Precise Diffusion Inversion: Towards Novel Samples and Few-Step Models
Authors: Jing Zuo
Luoping Cui
Chuang Zhu
Yonggang Qi
Venue: NeurIPS 2025 poster ()
Keywords: Diffusion model; Inversion; Diffusion based real image editing
Primary area: deep_learning
TL;DR: A general-purpose framework for accurate and efficient diffusion inversion via noise embedding optimization, enabling few-step inference and robust performance on novel samples.

Abstract: The diffusion inversion problem seeks to recover the latent generative trajectory of a diffusion model given a real image. Faithful inversion is critical for ensuring consistency in diffusion-based image editing. Prior works formulate this task as a fixed-point problem and solve it using numerical methods. However, achieving both accuracy and efficiency remains challenging, especially for few-step models and novel samples. In this paper, we propose ***PreciseInv***, a general-purpose test-time optimization framework that enables fast and faithful inversion in as few as two inference steps. Unlike root-finding methods, we reformulate inversion as a learning problem and introduce a dynamic programming-inspired strategy to recursively estimate a parameterized sequence of noise embeddings. This design leverages the smoothness of the diffusion latent space for accurate gradient-based optimization and ensures memory efficiency via recursive subproblem construction. We further provide a theoretical analysis of ***PreciseInv***'s convergence and derive a provable upper bound on its reconstruction error. Extensive experiments on COCO 2017, DarkFace, and a stylized cartoon dataset show that ***PreciseInv*** achieves state-of-the-art performance in both reconstruction quality and inference speed. Improvements are especially notable for few-step models and under distribution shifts. Moreover, precise inversion yields substantial gains in editing consistency for text-driven image manipulation tasks. Code is available at: https://github.com/panda7777777/PreciseInv

Precise Diffusion Inversion: Towards Novel Samples and Few-Step Models
Jing Zuo Luoping Cui Chuang Zhu Yonggang Qi
School of Artificial Intelligence, Beijing University of Posts and Telecommunications 2uoj07230gmail com, (lpcui, czhu, qiyg))bupt..... edu. cn Corresponding author
Abstract
The diffusion inversion problem seeks to recover the latent generative trajectory a diffusion model given a real image. Faithful inversion is critical for ensuring consistency in diffusion-based image editing. Prior works formulate this task a fixed-point problem and solve it using numerical methods. However, achieving both accuracy and efficiency remains challenging, especially for few-step models and novel samples. this paper, we propose Preciselnv, a general- purpose test- time optimization framework that enables fast and faithful inversion in as few two inference steps. Unlike root-finding methods, we reformulate inversion as learning problem and introduce dynamic programming-ing innpiieed strategy recursively estimate parameterized sequence of noise embeddings. This design leverages the smoothness of the diffusion latent space for accurate gradient-base based optimization and ensures memory efficiency via recursive subproblem construction. We further provide theoretical analysis of Preciselnv's convergence and derive a provable upper bound on its reconstruction eтror. Extensive experiments on COCO 2017, DarkFace, and a stylized cartoon dataset show that Preciselnv achieves state-of-the performance in both reconstruction quality and inference speed. Improvements are especially notable for few-step models and under distribution shifts. Moreover, precise inversion yields substantial gains in editing consistency for text-driven image manipulation tasks. Code is available hhtptss: ///::t////iii comm/aanda7777777PPecccccl
1 Introduction
32 33 have demonstrated strong generative capabilities in producing high-quality and diverse images. Built upon these models, many recent methods enable wide range of image editing operations by guiding the generative process with
Large-scale pre-trained diffusion models [10] 17
user inputs, such as text prompts 4 16,
21 22 29), reference images [ 6 23 25], and spatial masks 28 To ensure consistency and controllability in such edits, faithful inversion of real images into the diffusion process is essential B
Since the sampling process of diffusion models is inherently irreversible, mapping real image back into the model domain remains a fundamental challenge. Existing methods on diffusion inversion can be divided into three major categories: forward optimization, backward optimization, and invertible samplers. Invertible samplers, such as EDICT (38, BDIA 43), and BELM (39], introduce explicit constraints into the sampling procedure to enable bidirectional generation. Backward optimization methods 21 22 29] fix the forward noising trajectory of a real image and optimize the reverse diffusion process match this trajectory. Both types of methods improve reconstruction quality by modifying the denoising path, but often weaken the generative ability of the diffusion model. To address this issue, forward optimization methods estimate noising trajectory that can be faithfully
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Inpat Imuge
Easylny
Figure I: Qualitative comparison of diffusion inversion methods using SD v1.4 on challenging cases: novel sample (first row) and two-step inference (second row).
reversed by the diffusion model. For example, several methods into a fixed-point equation and solve it via Anderson acceleration 2] while ReNoise [3] refines an iterative renoising mechanism. However, these methods suffer from slow convergence and limited performance, especially under few-step inference or on novel samples, illustrated in Fig.
30
45
convert the problem
In this paper, we propose a general framework named Preciselnv that efficiently solves the diffusion inversion problem by progressively learning parameterized noising trajectory. Specifically, we refor- mulate diffusion inversion as a learning problem and decompose into T overlapping subproblems by leveraging the Markov property of the diffusion process. We then introduce dynamic programming- inspired strategy [5] to recursively solve these subproblems. In each subproblem, Preciselnv learns local noise embedding that approximates the optimal intermediate state along the inversion trajectory.
Benefiting from the smooth transitions in the latent space [44], this gradient- based optimization converges more accurately than numerical solvers. Moreover, the recursive formulation is highly memory-effciient: inversion on the SD v1.4 base model requires only 3.43 GB GPU memory, regardless of the number of inference steps. Extensive experiments show that Preciselnv achieves of-t-o--thheart reconstruction performance in both quality and efficiency (Section 4.1) The im- provements especially pronounced under few-step inference (e.g.. T= 4) and novel samples. Furthermore, precise inversion yields more semantically continuous latent representations (Fig. 55) which substantially improve consistency and controllability in text-driven editing tasks (Section 4.2)
Our main contributions are summarized follows: We propose Preciselnv, a general-purper test- time optimization framework for diffusion inversion that enables fast and faithful image reconstruction under few-step inference and distribution shift. (ii) We reformalize diffusion inversion as a sequence of non-overlapping learning subproblems and introduce a dynamic programming strategy to solve them efficiently. (iii) We demonstrate that precise inversion yields smoother latent trajectories, which in turn improve consistency and controllability in text-driven image editing.
2 Background
2.1 Diffusion Models
Given samples from the data distribution (xxo). diffusion models [17] define a generative process by learning to reverse fixed Markovian forward process that progressively corrupts data by adding Gaussian noise. The forward process is formulated as:
((xiTT xo) = II (xx x)-1), g(xe xx-1) == N(xii o x;- az).),,
(I)
where Xo (xn). {x latent variables, and {ar) If- (0, 1 is predefined noise schedule. The marginal distribution at an arbitrary timestep / is given by:
q(x xo) -Nxx; Va, xo. (1 āz I),
(2)

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where ān == IT ag.. The generative process is modeled as parameterized Markov chain:
po(Xo:T) = :=(TT)
II po (x:-1 xx), (x xx) = (ix Mo (), Ee (xe, 1)),
where p(xr) (xy; 0, I) and 9 denotes the model parameters. In practice, a denoising neural network Ep is trained to predict (x(x,, t), and (x,,, t) is set to a constant o, according to a,, The training objective minimizes a simplified variational bound:
Cimple (0) = Br-ut (...... (x00 (0.)) [Ile (xx,
where
X V X0 + a
(5)
Starting from X7 (xT; O, I), the DDPM sampling procedure step to generate Xy as follows:
iteratively applies the reverse
vI cx(xx,))
X
X1
o:S,
6
Vau
V1
ar-1
where z (2 I). To reduce the number of inference steps, the DDIM sampler 36 Eq. (6) into non-Markovian form:
converts
(1
-1
1
X
cx t).
at
/4-1
To further enhance the inference efficiency, recent efforts have focused on training few-step diffusion
models, such as Consistency Models (CM) (37 Latent Consistency Models (L.CM) 227. Adversarial
Diffusion Distillation (ADD) models [35 Shortcut models [12 and MeanFlow [14]
2.2 Image Inversion in Difffusion Models
Inverting real images into the latent space of pretrained diffusion model is critical for diffusion- based image editing methods. Given real image our goal is to estimate corresponding noisy latent Xy, such that X can be reconstructed by applying the reversed denoising trajectory to xy- Unfortunately, the neural network Eg do not inherently predict noise direction e from x,-1 to X DDIM Inversion Eq. 77. we obtain:
[ was among the earliest methods attempted address this issue. Rewriting the
1 at-1
X1-1
V ar-1
cs (x),
(8)
01-1
a1
DDIM Inversion assumes Ep Ex(xx11, t - 1) x (x t) and iteratively applies Eq. (8) from 1 to
f = T. However, the denoising trajectory nonlinear, resulting discrepancies between predicted x, and actual X4-
Subsequently, there are three main lines of work on diffusion inversion: modifying the reversed denoising trajectory, designing invertible samplers optimizing the initial noise latent Xy. A common practice of the former is to optimize the denoising process to better align with the trajectory obtained by DDIM inversion. For example, Null-Text Inversion (29] optimizes unconditional text embeddings to implicitly adjust the denoising trajectory, while Eta Inversion [22] uses a hyperparameter r to control the trade-off between the stochastic denoising trajectory and the vanilla DDIM Inversion trajectory. Moreover, a DDPM inversion method [2]] was proposed, which rectifies the DDPM denoising process using forward trajectory constructed by independently applying Eq. each timestep t. More recently, several invertible samplers [38 43 have been proposed for bidirectional generation. While, in general, manually modifying the denoising trajectory enhancing reconstruction quality, inevitably disrupts the original generative process the diffusion model.
To preserve the original generative process, another line of methods has been proposed to estimate more accurate value of e, (x,, 1) in Eq. (8). For example, ReNoise [3] ensembles multiple DDIM Inversion results at each iteration. In addition, several methods reformulates the diffusion inversion

