Published as a conference paper at ICLR 2025
LIGHTNING-FAST IMAGE INVERSION AND EDITING
FOR TEXT-TO-IMAGE DIFFUSION MODELS
Dvir Samuel1,3∗Barak Meiri1,2Haggai Maron4,5Yoad Tewel2,5Nir Darshan1
Shai Avidan2Gal Chechik3,5Rami Ben-Ari1
1OriginAI, 2Tel-Aviv University, 3Bar-Ilan University, 4Technion, 5NVIDIA Research
Israel
Figure 1: Consecutive real image inversions and editing using our GNRI with Flux.1-schnell (Black-
Forest, 2024) (0.4 sec on an A100 GPU).
ABSTRACT
Diffusion inversion is the problem of taking an image and a text prompt that de-
scribes it and finding a noise latent that would generate the exact same image.
Most current deterministic inversion techniques operate by approximately solving
an implicit equation and may converge slowly or yield poor reconstructed images.
We formulate the problem by finding the roots of an implicit equation and de-
vlop a method to solve it efficiently. Our solution is based on Newton-Raphson
(NR), a well-known technique in numerical analysis. We show that a vanilla ap-
plication of NR is computationally infeasible while naively transforming it to a
computationally tractable alternative tends to converge to out-of-distribution solu-
tions, resulting in poor reconstruction and editing. We therefore derive an efficient
guided formulation that fastly converges and provides high-quality reconstructions
and editing. We showcase our method on real image editing with three popular
open-sourced diffusion models: Stable Diffusion, SDXL-Turbo, and Flux with
different deterministic schedulers. Our solution, Guided Newton-Raphson In-
version, inverts an image within 0.4 sec (on an A100 GPU) for few-step models
(SDXL-Turbo and Flux.1), opening the door for interactive image editing. We fur-
ther show improved results in image interpolation and generation of rare objects.
1 INTRODUCTION
Text-to-image diffusion models (Rombach et al., 2022; Saharia et al., 2022; Ramesh et al., 2022; Bal-
aji et al., 2022) can generate diverse and high-fidelity images based on user-provided text prompts.
These models are further used in several important tasks that require inversion, namely, discover-
ing an initial noise (seed) that, when subjected to a backward (denoising) diffusion process along
∗Correspondence to: Dvir Samuel dvirsamuel@gmail.com
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Published as a conference paper at ICLR 2025
with the prompt, generates the input image. Inversion is used in various tasks including image edit-
ing (Hertz et al., 2022), personalization (Gal et al., 2023b;a), seed noise interpolation for semantic
augmentation (Samuel et al., 2023) and generating rare concepts (Samuel et al., 2024).
As inversion became a critical building block in various tasks, several inversion methods have been
suggested. Denoising Diffusion Implicit Models (DDIM) (Song et al., 2021) introduced a deter-
ministic and fast sampling technique for image generation with diffusion models. DDIM inversion
transforms an image back into a latent noise representation by approximating the inversion equa-
tion. Although this approximation makes it very fast, it also introduces an approximation error (as
explained in section 3), causing noticeable distortion artifacts in the reconstructed images. This is
particularly noticeable in few-step diffusion models (Luo et al., 2023; Sauer et al., 2023; Esser et al.,
2024), with large gaps between the diffusion time-steps, and where inference is achieved with only
2 – 4 steps. Several efforts have been made to address inconsistencies in DDIM Inversion, which
result in poor reconstruction quality (Mokady et al., 2023; Wallace et al., 2023; Pan et al., 2023).
For example, (Pan et al., 2023; Garibi et al., 2024) used fixed-point iterations to solve the DDIM-
inversion equation. Another approach in (Hong et al., 2024) tackled the minimization of residual
error in DDIM-inversion via gradient descent. Although these methods demonstrate improvements
over previous approaches, their editing quality and computational speed are still limited.
