_T$.\n- The experiments are wide breadth-wise, with multiple ablations that quantitatively show improvements.", "weaknesses": "Weaknesses:\n- The main weakness of this work that I've found is the limited theoretical grounding of their explanation on why the early inversion steps causes correlation with the original image. Their explanation for why the early steps cause correlation is mostly empirical, and the connection they make to the ODE curvature could be formalized further. In order to prove why the proposed simple fix works should be first followed why the early inversion steps are theoretically the root cause. I do not see the simple, heuristic fix the authors propose as a weakness, just that the cause should be diven into deeper.\n- The scope of their fix, especially in terms of image editing, is narrow as they demonstrate it on solely DDIM inversion. To the extent of my knowledge, most image editing tasks with text prompt inversion methods do not rely on plain DDIM inversion, but rather \"image-to-noise inversion techniques\" as described in section 2. Some of these inversion techniques might not be directly applicable to the proposed method, but when they are, I believe the proposed method should be demonstrated on them.\n\nComments:\n- Though not strictly a weakness, It would be better if how the plain background or surfaces are mathematically calculated was included in the main text (even just a breif 2-3 liner) instead of fully allocating it to appendix I.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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:

Decision: Accept (Poster)