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problem as fixed- fixed-point problem and solves the problem by improving Anderson accelcration 2 methods. Let the estimated value of Ep (x,,, (x,,)) t) be denoted e;, then have:
= E0(x,,
(9)
Substituting Eq. 9 into Eq.
8
obtain:
Ot:
Cxt
X
1 E
(10)
a4-1
at-1
0it-1
By replacing x; in Eq.
2 with Eq.
10
deduce that:
6 60
Ott
X
Ott
6
(1I)
01-1
O--1
0/-1
Ot
To effectively solve Fixed-Poin Eq. (I). AIDI uniformly mixes the outputs from two adjacent iterations in vanilla Anderson acceleration, while Easylnv [45] increases the influence of x in estimating xi- by directly predicting x; instead of e; Despite recent progress, achieving precise and efficient inversion remains challenging, especially under few-step inference or when the inputs are novel, illustrated in Fig.
3 Method
3.1
Reformulating Diffusion Inversion as Learning Problem
Given pretrained diffusion model that defines mapping X' Xy + XT-1 H ... Xo from latent space image space, we hypothesize that the inverse mapping X Xo + X1 . XT exhibits a smooth optimization landscape, owing to the smoothness of transitions in the latent space [44]. Based on this observation, we reformulate diffusion inversion as a learning problem. Let x be an observed image, and let ex denote learnable noise embedding. The objective is defined as:
arg min [x({x) xoll²;
(12)
ex
where
Xy a7 + v1 - är ej.
(13)
3.2 Progressive Denoising Trajectory Learning
Directly optimizing (12) requires backpropagation through all T timesteps. which incurs prohibitive memory and computational costs. To address this, we exploit the Markov property of the diffusion process decompose problem [2) into T subproblems and solve them efficiently using dynamic programming principles.
Subproblem Decomposition Let (x+)/= denote latent variables along the denoising trajectory from Xy to Xr, as indicated by the spherical markers along the blue arrow in Fig. [ Since only xo is observed, we adopt bottom-up dynamic programming strategy sequentially estimate latent states from to Xy. To this end, we define a collection of subproblems {P(t)) where each P(t) corresponds to the estimation of Xx. Specifically,
P(t) arg min [x((x)) xoll?
(14)
?
with
x = Vo + v1 ā, ;
(15)
where eç is the learnable noise embedding at timestep E ,1, T)..
Optimal Substructure The inverse mapping X' 11 + + ... + Xy inherits the Markov structure of X. implying that the optimal solution to each subproblem P(t) depends only on solution to the previous subproblem P(t 1) for all 1. > 2. In particular, P(1) depends solely on the known observation Xg. This recursive dependency establishes that the subproblems (P(1)
exhibit the optimal substructure property.

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ci
min (a(s)
ming (( - x2-
mina
((x))
ming, (u(x).))
-71l"
X
ming. plg; -)- al? xfalll
min ((bb))
X
XT
Figure 2: Overview of the proposed Preciselnv.
Overlapping Subproblems Each subproblem P(t) seeks latent variable such that the denoising trajectory from x, accurately reconstructs Xg- As adjacent subproblems P(t) and (t 1) share this reconstruction objective and lie on successive steps of the trajectory, their optimization processes overlap. Specifically, the solution to P( - 1) influences and partially informs the optimization of P((), resulting in substantial overlap across subproblems.
Bottom-Up Computation Without loss of generality, we adopt the DDIM sampling strategy. For convenience in the subsequent analysis, we reframe Eq. (7) as:
aor- =V
(v
p(xx)
cx(x
(16)
ar-1 at
Substituting into Eq. [4), the first subproblem becomes:
P(1) arg min ||x((x)) xul1? ";
(17)
arg min [|{(x;) x 1|
Exploiting the optimal substructure of the subproblems {P(t)) we derive a recursive formulation that maps P(t 1) to P(t):
P(t) arg min |x(xx) - xxol2
arg min [l((x)) x;_1 ||?
(18)
-((P(L-)),
where x denotes the optimized solution obtained from P(t - 1). Leveraging the recursive formulation f. we solve the subproblems (P(t)) iteratively from t 1 to T, as indicated by the red dotted arrows in Fig. 2 We define convergence threshold n for P(t), and stop the optimization when [|m(x;) x < .7. practice, we set r) the range of 10-2 10-3, and the inference step number 7 jointly control the trade-off between reconstruction accuracy and inference speed, as detailed in Table
Optimization Procedure. The overall optimization algorithm of Preciselmy is presented in Algo- rithm [ The procedure memory-efficied since backpropagation is performed only over a single timestep. Moreover, Preciselnv is general and model-agnostic. We show its adaptability to different diffusion backbones (e.g., rectified flow (66 and samplers (e.g., DDPM 17] in Appendix A and provide additional quantitative results in Appendix D.I
5

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Algorithm Preciselnv for Diffusion Models with DDIM Sampler
1: Input: Real image Xo, diffusion model co, convergence threshold 77, number of inference steps T
2: Output: Inverted latent x;
3: for trt== to T do
4: Initialize E ~ (N
5: if then
6: x - va--i Xn + VI 04-1 6-1
7: else
8:
X; + X0 end if
9:
10:
1/ Apply a single DDIM Inversion step
G7 vi (u(xi-1) vāpx) (u defined Eq. (16)
12:
Xi Vā, XD + vI E
13:
L + ||{((x;)
112
14:
while Liee 17 do
15:
X f Vāa Xy + /1 04 E
Lix |[(x) x;) x
17:
6 4- 6 VLrcc
18:
end while
19:
end for
return xi-
3.3 Theoretical Analysis of Convergence
While the progressive optimization strategy above is conceptually appealing, its convergence has to formally established. Here, we provide a theoretical proof to establish its convergence. We begin by stating two standard assumptions that widely used in diffusion models [37].
Assumption 1. The diffision model ea (xt, t) is Lipschitz continuous in Xt with constant Lis i.e., [|e,(xi, - (x( t)ll S. Lm ||x] X2ll-
Assumption 2. Let L, == |(((x)) x:-1 The function L, has L-Lipschitz continuous gradients with respect to Xt, i.e., (x.) VL,(x)) < L| xill-
Under these assumptions, standard non-convex optimization results 15] apply. With gradient descent using fixed step size 7 < L for each subproblem P()), the local loss L, decreases monotonically. After iterations,
min I IV kE[I,K]
(k) {=
(19)
indicating convergence to a stationary point á, Since each step minimizes local reconstruction loss and the optimization proceeds recursively, the global loss L is non-increasing. Given that is Lipschitz in X,, the accumulated reconstruction error satisfies:
[x((x)) xol12 <
5z-
(20)
m
If L < Lm < 1 (satisfies due to Assumption ! and let max(f1.... .8 88 bound follows:
a geometric upper
T T-Lm
[x(xx) - x0l12 <
à L <
(21)
t=1
Theorem Under Assumptions and 2 monotonically to a stationary point of Lt.
gradient descent on P(t) with step size 7 2/ converges
Theorem 2. Let l(t) == |x'(x;) 2 Under Assumption 1 and Theorem geometric upper bound, i.e.. I(T) 5/(1 Lm).
I(T) admits
Detailed proofs of Theorem and are provided in Appendix B

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3,4 Prompt-driven Image Editing
We apply Preciselnv to enable prompt-driven editing by replacing the inversion stage without modifying the editing pipeline. Let Xy denote the input image, and let c2 and e, denote the source and target prompts, respectively. We perform inversion conditioned on cs, following the progressive optimization strategy in Eq. (14). At each step 4, we solve
Pedi (t) = arg min (x;) x1-
(22)
where (-(-) generalizes Eq. (16) to conditional generation. This yields latent xi that faithfully reconstructs X under the conditioning of the source prompt.
To generate the edited image, we reuse xj and apply DDIM sampling under classifier-fres guidance (CFG) (18), where the target and source prompts act as positive and negative conditioning signals, respectively. The conditional mean of the guided denoising process is:
1 - 02-1 (V-L
a1-1 x,t
(v
- V Vot
(1+tw) ca(xe: l, Cpos) 6x 4, Cney)
Megas Coog (xx)
(23)
where Kepx. Eues denotes the deterministic denoising trajectory governed by Eq. (3 This pipeline procedure enables prompt-driven editing without task-specific designs and improves fidelity and localization by aligning the initial latent more precisely with the structure of the input image.
4 Experiments
In this section, we present experimental results with the aim of (i) demonstrating the state-of-the-art performance of Preciselnv for image reconstruction in terms of both quality and efficiency; (ii) verifying that faithful inversion enhances consistency in prompt-guided image editing; and (iii) providing insights into its local behaviors and interaction mechanisms.
4.1 Image Reconstruction
Datasets. We evaluate PreciseInv on three domains: LAION-aligned, low-light, and stylized. (i) The COCO 2017 (24] validation set contains 5,000 natural images with diverse everyday scenes. serves as close proxy the LAION distribution used in training most text-to-image diffusion models. (ii) The DarkFace [1] validation set includes 6,089 nighttime images captured in real- world low-light conditions, exhibiting extreme visibility degradation. (iii) The Cartoon dataset consists of 722 stylized images collected from the internet. These samples exhibit abstract shapes, exaggerated structures, and vivid palettes, reflecting rare visual styles far from the training distribution.
Baselines. We compare our method with forward optimization methods, including DDIM Inver- sion [8) ReNoise [33, and Easylnv [45]; and invertible samplers, including EDICT B8), BDIA [43, and BELM (39]. Following prior work 45 39), we don't 't compare with backward optimization methods, as they are not designed for recovering the original generative trajectory of diffusion models. We carefully tune hyperparameters for all methods.
We evaluate reconstruction quality using LPIPS, SSIM, and RSNR, which respectively measure perceptual similarity, structural alignment, and signal fidelity. To assess efficiency, also report the average inference time per image.
Metrics.
Results and Analysis. Table reports quantitative results on COCO, DarkFace, and Cartoon datasets using the SD v1.4 base model. With a tight convergence threshold (1=10-"), Preciselm achieves the lowest LPIPS, highest SSIM, and best PSNR across all datasets. Despite the high quality, its inference time remains competitive. With relaxed threshold (7=10-23) Preciselmv still surpasses most methods in LPIPS, SSIM, and PSNR, while reducing inference time 5.33 s. Among forward optimization methods, Easylnv and ReNoise underperform the 1000-step DDIM Inversion, which suggests that numerical or iterative methods suffer from performance bottleneck. In contrast, our method breaks through this bottleneck by large margin. In particular, on the stylized Cartoon dataset,
7