In this paper, we frame the deterministic diffusion inversion problem as finding the roots of an im-
plicit function. We propose a solution based on the Newton-Raphson (NR) numerical scheme (Bur-
den et al., 2015) - a very fast and well-tested optimization method for root finding. We further define
a scalar NR scheme for this problem that can be computed efficiently. However, NR has a main
disadvantage in our context. When applied to our highly non-convex function, it tends to find roots
that drift outside the distribution of latents that the diffusion model was trained on.To mitigate this,
we introduce a guidance term that leverages prior knowledge of the likely solution locations, steer-
ing the NR iterations toward in-distribution roots. This is done by adding this prior knowledge on
the noise distribution at each diffusion step. Ultimately, our approach enables rapid inversion while
maintaining state-of-the-art reconstruction and editing quality.
We name our approach GNRI, for Guided Newton Raphson Inversion. GNRI converges in just a
few iteration steps at each diffusion time step and achieves high-quality image inversions (in terms
of reconstruction accuracy). In practice, 1-2 iterations are sufficient for convergence that yields
significantly more accurate results than other inversion methods. Importantly, GNRI requires no
model training, fine-tuning, prompt optimization, or additional parameters, and is compatible with
all pre-trained diffusion and flow-matching models with deterministic schedulers. We demonstrate
its effectiveness for inverting different deterministic schedulers used with latent diffusion model
(Stable Diffusion) (Rombach et al., 2022), few-step latent diffusion model (SDXL-turbo) (Sauer
et al., 2023) and few-step flow matching model (Flux.1) (Black-Forest, 2024). Figure 1 demonstrates
the quality and speed of GNRI for iterative editing using few-step diffusion models. Using such
models models that require 4 denoising steps, our approach can edit real images within 0.4 seconds.
This allows users to edit images on the fly, using text-to-image models.
We conduct a comprehensive evaluation of GNRI. First, we directly assess the quality of inver-
sions found with GNRI by measuring reconstruction errors compared to deterministic inversion ap-
proaches. Our method suppresses all methods with ×2to ×40 speedup gain. We then demonstrate
the benefit of GNRI in two downstream tasks (1) In Image editing, GNRI smoothly changes fine
details in the image in a consistent and coherent way, whereas previous methods struggle to do so.
(2) In Seed Interpolation and Rare concept generation (Samuel et al., 2023) that require diffusion
inversion. In both of these tasks, GNRI yields more accurate seeds, resulting in superior generated
images, both qualitatively and quantitatively.
2 RELATED WORK
Text-to-image diffusion models (Rombach et al., 2022; Saharia et al., 2022; Ramesh et al., 2022;
Balaji et al., 2022; Esser et al., 2024) translate random samples (seeds) from a high-dimensional
space, guided by a user-supplied text prompt, into corresponding images. DDIM (Song et al., 2021)
is a widely used deterministic scheduler, that demonstrates the inversion of an image to its latent
noise seed. When applied to the inversion of text-guided diffusion models, DDIM inversion suffers
from low reconstruction accuracy that is reflected in further tasks, particularly when applied to few-
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step diffusion models that require only 3-4 denoising steps. This happens because DDIM inversion
relies on a linear approximation, causing the propagation of errors that result in inaccurate image re-
construction. Recent studies (Mokady et al., 2023; Wallace et al., 2023; Pan et al., 2023; Hong et al.,
2024) address this limitation. Null-text inversion (Mokady et al., 2023) optimizes the embedding
vector of an empty string. This ensures that the diffusion process calculated using DDIM inversion,
aligns with the reverse diffusion process. (Miyake et al., 2023) replace the null-text embedding with
a prompt embedding instead. This enhances convergence time and reconstruction quality but results
in inferior image editing performance. In both (Mokady et al., 2023) and (Miyake et al., 2023), the
optimized embedding must be stored, resulting in nearly 3 million additional parameters for each
image (using 50 denoising steps of StableDiffusion (Rombach et al., 2022)).