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Table 1: Quantitative comparison of diffusion inversion methods for image reconstruction using SD v1.4 on COCO, DarkFace, and Cartoon datasets.
LPIPS (C)
SSIM (1)
PSNR (t)
Time (s. 4)
Method
COCO
Dark. Cart.
COCO
Dark.
Cart.
COCO
Dark.
Cart.
Avg.
EDICT
0.430
0.329 0.032
0.367
0.630 0.931
14.04
20.42
29.87
45,50
Invertible
BDIA
0.431
0.329
0.033
0.366
0.630
0.946
14.04
20.42
30.89
172.40
Samplers
BELM
0.431
0.331
0.041
0.366
0.617 0.947
14.03
20.43
29.97
9.00
DDIM Inversion
0.118
0.073
0.145
0.714
0.871
0.879
24.67
30.89
23.50
41.30
ReNoise
0.120
0.086
0.323
0.724
0.869
0.851
25.00
30.84
22.21
38,20
Forward
Optimizing
EasyInv
0.210
0.210
0.165
0.666
0.780
0.883
23.13
27.60
21.95
23.60
PreciseInv (1 10
0.104
0.074 0.025
0.737
0.861 0.952
25.13
31.00
29.71
5.33
Precisetny (0=
0.078
0.052 0.018
0.756
0.878 0.960
25.86
31.79
31.42
23.29
Table 2: Quantitative comparison of diffusion inversion methods for image reconstruction using LCM-SD v1.5 and SDXL on the COCO dataset.
LCM-SD v1.5
SDXL
LPIPS (4)
SSIM (1)
PSNR (t)
Time (8, .)
LPIPS (L)
SSIM (t)
PSNR (t)
Time (s. ()
BELM
0.449
0,362
13.99
9.1
DDIM Inversion
0.626
0.420
15.74
35.5
0.492
0.464
16.24
154.8
ReNoise
0.603
0.414
15.59
83.1
0.424
0.533
18.26
27.4
EasyIny
0.194
0.683
20.89
35.1
Preciseluv (y) 10
0.103
0.753
25,55
8.83
0.185
0.763
27.00
7.43
Preciselnv by= 10
0,083
0.775
26.45
25.54
0.080
0.854
30.93
41.11
Table 3: Quantitative results of image reconstruction under the few-step inference setting for different inversion methods using SD v1.4 the COCO dataset.
T 2
T'
LPIPS (1)
SSIM (?)
PSNR (1)
LPIPS (1)
SSIM (?)
PSNR (1)
BELM
0.832
0.112
8.19
0.431
0.366
14.03
DDIM Inversion
0.331
0.591
20.62
0.306
0.593
20.65
ReNoise
0.199
0.671
22.92
0.158
0.702
23.53
EasyInv
0.563
0.357
14.97
0.537
0.332
13.66
PreciseInv
0.077
0.766
25.93
0.084
0.762
25.65
the performance gains are more pronounced, yielding lower LPIPS (-0.127), higher SSIM (+0.081), and better PSNR (+7.92 dB). Moreover, different invertible samplers exhibit similar reconstruction quality. Compared to EDICT and BDIA, BELM significantly decreases inference time from 45.5 to 9.00 s. Although they achieve remarkable success on the Cartoon dataset, their performance remains limited on COCO and DarkFace. By comparison, our method shows robustness across data types and further improves overall efficiency.
For generality. we also present the reconstruction results on the COCO dataset using the few-step model LCM-SD v1.5 and the high-resolution model SDXL in Table 2 Preciselnv consistently achieves the best reconstruction quality across the two base models. With 10=10-2 it already significantly outperforms all baselines while maintaining fast inference (8.83 for LCM-SD v1.5 and 7.43 s for SDXL). When using a tighter threshold (1=10--), the performance of Preciselnv is further improved. These results demonstrate that method is general across different model architectures.
As shown in Table the challenging few-step setting (T' 2, 4). ReNoise exhibits stronger few-step inference capability compared to other baselines. Nevertheless, our method achieves substantially better reconstruction quality across all metrics.
we report the reconstruction performance of different inversion methods under
4.2 Prompt-driven Image Editing
Here, we present the results of Preciselny on prompt-driven image editing, as shown in Fig. and compare its editing performance with existing methods in Fig. 4 We demonstrate that Preciselnv enables the preservation of fine-grained details that are irrelevant to the editing prompt across wide range of editing scenarios. For example, when editing a down jacket into a leather jacket, the original fabric folds are well preserved (left example of the first row in Fig. 3. Furthermore, compared to

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"a down leather jacket"
dark green clock"
wolf"
"a sketch style dress"
Figure 3: PreciseInv enables consistent and controllable image editing across diverse scenarios. From top left to bottom right: (1) texture editing (down leather), (2) color editing (light -> dark), (3) object transition (for - wolf), and (4) style transfer (photo - sketch). In each case, our method preserves non-edited attributes such as identity, pose, or background, demonstrating high fidelity in semantic consistency.
Original Images
DDIM
ReNoise
BDIA
BELM
Ours
desert grass surface"
O
"a with pink hair"
tiger lion'
"pixel kirby"
Figure 4: Comparison of different image editing results on prompt-driven image editing task.

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existing methods, Preciseltv enables more faithful and controllable prompt-based editing. As shown in the first row of Fig. our method better preserves both the tree structure and sky consistency during the texture transformation from desert to grassland, while baseline methods introduce sky artifacts (e.g., BELM) or distort tree details (e-g., ReNoise).
Notably, the purpose of these experiments is not to position PreciseInv as state-of-the the-art image editing method. As a generic inversion method without editing-specific design, is inherently not comparable to advanced pipelines that involve domain-specific training [20] 401, attention
manipulation 16 31
or test-time optimization 7 19 Rather, Preciselwv serves as
foundation that can be integrated with such techniques. Incorporating precise inversion into editing- oriented frameworks is promising direction for future work.
Ours
BELM
Eayllvv
ReNoise
Figure 5: Interpolating between leftmost and rightmost images with spherical linear interpolation.
To further explore why Preciselnv enables controllable and faithful editing, we perform an interpolation-basee diagnostic experiment, as shown in Fig. 5 Specifically, we first select two similar real images and apply different inversion methods to recover their corresponding latents. Then, we perform spherical linear interpolation (slerp) between the two inverted latents and re- construct all intermediate states using the same diffusion model. As shown in Fig, 5 Preciselnv produces a smooth and semantically meaningful transition, maintaining structural coherence and identity consistency throughout the interpolation path. In contrast, DDIM and EasyInv often yield abrupt domain shifts or introduce foreign objects, indicating a drift away from the correct semantic manifold. BELM fails preserve visual coherence due to accumulated noise artifacts, while ReNoise partially retains structure but suffers from geometric degradation. These findings suggest that accurate inversion leads latents that better respect the geometry of the diffusion space, thereby enabling more localized, stable, and prompt-aligned edits.
Conclusion
We propose Preciselnv, a general-purpose test-time optimization framework that enables fast and faithful inversion for pre-trained diffusion models, Unlike prior fixed-point methods, we reformulate diffusion inversion as a progressive learning problem and introduce dynamic programming-inst inspireed strategy to solve it effectively. Theoretical analysis shows that Preciselny converges under mild assumptions. Extensive experiments across diverse data domains and model architectures demonstrate that the proposed method achieves state-of of-the-ar art performance in image reconstruction. Notably, performance gains are especially pronounced under few-step settings and on novel samples. Moreover, we verify the effectiveness of PreciseInv in prompt-driven image editing tasks and further analyze underlying mechanism. In future, we attempt to integrate Preciselnv with diverse editing techniques to explore unified, controllable, and consistency- aware framework for image editing.
10

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Acknowledgment
This work was supported by the Hainan Provincial Joint Project of Li' an International Education Innovation Pilot Zone (Grant No.624LALHO0S) BUPT Kunpeng&Ascend Center of Cultivation, NSFC (Grant No.6160 No.61601042) the Program for Youth Innovative Research Team of BUPT (Grant No. 2023QNTD02), and the Super Computing Platform of BUPT.
References
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Appendix & Supplementary Materials
Contents
Introduction
1
2
Background
2.1
Dillusion Models
2.2
Image Inversion in Diffusion Models
3
Method
3.1
Reformulating Diffusion Inversion Learning Problem
3.2
Progressive Denoising Trajectory Learning
3.3
Theoretical Analysis of Convergence
3.4
Prompt-driven Image Editing
Experiments
4.1
Image Reconstruction
Prompt-driven Image Editing
5
Conclusion
10
Formulations
15
A.I Formulation of Stochastic Sampler: DDPM
15
A.2 Formulation of Rectified Flow Models: SD3
15
Proofs
16
B. Proof of Theorem
16
B.2 Proof of Theorem
17
Implementation Details
17
C.1 Training Details
17
Hyperparameters for Image Reconstruction
17
C,3
Pseudocode of Preciselm
17
D Additional Results
18
D.I Quantitative Results.
18
D.2
Qualitative Results.
20
14

---

A Formulations
In this section, we extend the formulation of Preciselnv different combinations base models and samplers, highlighting the generality and adaptability of our approach.
A.1 Formulation of Stochastic Sampler: DDPM
We begin with the stochastic DDPM sampler 17 For clarity, we first restate its sampling step:
vI ai Ea (x(xx,,)) + oiZe.
xx,, z;)
X
(24)
Vax
0:-1
The added noise term o, in Eq. 24 complicates the inversion task, deterministic reconstruction from x, is no longer guaranteed. To overcome this, we treat 2, as an additional learnable variable. Specifically, modify each subproblem (t)) (defined in Eq. (14) jointly optimize the noise embedding Ex and the stochastic component zi:
P(t) arg min [x zi) - xoll c7
(25)
where
x X v1 ā G
(26)
This formulation preserves the dynamic programming structure of our method. In particular, the optimal substructure property remains intact, with each subproblem P(() dependent only on the solution to the previous subproblem P(L-1):
arg min [|] z1) - -xoll" t= t=1,
ei
(27)
arg min [| xi-1l l 1.
By learning both the latent noise and the stochastic perturbations at each step, our method generalizes to stochastic samplers and enables accurate inversion under the DDPM setting.
A.2 Formulation of Rectified Flow Models: SD3
Preliminary. Rectified Flow 26 defines score-based diffusion modeling by learning velocity field over a linear interpolation path between the data distribution ((xo) and the Gaussian prior (O I). The forward process is formulated as:
X (1- t)xo te, E [0. 1].
(28)
neural network learns a time-dependent velocity field vo(x,, t) by minimizing the following training objective:
(RF( := Etxp((), xx_g(xx), (o.1) Nle-vexx.) t)||
(29)
The backward (generative) process recovers Xo from a sample x, ~ NV by solving the following ordinary differential equation (ODE) in reverse time:
dxi dl
ve(
(30)
Unlike discrete-ting time diffusion models such as DDPM and DDIM, Rectified Flow does not define an explicit update rule. Instead, the reverse trajectory is obtained by numerically integrating Eq. (30). typically via Fuler discretization:
X Al X At va (xx,,))..
(31)
refines Rectified Flow enable large-scale pretraining for text-to-image generation. First, instead of adopting uniform timestep schedule, it samples timesteps from a logit-normal [ distribution defined as:
SD3 10
Ti (t: m, 8) S/27 t(1 - exp (-logit(t)
(logit(t) -m)²
(32)
2s
This design allows SD3 to flexibly control the bias and width of the timestep distribution. It further introduces a multimodal diffusion transformer that unifies cross-attention and self-attention mechanisms. This results in improved alignment between text and image modalities.
15

---

Preciselny for the SD3 Model We further extend Preciselvv to the continuous-time rectified flow model, SD3. To construct a tractable denoising trajectory, we first sample sequence of timesteps (41,42.....4 (T) from the logit-normal distribution (i; m, 8) defined in Eq. (32). These sampled timesteps discretize the continuous-time trajectory into a sequence of latent variables {xto: xt1:..., ). where each Xr, is recursively approximated by Euler integration:
x Xx; (1 1) ox((x, 14),
(33)
with Xt7 (0, I) and i E (T,T , 2).
Following Section 3
define subproblems {P(4)) each targeting a local reconstruction step along the denoising path Xtr + ... Xt, For each t, we parameterize the latent variable xi, with learnable noise embedding Ei, as:
x (1 1.) xo + G.
(34)
Each subproblem P(4) seeks to minimize the reconstruction error between the estimated and true signal:
P(t.) arg min |x(xx)) x
(35)
where denotes the Euler-discretized backward trajectory from Xtr to Xt1 For clarity, we rewrite the Euler step in Eq. 33
pxx,, ti 14-1) = X - (t: 14-1) vo(x,,
(36)
With this notation, each subproblem can be reformulated recursively as:
arg min e
| (1 0) -xol?²
i=1,
P(t))
p(xt 22, ti-1) xx, ||? 1>1.
(37)
arg min fi
By progressively solving these subproblems from P(h)) to P((T), Preciselny achieves a precise inversion of the image Xy into the SD3 latent space X1.
B Proofs
provide formal proofs for the theoretical results presented Section 3
B.1 Proof of Theorem 1
Proof. For the function (x,) with L-Lipschitz continuous gradients (Assumption 2h we define the gradient-based update as:
(k+1)
x (k) ~ (x(( (2))
(38)
where & denotes the iteration index and is the learning rate. By the smoothness lemma 15 for any x and x',
f(x') < f(x) + (v)(x), x' - x) f x11
(39)
where f denotes any function with L-Lipschitz continuous gradients. Then, when < 2/L, we obtain
Lx(x) (xx s Lx(xx (1)) - -7(11 - [x(
4
(40)
After iterations, we have
| (k) 2 2
min k
(41)
which implies that L, converges to stationary point & during the optimization of Ptt).
16

---

B.2 Proof of Theorem 2
Proof. Let the accumulated reconstruction error of P(t) be r(t) == [|((x,,) -xoll² where denotes the estimated latent representation and X the ground-truth image. We define X' (xxo) From Theorem for all t {I,..., ".l...,,'' I' we have:
362 O, (x(x)) S 6c.
(42)
Considering Eq. 18 and Assumption I we obtain:
T T(t) S
L6
5y.
(43)
Under Assumption there exists a constant Ln < such that ( S Lm Hence,
I(t) S 4m l' - 1) + +
(44)
Let d = ma ................................ }.). By recursively applying Eq. 44 from = 1 to T, we derive:
r(1) S 6, T(2) S Lm 6 + 6,
(45)
T T(T) S 8
1- LT
8
k-1
6
<
m
1 Im
Imm
k=1
Thus, I(T) is bounded by 8/(1 Lm).
C
Implementation Details
C.1 Training Details
We implement our method using PyTorch and the Hugging Face diffusers library. All diffusion model weights are frozen during training, and only the per-timestep noise embeddings e are optimized via gradient descent. Following Easylnv, single step of DDIM Inversion. We use the AdamW optimizer with 3 = 0.9, 33 = 0.999, and weight decay of 0.01. The learning rate is set to 0.1 for SD v1.4, 0.05 for both LCM-SD v1.5 and SDXL, and 0.025 for SD3. We use the DDIM sampler unless otherwise specified; for SD3, the Euler discrete sampler is adopted due architectural compatibility. We keep the number of inversion steps equal to the number of sampling steps, denoted as T. All experiments are conducted under mixed precision: float16 used for SD v1.4, LCM-SD v1.5, and SDXL., while bf oat16 is used for SD3 to ensure numerical stability. We run all experiments on single RTX 4090 24GB GPU, except for SD3, which requires single A100 40GB GPU due to its higher memory and compute demands.
initialize the value of E by performing
C.2 Hyperparameters for Image Reconstruction
As described in Section we tune methods optimal reconstruction quality. We set the number of inference steps T as tollows: 1000 for DDIM Inversion, 50 for ReNoise and BDIA, 7-100 for Easylnv and BELM, and 2= for EDICT and our Preciselnv. For ReNoise, we disable the editing loss by setting x=0 and sweep the renoising steps
{1, (.... 9}. Easylnv, EDICT, BDIA. and BELM are used with default configurations from their respective papers. For Preciselnv, we set the convergence threshold 10-2 10-3 and 10-5, respectively. To eliminate the effect of text conditioning, all methods are evaluated with empty prompts and guidance scale set to zero.
C.3 Pseudocode of Preciselnv
We present the pseudocode of the proposed Preciselm. Specifically, three cases are covered: diffusion models using the DDIM sampler, diffusion models using the DDPM sampler, and rectified flow models using the Euler discrete sampler, shown in Algorithm 2 and 4 respectively.
17

---

Algorithm 2 Preciselnv for Diffusion Models with DDIM Sampler
1: Input: Real image Xo, diffusion model co, convergence threshold 77, number of inference steps T
2: Output: Inverted latent x;
3: for trt== to T do
4: Initialize E ~ (N
5: if then
6: x - Va--i Xn + VI 04-1 6-1
7: else
8:
X + X0 end if
9:
10:
1/ Apply a single DDIM Inversion step
G7 vi (u(xi-1) vāpx) (u defined Eq. (16))
12:
Xi Vā, XD + vI E
13:
Lree + ||{((x;)
112
14:
while Liee 17 do
15:
X f Vāa Xy + /1 04 E
Lix |[(x) x;) x
17:
6 4- 6 VLre
18:
end while
19:
end for
return xi-
Algorithm 3 Preciselnv for Diffusion Models with DDPM Sampler
Input: Real image Xu, diffusion model Cø. convergence threshold 17, number of inference steps T
2: Output: Inverted latent xy, additional noise terms {zz 27:1:" "
3: for to T do
4: Initialize et ~ I)
5: Initialize 2 ~
6: if then
7:
x va- + v1 δc-1 G-
8:
else
9:
x t x0
10:
end if
11:
Ei
1 1 VI-ai (1(x;-1)
va(xo)
(μ defined Eq. (24)
x Vān X + /1 11-0p 5₁ E
13:
Cree + |||x(x; z - x;-111
while Liee < 17 do
15:
x f Vā, Xy + 11
c
Lrxe +- || ;2) ) x;_
17:
G +- E,-
V Loee
2 c zi V Lrve
19:
end while
20:
end for
21:
return x (z - ... zi}
D Additional Results
D.1 Quantitative Results.
We provide additional quantitative results of our method on the image reconstruction task. Table presents the performance of Preciselnv with different combinations base models and samplers, as described in Section A The experiments run on the COCO 2017 validation set 24). We set the number of inference steps to threshold 7 10 is used for all models.
for SD3 and T for the other models. The convergence
18

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Algorithm 4 Preciselnv for Rectified Flow with Euler Discrete Sampler
1: Input: Real image Xo, rectified flow model cø, convergence threshold 77 number of inference
steps T, scalars 8, m
2: Output: Inverted latent
// Initialize discrete timesteps
3: for i = 1 to T do
4: 4 6 Thn (1; 8,
5: end for
6: for 1 T do
7: Initialize E (0,1))
8: if 1 then
9:
X t (1 (1-t:- 1--1 X + 1--1 G
else
11:
Xi,-1 X0
12:
end
Xi, (1-
t.) x0 + 14 Et:
Lee + -Ilu(xi,, tt. (,,t-1) x 1|?
(μ defined in Eq. 36
15:
while free > 17 do
16:
Xi, - (1- --t))x0 xo + to Ei,
17:
Lie - 11l1(xx,,, tis 1)- x
18:
E c- E ----4 Lrec
end while
20:
end for
xi, (1 tT) xo + tr E
22:
return X-
Table shows that all models achieve comparable reconstruction quality. SD3 attains higher SSIM and PSNR scores, while other models perform better on LPIPS. Compared to the results reported in Tables Preciselnv maintains state-of-the-art reconstruction performance, further demonstrat- ing the generality and robustness of our method. However, SD3 exhibits lower inference efficiency relative other models, which can be attributed its larger model size and the absence of an effective initialization manner.
To address this, future work will explore progressively decreasing timestep optimization strategy for large models such as SD3. We believe that this strategy will result in a smoother optimization landscape. Additionally, exploring better initialization techniques, such using initial values derived from existing flow-based inversion methods, would also be a promising direction.
Table 4: Additional quantitative results for image reconstruction, including: (i) Stable Diffusion 3.5 medium model with default Euler Discrete sampler, and (ii) Stable Diffusion v1.4, Latent Consistent Model Stable Diffusion v1 v1.5, and Stable Diffusion XL. with DDPM sampler.
Model
Sampler
LPIPS (L)
SSIM (1)
PSNR (t)
Time (s. L)
SD3 SD v1.4
Euler
0.104
0.896
30.12
403.31 1
DDPM
0.080
0.764
25.93
9.08
LCM-SD v1.5
DDPM
0.076
0.784
26.84
12.07
SDXL
DDPM
0.091
0.842
30.39
18.59
also report reconstruction performance under varying convergence thresholds r, and inference step counts 7' in Table We randomly sample 20 images from the COCO 2017 validation set and evaluate using the Stable Diffusion v1.4 model with a DDIM sampler. The number of inference steps is varied as T E 2, 5, 10, 20, 50, 100 and the convergence threshold 17 10 1 10 5 10-6 1 We report metrics including LPIPS, SSIM, and PSNR, as well as inference time in seconds.
From Table 5 we draw the following observations. First, for fixed number of inference steps T, decreasing the convergence threshold v consistently improves reconstruction quality across all metrics-LPII decreases, while SSIM and PSNR increase. However, this comes at the cost of
19