EDICT (Wallace et al., 2023) introduced invertible neural network layers, specifically Affine Cou-
pling Layers, to calculate both backward and forward diffusion paths. While effective, it comes at
the cost of prolonging inversion time. BDIA (Zhang et al., 2023) introduced a novel approximation
tailored for EDICT, enhancing its computational efficiency while maintaining the accuracy in diffu-
sion inversion. However, it still demands considerably more time, approximately ten times longer
than DDIM Inversion. TurboEdit (Wu et al., 2024) introduced an encoder-based iterative inversion
technique for few-step diffusion models, enabling precise image inversion and disentangled image
editing. DirectInv (Ju et al., 2023) separates the source and target diffusion branches for improved
text-guided image editing, leading to better content preservation and edit fidelity. AIDI (Pan et al.,
2023) and ReNoise (Garibi et al., 2024) used a fixed-point iteration technique at each inversion step
to find a better solution for the implicit function posed by DDIM equations and thereby achieving
improved accuracy. ExactDPM (Hong et al., 2024), similar to (Pan et al., 2023; Garibi et al., 2024)
proposed gradient-based methods for finding effective solutions for the implicit function.
Alternative methods proposed in (Huberman et al., 2023; Brack et al., 2024; Deutch et al., 2024)
use a stochastic DDPM inversion instead of a deterministic one. Although it can recover the exact
image during reconstruction, the stochastic nature of these approaches usually causes the method to
struggle with reconstructing fine details during editing. These methods require many steps for high-
quality editing, making the process time-consuming. Additionally, they demand a larger memory
footprint, as they need to store T+ 1 latents for each inverted image, restricting their use only to
reconstruction and editing tasks. We also compare our approach with these methods in terms of
editing quality and demonstrate that our method outperforms them all.
3 PRELIMINARIES
We first establish the fundamentals of Denoising Diffusion Implicit Models (DDIMs). In this model,
abackward pass (denoising) is the process that generates an image from a seed noise. A forward
pass is the process of adding noise gradually to an image until it becomes pure Gaussian noise.
Inversion (Song et al., 2021) is similar to the forward pass but the goal is to end with a specific
Gaussian noise that would generate the image if denoised.
Forward Pass in Diffusion Models. Diffusion models (Rombach et al., 2022) learn to generate
images through a systematic process of iteratively adding Gaussian noise to a latent data sample
until the data distribution is mostly noise. The data distribution is subsequently gradually restored
through a reverse diffusion process initiated with a random sample (noise seed) from a Gaussian
distribution. In more detail, the process of mapping a (latent) image to noise is a Markov chain
that starts with z0, and gradually adds noise to obtain latent variables z1, z2, . . . , zT, following
a distribution q(z1, z2, . . . , zT|z0) = ΠT
t=1q(zt|zt−1), where ∀t:zt∈Rdwith ddenoting the
dimension of the space. Each step in this process is a Gaussian transition, that is, qfollows a
Gaussian distribution
q(zt|zt−1) := N(zt;µt=γtzt−1,Σt=βtI),(1)
parameterized by a schedule (β0, γ0),...,(βT, γT)∈(0,1)2. As discussed below, in DDIM, γt=
√1−βtand in Euler scheduling βt=γt= 1 ∀t.
Deterministic schedule diffusion models. It has been shown that one can “sample” in a determin-
istic way from the diffusion model, and this accelerates significantly the denoising process. Several
deterministic schedulers have been proposed (Song et al., 2021; Lu et al., 2022; Karras et al., 2022),
we describe here two popular ones, DDIM and Euler schedulers.
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Denoising Diffusion Implicit Models (DDIM). Sampling from diffusion models can be viewed
as solving the corresponding diffusion Ordinary Differential Equations (ODEs) (Lu et al., 2022).
DDIM (Song et al., 2021), a popular deterministic scheduler, proposed to denoise a latent by
zt−1=rαt−1
αt
zt−√αt−1·∆ψ(αt)·ϵθ(zt, t, p),(2)
where αt= 1−βt,ψ(α) = q1
α−1, and ∆ψ(αt) = ψ(αt)−ψ(αt−1)and ϵθ(zt, t, p)is the output
of a network that was trained to predict the noise to be removed.
Euler schedulers. Euler schedulers follow a similar deterministic update rule
zt−1=zt+ (σt−1−σt)vθ(zt, t, p),(3)
here σt, σt−1are scheduling parameters and vθis the output of the network that was trained to
predict the velocity.
Diffusion inversion. We now focus on inversion in the latent representation. We describe our
approach first for DDIM, and extension to other schedulers is discussed below. Given an image
representation z0and its corresponding text prompt p, we seek a noise seed zTthat, when denoised,
reconstructs the latent z0. Several approaches were proposed for this task. DDIM inversion rewrites
Eq. (2) as:
zt=f(zt)
f(zt) := rαt
αt−1
zt−1+√αt·∆ψ(αt)·ϵθ(zt, t, p).(4)
DDIM inversion approximates this implicit equation in ztby replacing ztwith zt−1
f(zt)≈rαt
αt−1
zt−1+√αt·∆ψ(αt)·ϵθ(zt−1, t, p).(5)
The quality of the approximation depends on the difference zt−zt−1(a smaller difference would
yield a small error) and on the sensitivity of ϵθto that zt. See (Dhariwal & Nichol, 2021; Song et al.,
2021) for details. By applying Eq. (5) repeatedly for every denoising step t, one can invert an image
latent z0to a latent zTin the seed space.
DDIM inversion is fast, but the approximation of Eq. (5) inherently introduces errors at each time
step. As these errors accumulate, they cause the whole diffusion process to become inconsistent in
the forward and the backward processes, leading to poor image reconstruction and editing (Mokady
et al., 2023; Wallace et al., 2023; Pan et al., 2023). This is particularly noticeable in few-step and
consistency models with a small number of denoising steps (typically 2-4 steps), where there’s a
significant gap between ztand zt−1Garibi et al. (2024).
This inversion technique can also be applied to other deterministic schedulers. For instance, for
Euler scheduler, one defines zt=f(zt),f(zt) := zt−1+ (σt−σt−1)vθ(zt, t, p),and this is ap-
proximated by zt−1+ (σt−σt−1)vθ(zt−1, t, p).
Iterative inversion and optimization methods. Several papers proposed to improve the approxi-
mation using iterative methods. AIDI (Pan et al., 2023) and ReNoise (Garibi et al., 2024) proposed
to directly solve Eq. (4) using fixed-point iterations (Burden, 1985), a widely-used method in nu-
merical analysis for solving implicit functions. In a related way, (Hong et al., 2024) solves a more
precise inversion equation, obtained by employing higher-order terms, using gradient descent.
Newton-Raphson Root finding. The Newton-Raphson method is a widely used numerical tech-
nique for finding roots of a real-valued function F(Burden et al., 2015). It is particularly effective
for solving equations of the form F(z)=0, when F:RD→RDfor an arbitrary dimension D.
It provides fast convergence, typically quadratic, by requiring the evaluation of the function and the
inversion of its Jacobian matrix. It has also been shown that when initialized near a local extremum,
NR may converge to that point (oscillating around it) (Kaw et al., 2003). The NR scheme in general
form, is given by
zk+1
t=zk
t−J(zk
t)−1F(zk
t),(6)
where J(zk
t)−1presents the inverse of a Jacobian matrix J∈RD×Dfor F(all derivatives are w.r.t
to z), and kstands for the iteration number. The iteration starts with an initial guess, z=z0.
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Figure 2: Newton-Raphson Inversion iterates over an implicit function Eq. 4 using Eq. 10 scheme,
at every time-step in the inversion path. Initialized with z0
t=zt−1it converges within ≈2 iterations,
to zt. Each box denotes one inversion step; black circles correspond to intermediate latents in the
denoising process; green circles correspond to intermediate Newton-Raphson iterations.
4 OUR METHOD: GUIDED NEWTON RAPHSON INVERSION
Existing inversion methods are either fast-but-inaccurate, like DDIM inversion, or more precise-but-
slow, like (Pan et al., 2023) and (Hong et al., 2024). This paper presents a method that achieves a
balance of speed and improved precision compared to these existing approaches.
To achieve these features we introduce two key ideas. First, we frame inversion as a scalar root-
finding problem that can be solved efficiently, and use the well-known Newton-Raphson root-finding
method. Second, we make the observation that an inversion step is equivalent to finding a specific
noise vector, and we use a strong prior obtained from the distribution of that noise. This prior during
the iterative solution guides Newton-Raphson towards finding a root that adheres to the correct
distribution of latents. See Figure 2 for illustration.