---

significantly longer inference time, especially / drops below 10 10-5, Second, we observe diminishing returns reconstruction quality when 17 10 particularly for small-step regimes (e.g., I 10). This suggests that extremely strict convergence criteria may be unnecessary when the number of inference steps is limited. Third, when y fixed, increasing the number of inference steps initially degrades the reconstruction quality before improving it. This phenomenon results from trade- off: while smaller per-step initialization errors benefit from higher T, the total accumulated error at convergence (approximately T ?7) also increases. Notably, due the smooth structure of the diffusion latent space, error accumulation sublinear and does not dominate overall performance. Fourth, inference time exhibits
monotonic trend with respect to T. When 7) 2 10 10-5, increasing initially reduces inference time- time-likely due to faster convergence from smaller per-step errors but then increases it again the step count becomes the dominant factor. In contrast, for stricter thresholds (1) S 10 10-5,, inference time generally decreases with larger T, implying that the time saved through easier optimization outweighs the overhead introduced by additional steps. Finally, when < 10, tightening the threshold from = 10-5 to 10-6 yields negligible gains in reconstruction quality. Moreover, for large-step configurations (T 10), using 1j 10- achieves reconstruction performance on par with small-step setups suggest that setting f 10-3 and T 2 strikes favorable balance between efficiency and quality.
10-5 Taken together, these findings
Table 5; Image reconstruction results under varying convergence thresholds 7 and inference steps T. The table reports four metrics: LPIPS (4), SSIM (t), PSNR (t), and inference time in seconds (L).
Metric
7
5
= 10
T 50
T
100
10
0.069
0.205
0.138
0.095
0,044
0.036
3
0.037
0.052
0.139
0.096
0.044
0.036
LPIPS
10-5
0.031
0.031
0.034
0.074
0.044
0.036
10-6
0.031
0.031
0.031
0.037
0.045
0.036
10-7
0.031
0.036
0.032
10-2
0.876
0.839
0.864
0.877
0.894
0.896
10-3
0.894
0.886
0.867
0.877
0.894
0.896
SSIM
10-5
0.897
0.898
0.896
0.059
0.895
0.896
10-6
0.897
0.898
0.898
0.896
0.895
0.897
10-7
0.898
0.897
0.898
10-2
31.72
26.75
26.42
26.91
31.30
32.65
10-3
33.12
29.75
26.15
26.89
31.30
32,65
PSNR
10-5
33.33
33.33
32.76
28.04
31.10
32.63
10
33.33
33.35
33.37
33.03
30.62
32.63
10-7
33.33
33.11
33.29
10-2
4.05
2.27
1.50
2.42
5.18
9.56
10-3
8.25
7.13
2.61
3.85
5.08
9.82
Time (s)
10-5
23.76
24.82
37.77
21.44
7.16
12.23
10-6
99.60
82.06
55.77
68.18
62.99
26.68
10-7
242.63
160.51
107.98
D.2
Qualitative Results.
Here, we present additional qualitative results on image reconstruction, prompt-based image editing, and image interpolation.
20

---

Input Image
DDIM Inversion
ReNoise
Fasylnv
BELM
Ours
Figure 6: Qualitative comparison of image reconstruction results from different diffusion inversion methods using Stable Diffusion v1.4 on the Cartoon dataset.
21

---

Input Image
DDIM Inversion
ReNoise
Fasylax
BELM
Ours
Figure 7: Qualitative comparison of image reconstruction results from different diffusion inversion methods using Stable Diffusion v1.4 on the DarkFace dataset.
22

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Input Image
DDIM Inversion
ReNoise
Easy lav
BELM
Ours
STOP MOVERTIVE
STOP
LOO1
STOP
STOP HAMERTINE
WANERTINE
MKKIIN
HOMERTIE
Figure 8: Qualitative comparison of image reconstruction results from different diffusion inversion methods using Stable Diffusion v1.4 on the COCO dataset.
23

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Input Image
DDIM Inversion
ReNoise
BELM
Ours
Figure 9: Qualitative comparison of image reconstruction results from different diffusion inversion methods using the Latent Consistency Model with Stable Diffusion v1.5 on the Cartoon dataset.
24

---

Input Image
DDIM Inversion
ReNoise
BELM
Ours
Figure 10: Qualitative comparison of image reconstruction results from different diffusion inversion methods using the Latent Consistency Model with Stable Diffusion v1.5 on the DarkFace dataset.
25

---

Input Image
DDIM Inversion
ReNoise
BELM
Ours
Figure 11: Qualitative comparison of image reconstruction results from different diffusion inversion methods using the Latent Consistency Model with Stable Diffusion v1.5 on the COCO dataset.
26

---

Input Image
DDIM Inversion
ReNoise
Easylnv
Ours
Figure 12: Qualitative comparison of image reconstruction results from different diffusion inversion methods using the Stable Diffusion XL on the Cartoon dataset.
27

---

Input Image
DDIM Inversion
ReNoise
EasyInv
Ours
Figure 13: Qualitative comparison of image reconstruction results from different diffusion inversion methods using the Stable Diffusion XL on the DarkFace dataset.
28

---

Input Image
DDIM Inversion
ReNoise
EasyIny
Ours
16
16
70
16
16
Figure 14: Qualitative comparison of image reconstruction results from different diffusion inversion methods using the Stable Diffusion XL on the COCO dataset.
29

---

Original
DDIM
ReNoisc
BDIA
BELM
Ours
"a rod light moon"
hise green hag"
"querte headed bracelet"
"a sheep deer"
"a colorful style boot"
"a man stmmbrtiome gets on vehicle at the crosaroads'
fnbeie leather sofa""
tren hotdeg"
Figure 15: Qualitative comparison of prompt-driven image editing results from different diffusion inversion methods using the Stable Diffusion v1.4.
30

---

Original Images
DDIM
BELM
ReNoise
Ours
a dog tiger"
a vireet leather hal"
pink natural handphones"
an-range car"
Figure 16: Qualitative comparison of prompt-drive driven image editing results from different diffusion inversion methods using the Latent Consistency Model with Stable Diffusion v1.5.
Original Images
DDIM
ReNoise
Ours
orange red car"
abstract painting style man"
Figure 17: Qualitative comparison of prompt-driver image editing results from different diffusion inversion methods using the Stable Diffusion SDXL.
31

---

BELM
RcNebe
BELM
Kaslas
DRIM
Figure 18: Qualitative comparison image interpolation from different diffusion inversion methods using the Stable Diffusion v1.4.
32

---

Figure 19: Additional qualitative result of image interpolation from the proposed Preciselny using the Stable Diffusion v1.4.
33