4.1 FRAMING INVERSION AS EFFICIENT ROOT-FINDING
Diffusion inversion can be done by finding the fixed point of the function f(z)in Eq. 4. This is
equivalent to finding the zero-crossings or roots, ztof the residual function r:RD→RDdefined
as r(zt) := zt−f(zt). One could now apply Newton-Raphson (NR) to find a root. However, in our
case, ztis a high dimensional latent(D≈16Kin StableDiffusion (Rombach et al., 2022)), making
it computationally infeasible to compute the Jacobian (Eq. 6), explicitly and invert it. To address
this computational limitation, we apply a norm over r(zt),ˆr:Rd→R+
0yielding a multi-variable,
scalar function, which has the same set of roots:
ˆr(zt) := ||zt−f(zt)||1,(7)
and seek the roots ˆr(zt)=0where ||·|| denotes a L1norm which simply sum over all absolute values
of ˆr. Applying the norm on the residual has be done in previous work (Hong et al., 2024; Garibi
et al., 2024), however here it is used to reduce the Jacobian to a vector and that can be computed
quickly (see derivation in Appendix A). We call this method Newton-Raphson Inversion, NRI.
This method is efficient and converges quickly in practice. However, NRI in our case has a key
limitation: Eq. (4), and thus ˆr, can have multiple solutions or local minima. The accelerated con-
vergence of NR due to linear “extrapolation”, can cause it to ”jump” to solutions outside the latent
variable distribution for the diffusion model. Indeed, in practice, we find that solving Eq. (7) for
ˆr(zt) = 0 often converges quickly to a solution that results with poor image reconstruction. We
quantify and illustrate this phenomenon in section 5.1. Next, we describe a remedy to this problem.
4.2 GUIDED NEWTON RAPHSON INVERSION
The NR procedure discussed above may find roots that are far from the modes of the latent distribu-
tion. How can we guide NR to converge to useful roots among all possible ones?
Note that determining a ztgiven zt−1, is equivalent to finding which noise term is added during the
forward pass of the diffusion process. Luckily, the distribution of that noise is known by the design
of the diffusion process and we can use it as prior information. More precisely, since each step in the
diffusion process follows a Gaussian distribution q(zt|zt−1)(Eq. 1), we define a positive function
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that obtains a zero value at the maximum likelihood of the qdistribution by taking the negative log
of the exponent part of the distribution (without the normalizing factor). This can be simplified to
G(zt) = (1
βt||zt−µt|| DDIM,
||zt−µt|| Euler.(8)
where µt,βtwere defined in Section 3, see Eq (1). To guide NR to select an ”in-distribution”
solution, we define a new objective F:RD→R+
0:
F(zt) := ||zt−f(zt)||1+λG(zt).(9)
Here, λ > 0is a hyperparameter weighting factor for the guidance term. See Appendix E for
ablation of λvalues. Note that this guidance term incorporates prior knowledge about the probable
locations of the solutions in zspace.
We then seek to drive F(zt)near zero. Applying the Newton Raphson iteration scheme for Eq. (9)
then emerges as (see derivation in Appendix A):
z0
t=zt−1
zk+1
t(i) = zk
t(i)−1
DF(zk
t)
gi(zk
t) + η.(10)
Here gi:= ∂F(zt)
∂zt(i)is the partial derivative of Fwith respect to the variable (descriptor) zt(i). The
index i∈[0,1, ..., D]indicates z’s components and kstands for the iteration number, while ηis
a small constant added for numerical stability. The function gcan be computed efficiently using
automatic differentiation engines. We initialize the process with zfrom the previous diffusion time-
step zt−1. We call our approach GNRI for Guided Newton Raphson Inversion. For discussion on
applying NR on our objective function and the guidance term see Appendix B.
5 EXPERIMENTS
Here, we first provide motivation and analysis for the guidance term presented in Section 4.2.
Then, we show evaluation results of GNRI on three main tasks: (1) Image inversion and recon-
struction: Here, We assess the inversion fidelity by evaluating the quality of the reconstructed
images. (2) Image Editing: We demonstrate the efficacy of our inversion scheme in image editing,
highlighting its ability to facilitate real-time editing. (3) Rare Concept Generation: We illustrate
how our method can be applied to improve the generation of rare concepts.