---

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Reviews:
[{"review_id": "ivCjNWGQ8V", "reviewer": "Reviewer_4z49", "summary": "The paper proposes PreciseInv, which is a novel learning-based method for diffusion model inversion that achieves accurate and efficient inversion in a few inference steps. The previous methods are usually based on fixed-point or root-finding. Different from them, PreciseInv reformulates inversion as a progressive learning task. In detail, it leverages the Markov property of diffusion models. It decomposes the problem into several overlapping subproblems and solves them using a dynamic programming-inspired strategy. The authors conduct experiments on COCO 2017, DarkFace, and a cartoon dataset. The results show that PreciseInv achieves better reconstruction quality and efficiency compared with existing methods. Besides, it also improves semantic consistency in image editing.", "questions": "1. Could the author provide the analysis of convergence or approximation error about the optimization?\n2. Could the author provide a quantitative comparison in image editing? BIE-Benchmark is a good choice.\n3. How sensitive is the method to the choice of threshold?", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. The paper addresses an important problem. Diffusion inversion is important for image editing. The current fixed-point and root-finding method cannot find an accurate noise embedding. The paper aims to propose an accurate and efficient inversion method.\n2. The method is novel. The paper reformulates diffusion inversion as a learning problem. It also decomposes the problem into recursive subproblems and proposes a dynamic programming-inspired strategy to solve it.\n3. The results are good. The proposed method achieves strong trade-offs between reconstruction accuracy and efficiency under a step inference. The method also improves semantic consistency and controllability in image editing. The results demonstrate good performance in various datasets and diffusion architecture.\n\n\nWeaknesses:\n1. The theoretical analysis is missing. Although the proposed method is straightforward, the analysis of convergence or approximation error in the optimization should be provided.\n2. Comparison in image editing is limited. The paper only provides a qualitative comparison of image editing. However, quantitative metrics are missing.\n3. Some ablation studies are missing. The paper uses different thresholds. The studies about the choice should be provided.", "was_revised": true, "final_justification": "The authors have addressed my concerns regarding the image editing evaluation and the choice of convergence threshold. They also provided additional convergence analysis. However, formal theoretical guarantees are still lacking. Therefore, I will maintain my original score.", "rebuttal": "Our sincere thanks to Reviewer **4z49** for their thoughtful and insightful comments. We've addressed each of the specific questions and concerns they brought up in our detailed, point-by-point responses below.\n***\n**Q1: The theoretical analysis is missing. Although the proposed method is straightforward, the analysis of convergence or approximation error in the optimization should be provided.**\n\nA1: Thank you for the suggestion. While our method is primarily empirical, we provide convergence-related evidence through additional experiments shown in Table 1 and Table 2. Table 1 illustrates the local reconstruction error across iterations for each subproblem $P(t)$, showing smooth convergence. This behavior stems from the Lipschitz continuity of the diffusion latent space, which facilitates stable gradient-based optimization. Table 2 analyzes the global reconstruction error over T subproblems under varying upper bounds $\\eta$ on local error. Notably, global error does not accumulate linearly with T. Moreover, fixing T and progressively reducing $\\eta$ leads to a converged global error around 0.0019, which reflects the intrinsic reconstruction limit of the VAE in latent diffusion. These findings demonstrate that our method enjoys stable convergence and favorable approximation accuracy under varying inference steps T. We will incorporate these results and discussions into our revised version.\n\n**Table 1: Local reconstruction error at each optimization step in subproblem $P(t)$. Results are averaged over 32 images from the COCO 2017 validation set.**\n| Step | 1    | 2    | 5    | 10   | 25   | 50   |\n|------|------|------|------|------|------|------|\n| $\\|\\|\\mu(x_t^*)-x_{t-1}^\\*\\|\\|^2$ | 0.14 | 0.11 | 0.08 | 0.06 | 0.02 | 0.01 |\n\n**Table 2: Global accumulated reconstruction error over $T$ subproblems. The hyperparameter $\\eta$ defines the error bound for each subproblem $P(t)$: if and only if the local reconstruction error drops below $\\eta$, the optimization moves to the next subproblem $P(t+1)$.**\n|                | T=2           | T=5           | T=10          | T=20          | T=50          | T=100         |\n| -------------- | ------------- | ------------- | ------------- | ------------- | ------------- | ------------- |\n| $\\eta = 10^{-2}$ | 0.0025        | 0.0243        | 0.1363        | 0.1767        | 0.2015        | 0.2181        |\n| $\\eta = 10^{-3}$ | 0.0019 | 0.0033        | 0.0091        | 0.0552        | 0.0721        | 0.1754        |\n| $\\eta = 10^{-4}$ | **0.0019**    | 0.0020 |0.0020 | 0.0036        | 0.0431        | 0.0818        |\n| $\\eta = 10^{-5}$ | -             | **0.0020**    | **0.0019**    |0.0020 | 0.0033        | 0.0077        |\n| $\\eta = 10^{-6}$ | -             | -             | -             | **0.0019**    | 0.0020 | 0.0029        |\n| $\\eta = 10^{-7}$ | -             | -             | -             | -             | **0.0019**    | 0.0019 |\n| $\\eta = 10^{-8}$ | -             | -             | -             | -             | -             | **0.0019**    |\n\n**Q2: Could the author provide a quantitative comparison in image editing? PIE-Benchmark is a good choice.**\n\nA2: Thank you for the construction comments. Following your suggestion, we provide additional quantitative results on PIE-Bench [a] in Table 3, where PreciseInv significantly outperforms baseline methods in terms of structural consistency, background preservation, and instruction fidelity. This improvement stems from our accurate reconstruction of the original generative trajectory, which retains more information from the source image $\\mathbf{x}_0$ and produces a latent $\\mathbf{x}_T$ situated in a smoother, semantically meaningful space. These quantitative results are also consistent with the qualitative comparisons shown in Fig. 4.\n\n[a] PNP Inversion: Boosting diffusion-based editing with 3 lines of code. ICLR, 2024.\n\n**Table 3: Quantitative results on the PIE-Bech subset. For each category, we randomly sample 10 test instances. We adopt Stable Diffusion v1.4 as the base model for all methods.**\n\n|               | Methods       | Structure Distance | Background Preservation |       |       |       | CLIP Score |\n|---------------|---------------|--------------------|--------|-------|-------|-------|------------|\n|               |               |                    | PSNR   | LPIPS | MSE   | SSIM  |            |\n| Invertible Samplers| EDICT         | 24.70              | 27.25  | 59.20 | 38.83 | 90.36 | 23.82      |\n|               | BDIA    | 35.91              | 22.29  | 78.27 | 58.95 | 87.26 | 24.04      |\n|               | BELM          | 11.25              | 28.55  | 51.44 | 33.93 | 90.44 | 24.25      |\n|               | DDIM Inversion| 72.28              | 17.61  |186.04 |173.05 | 80.74 | 23.61      |\n| Forward Optimizing | ReNoise  | 12.36              | 28.41  | 67.32 | 29.81 | 87.05 | 22.18      |\n|               | PreciseInv    | **9.44**           |**30.29**|**44.98**|**13.69**|**91.47**|**25.16**|\n\n**Q3: How sensitive is the method to the choice of the convergence threshold $\\eta$?**\n\nA3: Thank you for the question. In fact, we have thoroughly analyzed the sensitivity of our method to the convergence threshold $\\eta$, as shown in Table 5 of Appendix C.3 in the original manuscript.\nWe observe that lowering $\\eta$ from $10^{-2}$ to $10^{-5}$ consistently improves reconstruction quality across metrics such as LPIPS, SSIM, and PSNR. However, further tightening (e.g., to $10^{-6}$ or $10^{-7}$) leads to diminishing returns, especially when the number of inference steps T is small.\n\nIn terms of efficiency, smaller $\\eta$ values do increase inference time. Nevertheless, thanks to the smoothness of the latent space and our progressive optimization strategy, the runtime remains practical (e.g., 5.33s per image at $\\eta = 10^{-5}$) and becomes very fast under relaxed settings like $\\eta = 10^{-2}$.\n\nCrucially, PreciseInv remains robust across a wide range of $\\eta$ values, outperforming all baselines in both accuracy and speed even with loose thresholds. This indicates that the method does not require fine-grained tuning to deliver strong and reliable results."}, {"review_id": "8JD6zFwWs3", "reviewer": "Reviewer_v5Ud", "summary": "The paper proposes a diffusion inversion method that allows few-step inversion and generalization to novel samples by reformulating diffusion inversion as a progressive learning problem and using DP like strategy to solve this. The proposed method outperforms baseline methods in most settings and the difference is the most pronounced in the few-step inference setting.", "questions": "- Can the method be used with shortcut models as well?\n- Do you have a particular explanation as to why the proposed method results in a smoother interpolation between latents? It would be interesting to know a more detailed reasoning behind this.\n- It is unclear as to whether the method is viable for SD3 just looking at Table 3 as there is no baseline comparison. How does this inference speed compare to other baselines in SD3?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n- By solving subproblems separately, the given method is more memory-efficient compared to baseline methods, which might be helpful for applying to larger models. \n- The proposed method consistently shows better reconstruction accuracy compared to baseline methods with a much faster speed (Table 1).\n- The proposed method works better than baseline methods especially under a few-step setting.\n- Qualitative examples are still impressive, including the editing applications.\n- Performing slerp between inverted latents results in a better qualitative result across all interpolated positions.\n- The method can be extended to rectified flow models such as SD3 as well (Appendix A.2), and still shows a good reconstruction performance..\n\n**Weaknesses**\n- When adjusting the convergence threshold, the computation time seems to increase quite a lot, especially in the the case of SDXL. The speed-quality tradeoff needs to be discussed.\n- In fact, the method seems to be quite slower for SD3 (Appendix C.1, Table 4), which may suggest that the computation time saving might not scale to larger models such as SD3 or FLUX, which can limit the applicability. A comparison against baseline methods for SD3 or FLUX might also be necessary.", "was_revised": true, "final_justification": "The provided method shows promise especially regarding the qualitative demonstration and out-of-distribution examples such as flat style illustrations. The authors addressed most of my concerns through their rebuttal, including application to more recent paradigm (flow matching DiTs). Therefore, I think this work is worth being considered for NeurIPS conference, and I keep my score of 4.", "rebuttal": "We sincerely thank reviewer **v5Ud** for the insightful feedback! The suggestions have helped us further clarify key aspects of the work.\n***\n**Q1: When adjusting the convergence threshold, the computation time seems to increase quite a lot, especially in the case of SDXL. The speed-quality tradeoff needs to be discussed.**\n\nA1: We thank the reviewer for the helpful suggestion. We, indeed, have analyzed the speed–quality tradeoff under different convergence thresholds $\\eta$ in Table 5 (Appendix C.1). Empirically, smaller $\\eta$ leads to better reconstruction quality (lower LPIPS, higher SSIM/PSNR) but increases inference time due to stricter convergence.\n\nWe also observe that this effect is more pronounced for large-scale models such as SDXL, as noted by the reviewer. This is expected, since SDXL has a deeper denoising UNet and a larger latent space, which increases the per-iteration computation cost. However, PreciseInv provides a flexible tradeoff mechanism: users can adjust $\\eta$ based on available computational budget. For example, using a relatively loose threshold (e.g., $\\eta = 10^{-2}$ with T=2), PreciseInv still achieves competitive reconstruction performance on SDXL while being significantly faster than optimization-based baselines.\n\n**Q2: The method seems to be quite slower for SD3, which may suggest that the computation time saving might not scale to larger models such as SD3 or FLUX, which can limit the applicability. A comparison against baseline methods for SD3 or FLUX might also be necessary.**\n\nA2: Thank you for pointing this out. We acknowledge that inference time on SD3 is longer than on SDv1.4 or SDXL due to its larger model size. However, accurately inverting the generative trajectory of such a large-scale model is inherently challenging, and to the best of our knowledge, our method is the first to achieve this effectively.\n\nSince our method belongs to the forward optimization family, it is generally not compared with backward correction-based approaches like [a, b]. While method [c] also follows a forward approach, its implementation is only available for SDXL-Turbo, not SD3 or Flux.\n\nThus, we compare against FPI on SD3 with carefully tuned settings. As shown in the following table, although FPI is faster, our method significantly outperforms it in LPIPS, SSIM, and PSNR. Qualitative results further reveal that FPI reconstructions are often blurry or semantically inconsistent. We will include these results and discussions in the revised version.\n\n|                | LPIPS  | SSIM  | PSNR  | Time    |\n| -------------- | ------ | ----- | ----- | ------- |\n| Fixed Point Inversion | 0.6080 | 0.3121 | 13.01 | 226.73  |\n| PreciseInv (Ours)     | 0.104  | 0.896 | 30.12 | 403.31  |\n\n[a] Stable Flow: Vital Layers for Training-Free Image Editing. CVPR, 2025.\n\n[b] Unveil Inversion and Invariance in Flow Transformer for Versatile Image Editing. CVPR, 2025.\n\n[c] Lightning-fast image inversion and editing for text-to-image diffusion models. ICLR, 2025.\n\n**Q3: Can the method be used with shortcut models as well?**\n\nA3: Good spot! Yes, PreciseInv can be naturally extended to Shortcut models [d], as both SD3 and Shortcut adopt the flow-matching paradigm. Our method does not rely on any specific architecture; it only requires a differentiable and continuous mapping from $\\mathbf{x} _ t$ to $\\mathbf{x}_{t-\\Delta}$, which remains valid in both SD3 and Shortcut. Although Shortcut introduces a step-size indicator $\\Delta$ and reduces parameter count, it preserves key properties such as Lipschitz continuity of the velocity field. Since PreciseInv is already formally defined and empirically validated on SD3, it can be directly applied to Shortcut without modification. We plan to support this extension in our public code release.\n\n[d] One Step Diffusion via Shortcut Models. ICLR, 2025.\n\n**Q4: It would be interesting to know a more detailed reasoning behind why the proposed method results in a smoother interpolation between latents.**\n\nThank you for the insightful question. Prior work [e] has demonstrated that the latent space of diffusion models exhibits inherent semantic continuity. Our method does not introduce any explicit regularization or interpolation constraints. Instead, it accurately reconstructs the model’s own generative trajectory, allowing the inferred latent $\\mathbf{x} _ T$to reside naturally within a semantically coherent region. This results in significantly smoother interpolation between latents.\n\nWe further conducted empirical analysis and observed that this continuity deteriorates as the reconstruction precision decreases. In particular, when the convergence threshold $\\eta$ exceeds approximately 0.025, the interpolated results begin to show noticeable semantic discontinuities. This observation underscores the importance of precise inversion in preserving the smoothness and structure of the semantic latent space. However, the deeper mechanism behind this phenomenon remains an open question and is an exciting direction for future exploration.\n\n[e] Unsupervised representation learning from pre-trained diffusion probabilistic models. NeurIPS, 2022."}, {"review_id": "MP6JyoRUDS", "reviewer": "Reviewer_48AE", "summary": "This paper proposes to reframe the diffusion inversion problem as a series of step-wise optimization sub-problems, rather than treating it as a traditional fixed-point problem. The method specifically addresses challenges related to accuracy and efficiency in inverting few-step inference diffusion models. Experimental results on both reconstruction and editing tasks demonstrate the effectiveness of the proposed method.", "questions": "- Q1. *(This question arose before I read Appendix B, but I'm still uncertain whether my interpretation is correct, so I'm leaving it here for clarification.)* What is the architecture of the PreciseInv model? Given that it appears to be comparable in size to the denoising backbone $\\epsilon_\\theta$, wouldn't such a large model introduce inefficiencies for inversion? Moreover, according to Eq. 20, $\\epsilon_\\theta$ must also reside in memory during PreciseInv training. Has the computational burden imposed by this requirement been analyzed, particularly in terms of limiting model size?\n  - Training denoisers for T2I diffusion models is computationally expensive. Wouldn't training an inversion model that generalizes across diverse prompts and image (=$x_0$) also require substantial data and training time? How much training data is required?\n  - Sec. 4.1 mentions only a validation set. What dataset was used for training?\n\n- Q2. According to l29-32, backward optimization methods improve reconstruction quality by following the reverse diffusion trajectory. However, l179-180 claim these methods are not designed for accurate reconstruction and are excluded from comparison. Isn't this contradictory?\n- Q3. What does the threshold $\\eta$ in l186 represent?\n- Q4. In Table 1 and Table 2, are the number of inversion steps for the proposed method and the baseline algorithms the same? The proposed method appears to use gradient descent to optimizer $\\epsilon_t^*$, which involves both forward and backward passes through the diffusion model at each iteration. Since one gradient descent step is unlikely to suffice per time step, it seems that the proposed method would require more iterations to reach a final output if the number of time steps is fixed. Then, why is it claimed to be faster?\n- Q5. In Sec. 3.3 on prompt-driven image editing, what is the rationale for denoising from the inverted latent $x_T^*$ using Eq. 21? Is there any theoretical justification for Eq. 21? Why is denoising not performing using $x_{c_t, \\emptyset}$?\n- Q6. In Figure 5, what prompt was used for denoising the interpolated latent $x_T^*$? Were interpolation-aware prompts also used in the baseline methods for a fair comparison?", "limitations": "The authors do not discuss the limitations of their proposed method", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 1, "significance": 2, "originality": 2, "strengths_and_weaknesses": "**Strengths**\n- S1. The proposed inversion method appears reasonable, and the experimental results are convincing.\n- S2. The proposed method performs well on few-step inference diffusion models such as LCM, showing improvements over comparison methods.\n\n**Weaknesses**\n- W1. The most critical issue is that, despite the paper framing the method as a **learning-based** inversion approach, it does not actually involve **learning** in the conventional sense. Throughout the main text, it is unclear what model or parameters are being trained. Only in Appendix B is it clarified that the proposed method **directly optimizes** the inverted noise, indicating that it is a direct optimization procedure rather than a learning-based model. This mischaracterization may mislead readers. Conventionally, learning-based inference using parametric or non-parametric models is expected to perform worse than direct optimization. Therefore, presenting the method as \"learning-based\" could result in an overestimation of its generality and performance.\n- W2. The analysis and experimental results on image editing is insufficient. In the context of image generation models, the primary motivation for inversion is to enable controlled editing through manipulation of the inverted input or generation trajectory. However, the editing examples provided are limited to minor modifications. Color editing reflects only simple intensity changes, and style transfer is demonstrated only through sketching or pixelation, lacking complexity. Moreover, no quantitative evaluation is provided. The authors should include a broader range of edit prompts and define a standardized prompt set for benchmarking, to ensure reproducibility and diversity. Additionally, quantitative metrics and user studies are necessary to objectively validate editing performance.\n- W3. The set of baseline algorithms is limited and includes outdated methods. To better establish the advantages of the proposed method, comparisons with more diverse and recent works are needed.", "was_revised": true, "final_justification": "During the author discussion phase, the authors addressed the concerns by clarifying the mis-framing and missing details of the proposed method. They also presented additional experiments, via PIE-Bench, demonstrating applications which inversion problem is fundamentally targeting. Furthermore, they provided theoretical justification for the proposed method to align with general NeurIPS standards. While the authors' responses to the reviewers' concerns necessitate substantial revisions to the original manuscript, the updated version still lacks the PIE-Bench experimental results and theoretical justification regarding convergence. This leaves some uncertainty about the final form of the paper. Accordingly, my final rating reflects both positive assessment of the resolved concerns and the remaining issues that have yet to be addressed.", "rebuttal": "We sincerely thank reviewer **48AE** for the critical and constructive feedback! Below, we provide point-by-point responses to the specific questions and concerns raised, and we hope these clarifications adequately address the issues.\n***\n**Q1: The paper should avoid presenting the method as a learning-based inversion approach, as it primarily functions at inference time. In addition, the denoising backbone appears overly large, which may result in suboptimal efficiency for the inversion task.**\n\nA1: Thank you for pointing this out, and sorry for the confusion. Our method is indeed a test-time optimization approach, not a conventional learning-based method. We will revise the manuscript to avoid potentially misleading terms like \"learning framework\" and clarify that no offline training is involved.\n\nRegarding the backbone, we agree it may be overparameterized for simple reconstructions. However, we intentionally retain the original denoiser (e.g., SDXL) to ensure faithful alignment with the model’s generative process. This design choice reflects the flexibility of our framework, it can readily accommodate lighter or customized backbones if efficiency is prioritized.\n\nHowever, we also want to emphasize that our contributions remain despite the imprecise phrasing, i.e., (i) a general framework for diffusion inversion based on sequential subproblem solving; (ii) a dynamic programming-inspired strategy for efficient optimization; (iii) state-of-the-art reconstruction quality; and (iv) latent inference that preserves semantic continuity in the diffusion space.\n\n**Q2: The analysis and experimental results on image editing is insufficient.**\n\nA2: Thank you for the critical comments. While our method is designed as a general-purpose diffusion inversion framework (as noted in Lines 219–224) rather than a dedicated image editing algorithm, we agree that standardized evaluation on editing tasks is valuable.\n\nTo address this, we now include quantitative results on the PIE-Bench subset (as suggested by reviewer **4z49**) using the SD v1.4 model. As shown in the table below, our method significantly outperforms baselines in structural consistency, background preservation, and CLIP score, consistent with the qualitative results in Figure 4.\n\n|               | Methods       | Structure Distance | Background Preservation |       |       |       | CLIP Score |\n|---------------|---------------|--------------------|--------|-------|-------|-------|------------|\n|               |               |                    | PSNR   | LPIPS | MSE   | SSIM  |            |\n| Invertible Samplers| EDICT         | 24.70              | 27.25  | 59.20 | 38.83 | 90.36 | 23.82      |\n|               | BDIA    | 35.91              | 22.29  | 78.27 | 58.95 | 87.26 | 24.04      |\n|               | BELM          | 11.25              | 28.55  | 51.44 | 33.93 | 90.44 | 24.25      |\n|               | DDIM Inversion| 72.28              | 17.61  |186.04 |173.05 | 80.74 | 23.61      |\n| Forward Optimizing | ReNoise  | 12.36              | 28.41  | 67.32 | 29.81 | 87.05 | 22.18      |\n|               | PreciseInv    | **9.44**           |**30.29**|**44.98**|**13.69**|**91.47**|**25.16**|\n\n**Q3: According to l29-32, backward optimization methods improve reconstruction quality by following the reverse diffusion trajectory. However, l179-180 claim these methods are not designed for accurate reconstruction and are excluded from comparison. Isn't this contradictory?**\n\nA3: Thank you for pointing this out. We apologize for the confusion. Lines 179–180 aim to clarify that backward optimization methods do not reconstruct the original generative trajectory of the diffusion model. Instead, they rely on recording the forward noising process and then manually adjusting the denoising steps to match the target image, thus effectively bypassing the need for optimization.\n\nWhile this enables accurate reconstructions in some cases, it deviates from the generative process and limits generalizability. Therefore, consistent with recent works focusing on forward optimization [a–d], we exclude these methods from direct comparison in our reconstruction experiments.\n\n[a] ReNoise: Real image inversion through iterative noising. ECCV, 2024.\n\n[b] EASYINV: Toward fast and better DDIM inversion. ArXiv, 2025.\n\n[c] Lightning-fast image inversion and editing for text-to-image diffusion models. ICLR, 2025.\n\n[d] Fixed-point inversion for text-to-image diffusion models. ArXiv, 2023.\n\n**Q4: What does the threshold $\\eta$ in l186 represent?**\n\nA4: Apologies for the confusion. The threshold η defines the stopping criterion for each subproblem P(t): once the reconstruction error falls below η, optimization proceeds to the next step. It provides a flexible trade-off between accuracy and inference time. We will clarify this in the main text.\n\n**Q5: In Table 1 and Table 2, are the number of inversion steps for the proposed method and the baseline algorithms the same?**\n\nA5: Sorry for the unclear. As described in Appendix B.2 (Lines 333–339), we tuned the number of inference steps T and other hyperparameters for each baseline on 100 randomly sampled COCO images to ensure optimal reconstruction. The same settings were then applied across all datasets to avoid overfitting, ensuring a fair and reliable comparison.\n\n**Q6: Gradient-based optimization typically requires multiple iterations. Why, then, is it faster than numerical solvers?