Compared Methods: We compared our approach with the following methods. Standard DDIM
Inversion (Song et al., 2021), SDEdit Meng et al. (2022), Null-text (Mokady et al., 2023) and
EDICT (Wallace et al., 2023). Two fixed-point based methods: AIDI (Pan et al., 2023) and
ReNoise (Garibi et al., 2024) with further comparison to Anderson Acceleration Pan et al. (2023)
shown in Appendix I. Gradient-based method ExactDPM (Hong et al., 2024). Wu2024Turbo (Wu
et al., 2024) and two DDPM inversion methods: EditFriendly Huberman et al. (2023) and
Gal2024Turbo (Deutch et al., 2024). In all experiments, we used code and parameters provided
by the respective authors.
Implementation details: To demonstrate the versatility of our approach, we conducted experiments
on latent diffusion model SD2.1 Rombach et al. (2022) and two few-step models: SDXL-turbo
(Sauer et al., 2023) and the newly introduced flow matching Flux.1-schnell model (Black-Forest,
2024). Sampling steps were set to 50 for SD2.1 and 4 for SDXL-turbo and Flux.1. All methods ran
until convergence. All methods were tested on a single A100 GPU for a fair comparison. PyTorch’s
built-in gradient calculation was used for computing derivatives of Eq. (9). Editing for all iterative
methods was done using Prompt-to-Prompt (Hertz et al., 2022).
5.1 GUIDANCE TERM MOTIVATION AND COMPARISON TO OTHER NUMERICAL SCHEMES
To illustrate the motivation behind our guidance term, we compare the reconstruction quality of
non-guided NRI a ”vanilla” NR inversion method with two iterative numerical schemes: Fixed-
point Iteration (FPI) ((Pan et al., 2023) and Gradient Descent (GD) (Hong et al. (2024). We test the
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Figure 3: The effect of GNRI guiding term on NR inversion, and comparison to other iterative
inversion methods. All results are averages computed with SDXL-Turbo applied to 5,000 COCO
images. (a) Average residuals throughout optimization. NR-based methods are the fastest to
converge. Gradient-descent was run with the largest learning rate that was stable but still is slowest.
(b) Reconstruction quality (PSNR). Adding guidance (blue) to NRI (green) significantly improves
the quality of the converged solution. (c) Likelihood of inferred noise. Without the guiding term,
NRI (green) finds solutions that are substantially different from those found by other methods, which
explains the low reconstruction quality.
Figure 4: (Left) Reconstruction qualitative results: Comparing image inversion-reconstruction
performance. While all baseline methods struggle to preserve the original image, GNRI successfully
excels in accurately reconstructing it. (Right) Inversion Results: Mean reconstruction quality (y-
axis, PSNR) and runtime (x-axis, seconds) on the COCO2017 validation set. Our method achieves
high PSNR while reducing inversion-reconstruction time by a factor of ×2(compared to DDIM)
and up to ×40 (compared to ExactDPM) on SDXL-turbo and ×10 to ×40 on Flux.1, compared to
other approaches.
reconstruction of 5,000 image-caption pairs from COCO Lin et al. (2014), presenting three metrics
in Fig. 3. Fig 3a shows that FPI, GD and non-guided NRI, all converge to low residual values but the
reconstruction values for NRI (green line) in Fig. 3b are notably lower. This suggests that solutions
reached by NRI are in areas of the latent space that yield poor results. Comparing the blue curve in
Fig 3 to the green curve highlights the significant impact of adding a guidance term. It accelerates
convergence (Fig. 3a), improves reconstruction (PSNR) (Fig 3b) and reaches a better likelihood
(Fig. 3c).
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Figure 5: (Left)Qualitative results of image editing. GNRI edits images more naturally while
preserving the structure of the original image. All baselines were executed until they reached con-
vergence. (Right) Evaluation of editing performance: GNRI achieves superior CLIP and LPIPS
scores, indicating better compliance with text prompts and higher structure preservation.