**\n\nA6: Good observation, thank you for the insightful feedback. As shown in Tables 1 and 2, our method achieves comparable reconstruction quality with significantly lower inference time. This efficiency comes from two key factors: (i) our approach uses far fewer diffusion steps (e.g., $T=2$) compared to the dozens or hundreds used by baseline methods; and (ii) gradient-based optimization leverages GPU acceleration through modern deep learning frameworks. To address your concern directly, we provide additional results showing that with $\\eta=10^{-2}$ and $T=2$, the local error drops smoothly and meets the threshold within just 50 steps, requiring only 3.61 seconds in total. We will clarify this in the revised version.\n\n| Time (s) | 0.076 | 0.153 | 0.362 | 0.779 | 1.895 | 3.61 |\n|----------|-------|-------|-------|-------|-------|------|\n| Step     |   1   |   2   |   5   |  10   |  25   |  50  |\n| MSE      | 0.14  | 0.11  | 0.08  | 0.06  | 0.02  | 0.01 |\n\n**Q7: In Sec. 3.3 on prompt-driven image editing, what is the rationale for denoising from the inverted latent  using Eq. 21? Is there any theoretical justification for Eq. 21? Why is denoising not performing using ?**\n\nA7: Thank you for the thoughtful question. Following prior work [a], we adopt the standard inversion-then-generation paradigm without altering the editing pipeline. In Eq. (21), we reuse the inverted latent $x_T^*$, swapping the prompt roles—using the target as the positive prompt and the source as the negative, to steer generation away from the original semantics. This heuristic is widely used in existing methods. We also tested removing classifier-free guidance (CFG) during inversion (Eq. 19) and observed similar results, suggesting that CFG primarily influences sampling rather than inversion.\n\n[a] ReNoise: Real image inversion through iterative noising. ECCV, 2024.\n\n**Q8: In Figure 5, what prompt was used for denoising the interpolated latent ? Were interpolation-aware prompts also used in the baseline methods for a fair comparison?**\n\nA8: Thank you for the question. In Figure 5, we used an empty string as the prompt, and all methods used the same prompt to ensure a fair comparison. To further validate this, we also tested with a category prompt like “a photo of a car” and observed consistent results, i.e., our method produces an $x_T$ that lies in a smoother semantic region of the latent space. Prior work [e] shows that diffusion latent spaces are semantically continuous. By accurately recovering the model’s native generative trajectory, our approach yields latent representations that better align with this structure.\n\n[e] Unsupervised representation learning from pre-trained diffusion probabilistic models. NeurIPS, 2022."}, {"review_id": "ocgROl1skF", "reviewer": "Reviewer_SWAE", "summary": "This paper studies *inverse* diffusion, the goal is to find the noisy $x_T$, which has generated the provided image $x_0$. Where $x_T$ is the noise in the *latent* space of a Latent Diffusion Model. This is not a trivial task, given that the diffusion model itself is asymmetric, and simply inverting the sampler does not yield satisfactory results. In this paper inverse diffusion is seen as an optimization problem, where iteratively the optimal noise is sought, based on the optimal noise of the previous time: $x_{t-1} \\rightarrow x_t$. This makes use of the Markov property of diffusion, and is solved iteratively starting from $t=1$ to $t=T$. Experimentally the method is validated on 3 different datasets and in various settings (different values for T, different LDMs), the results show that compared to related works the proposed method is advantageous (especially in LPIPS). Moreover for prompt rewriting some quantitative results are shown and also an interpolation between two images.", "questions": "Please provide more details and insight on the optimization implementation: how is the threshold used, what is the impact of the value of $T$, how do the obtained latents look like, and is it really easy to use a different sampler?", "limitations": "Limitations are not discussed in the main paper.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### Strengths\n* To my opinion the current manuscript is excellent in describing the setting of inverse diffusion, the difficulties and the proposed solution.\n\n### Weakness\n* The manuscript has some confusing elements, it puts emphasize on a 'learning framework' (*e.g.* in the abstract and introduction), and hence I was first convinced that $\\epsilon_\\theta$ would be **learned** to predict the inverse diffusion problem. But, after a second and third read, it seems that is not the case, this is a 'test-time algorithm', where the dynamic programming optimization is run for each example at test/evaluation time, without learning any parameters. In that sense nothing is learned. Please clarify that (eg in the introduction, below Eq 18, and in the experiments) and add pseudo code for the final algorithm.\n* A part of the experimental setup is not clear to me, how is $T$ used. And why does smaller T values lead to better results? From the results it seems that using T=1 gives better results than using T=2 or T=4, while in general for Diffusion holds that a larger T value will provide better results.\n* In the experiments there is a convergence threshold ($\\eta=10^{-5}$), which is not discussed before. Please describe how the threshold is used during optimization.\n* In **Bottom up computation** it is stated that *without loss of generality, we adopt the DDIM sampling strategy*. Would it be possible to use the DDPM strategy (Eq 6), and would that be easier or more difficult due to the additional noise term $z$?\n\n\n### Remaining remarks\n* I would like to get more insights in the optimization, how many steps (on average) are needed to reach the threshold? Is the resulting noisy image indeed a sample from a N(0,1) Gaussian? Is there a clear tradeoff between the used threshold, the number of steps T, and the image reconstruction quality.\n* Table 2: How many iterations are used, ie what is the value for T?\n* Table 2 & 3: It seems that using T=2 performs better than T=4 (on LPIPS, SSIM, PSNR). Is that expected? Is there a trade-off of quality versus number of steps T? (And is it better to have a few steps with a stricter convergence threshold or more steps with a tighter threshold?)\n* In Figure 2, there are two $\\epsilon^{*}_{t}$ depicted.\n  * Fix: one of these should be $\\epsilon^*_{t+1}$", "was_revised": true, "final_justification": "The rebuttal of the author did address my concerns. The influence of T and the threshold $\\eta$ should be discussed in the main paper. Also, the optimal number of T steps: please include an explanation why some methods require a high value for optimal results (eg DDIM Inversion uses T=1000) and for some (including the proposed method) low?", "rebuttal": "We sincerely thank the reviewer **SWAE** for their thoughtful feedback. The reviewer’s comments helped us identify important issues and improve the clarity and rigor of the paper.\n***\n**Q1: The proposed method should be described as a test-time algorithm rather than a learning framework. The manuscript should clarify this distinction and include pseudocode for the final algorithm.**\n\nA1: Thank you for pointing out the misrepresentation, and we apologize for any confusion. The proposed method is indeed a test-time optimization algorithm, not a conventional learning framework. No model parameters are trained; instead, we perform gradient-based optimization for each test instance. We will revise the abstract, introduction, and conclusion to remove references to a \"general learning framework\" and clarify that our approach is a test-time procedure. Additionally, we will try to move the pseudocode for the DDIM-based version from Appendix B.2 to follow Eq. (18) in the main text.\n\n**Q2: In the experiments there is a convergence threshold $\\eta$, which is not discussed before. Please describe how the threshold is used during optimization.**\n\nA2: We apologize for the lack of clarity. The convergence threshold $\\eta$ sets an upper bound on the local reconstruction error for each subproblem $P(t)$ during optimization. Specifically, when the reconstruction error falls below $\\eta$, we terminate the optimization for that subproblem and move on to the next. We will clarify this in both the method and experimental sections of the revised manuscript.\n\n**Q3: Table 2 & 3: Why does smaller T lead to better results?**\n\nA3: Great observation! As explained in A2, each subproblem is optimized until the local reconstruction error reaches the threshold $\\eta$. When T increases, local errors accumulate, leading to higher global error and lower reconstruction quality. However, as shown in the table below, the error grows sublinearly with T, due to the Laplacian continuity of the diffusion latent space. From an efficiency standpoint, smaller T reduces the total number of optimization problems, speeding up inference. This underscores the core advantage of our method: accurate inversion with fewer steps, enabling both high-quality and fast real image reconstruction.\n\n|              | T=2    | T=5    | T=10   | T=20   | T=50   | T=100  |\n|--------------|--------|--------|--------|--------|--------|--------|\n| $\\eta = 10^{-2}$ | 0.0025 | 0.0243 | 0.1363 | 0.1767 | 0.2015 | 0.2181 |\n| $\\eta = 10^{-3}$ | 0.0019 | 0.0033 | 0.0091 | 0.0552 | 0.0721 | 0.1754 |\n| $\\eta = 10^{-4}$ | **0.0019** | 0.0020 | 0.0020 | 0.0036 | 0.0431 | 0.0818 |\n| $\\eta = 10^{-5}$ | -      | **0.0020** | **0.0019** | 0.0020 | 0.0033 | 0.0077 |\n| $\\eta = 10^{-6}$ | -      | -      | -      | **0.0019** | 0.0020 | 0.0029 |\n| $\\eta = 10^{-7}$ | -      | -      | -      | -      | **0.0019** | 0.0019 |\n| $\\eta = 10^{-8}$ | -      | -      | -      | -      | -      | **0.0019** |\n\n**Q4:  Is there a trade-off of quality versus number of steps T?**\n\nA4: Thank you for the question. This trade-off is analyzed in Appendix C.2 (Lines 372–375). As shown in Table 5, with a fixed $\\eta$, increasing T initially improves reconstruction quality and reduces inference time. However, beyond a certain point, both quality and efficiency decline. This reflects the trade-off: while larger T reduces initialization errors for each subproblem, it also increases the risk of error accumulation across steps.\n\n**Q5: In Bottom up computation it is stated that without loss of generality, we adopt the DDIM sampling strategy. Would it be possible to use the DDPM strategy (Eq 6), and would that be easier or more difficult due to the additional noise term?**\n\nA5: Thanks for the question! We have extended PreciseInv to support both the DDPM sampler and the Euler Discrete Sampler of flow matching. In the DDPM setting, the additional noise term in Eq. (6) is treated as a learnable variable and optimized during inference. Formal derivations for both extensions are provided in Appendix A.1, and we report quantitative results on a COCO 2017 subset in Table 4 of Appendix C.2. A direct comparison between DDIM and DDPM samplers using the SD v1.4 model is shown in the table below. The results demonstrate that our method converges reliably with both samplers and achieves comparable reconstruction quality. Interestingly, inference with DDPM is slightly faster, likely due to the added flexibility of the parameterized noise in fitting the generative trajectory. We will clarify this in the revised manuscript.\n\n| Sampler | LPIPS | SSIM  | PSNR  | Time (s) |\n|---------|-------|-------|-------|----------|\n| DDPM    | 0.080 | 0.764 | 25.93 | 9.08     |\n| DDIM    | 0.079 | 0.761 | 25.83 | 10.05    |\n\n**Q6: Table 2: What is the value for T?**\n\nA6: We apologize for the confusion. In Table 2, we used the optimal number of inference steps T for each method to ensure a fair comparison in reconstruction quality. As detailed in Appendix B.2: DDIM Inversion uses T=1000; ReNoise and BDIA use T=50; EasyInv and BELM use T=100; and both EDICT and our PreciseInv use T=2. We will clarify this setting in the main text in the revised version.\n\n**Q7: In Figure 2, there are two $x_t$ depicted. One of them should be $x_{t+1}$.**\n\nA7: Thank you for pointing this out. We will fix the notation error in Figure 2 in the revised version.\n\n**Q8: Please provide more details and insight on the optimization implementation: how is the threshold used, what is the impact of the value of $\\eta$, how do the obtained latents look like, and is it really easy to use a different sampler?**\n\nA8: Sorry for the unclear. For details on the use and impact of the convergence threshold $\\eta$, please refer to A2. In addition, our method is sampler-agnostic and can be easily adapted to DDPM and other samplers, as shown in A5.\n\n**Q9: I would like to get more insights in the optimization, how many steps (on average) are needed to reach the threshold? Is the resulting noisy image indeed a sample from a N(0,1) Gaussian? Is there a clear tradeoff between the used threshold, the number of steps T, and the image reconstruction quality.**\n\nA9: Thank you for the insightful question. We computed the KL divergence between the optimized $x_T$ from 100 randomly sampled test images and 100 samples from a standard Gaussian $N(0,1)$. The divergence was below $10^{−2}$, indicating that the optimized latents are effectively drawn from a Gaussian distribution. We will also include visualizations of the optimized latents in the appendix in our revised version. Please refer to **A4** for the discussion on the tradeoff between parameters and reconstruction outcomes."}]

Author rebuttal:

Meta-review: This paper introduces a precise diffusion inversion framework that improves reconstruction fidelity and enables few-step generation. The problem is timely, and the approach is well-motivated and clearly presented. Reviewers appreciated the strong experimental results and the careful analysis. Concerns about incremental novelty, computational cost, and limited evaluation breadth were raised initially, but the rebuttal provided clarifications on efficiency, scalability, and the positioning of contributions relative to prior work. These responses helped mitigate the main reservations. Overall, the work is technically sound, addresses an important problem, and offers meaningful improvements over existing inversion methods. 

I urge the Authors to incorporate all the promised changes in the final draft including the new experiments and convergence proofs and related discussions.
Decision: Accept (poster)