5.2 IMAGE RECONSTRUCTION
To evaluate the fidelity of our approach, we measure the PSNR of images reconstructed from seed
inversions. Specifically, we used the entire set of 5000 images from the MS-COCO-2017 validation
dataset (Lin et al., 2014), along with their corresponding captions. For each image-caption pair, we
first found the inverted latent and then used it to reconstruct the image using the same caption. Given
that the COCO dataset provides multiple captions for each image, we used the first listed caption as a
conditioning prompt. Figure 4 (left) demonstrates a qualitative comparison of reconstructed images.
Figure 4 (right) illustrates the PSNR of reconstructed images versus inversion time, highlighting
the performance of our method compared to SoTA inversion techniques. The dashed black line
represents the upper bound set by the Stable Diffusion VAE, showing that our method achieves the
highest PSNR among SoTA methods and approaches the VAE upper bound, while also being the
fastest. Additional qualitative comparisons for SD2.1 and further analysis are in Appendix H.
5.3 REAL-TIME IMAGE EDITING
Current state-of-the-art methods for editing images start by inverting a real image into latent space
and then operating on the latent. As a result, the quality of editing depends strongly on the quality
of inversion (Mokady et al., 2023).
We now evaluate the effect of inverting images with GNRI, compared to SoTA inversion baselines.
We show that GNRI outperforms all baselines in editing performance while requiring the shortest
time. This opens the door for real-time editing capabilities. We present below both qualitative and
quantitative results. For Neural Function Evaluations (NFE) comparison see Appendix H.
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Table 1: Image editing comparison using descriptive text in PIE-Bench (Ju et al., 2023) dataset
with SDXL-turbo. The efficiency is measured in a single A100 GPU. Our method achieves the best
background preservation and clip similarity while being significantly faster than other methods.
PIE-Bench Background Preservation CLIP Similarity Efficiency
PSNR LPIPS MSE SSIM Whole Edited Inverse Forward
↑103↓104↓102↑ ↑ ↑ (s) ↓(s) ↓
DDIM 18.59 177.96 184.69 66.86 23.62 21.20 0.454 0.445
ReNoise (Garibi et al., 2024) 27.11 49.25 31.23 72.3 23.98 21.26 5.41 0.445
ExactDPM (Hong et al., 2024) 24.54 59.88 36.49 69.18 23.77 21.23 15.11 0.445
EditFriendly (Huberman et al., 2023) 24.55 91.88 95.58 81.57 23.97 21.03 32.3 23.1
Direct Inv (Ju et al., 2023) 27.22 54.55 62.86 84.76 25.02 22.10 4.3 50
TurboEdit (Wu et al., 2024) 29.52 44.74 26.08 91.59 25.05 22.34 0.981 0.569
GNRI (Ours) 30.22 40.15 20.10 98.66 26.15 23.26 0.521 0.445
Interpolation Centroid
ACC ↑FID ↓ACC↑FID ↓
DDIM Inversion 51.59 6.78 67.24 5.48
ExactDPM (Hong et al., 2024) 52.01 6.13 68.14 5.32
ReNoise (Garibi et al., 2024) 52.51 6.0 69.14 5.22
GNRI (ours)54.98 5.91 70.18 4.59
Table 2: Image interpolation and
centroid finding. In interpola-
tion, two images x1, x2are in-
verted to generate images between
their seeds z1
T, z2
T. In centroid-
finding, a set of images is inverted
to find their centroid. Best perfor-
mance is achieved with our GNRI.
Qualitative results. Figure 5(left) gives a qualitative comparison between SoTA approaches and
GNRI in the context of real image editing. GNRI excels in accurately editing with target prompts
producing images with both high fidelity to the input image and adherence to the target prompt.
The examples illustrate how alternative approaches may struggle to retain the original structure or
tend to overlook crucial components specified in the target prompt. As an example, in the first
row of Figure 5(left), GNRI exclusively converts the cat into a dog without changing the text in
the sign whereas other methods either fail to generate a proper dog or change the text in the sign.
Results for SD2.1 in Appendix H. For additional qualitative results see also Appendix H,G and K.
User Study. We further evaluated editing quality using human raters. We followed the evaluation
process of Mokady et al. (2023) and asked human raters to rank edits made by the three leading
methods: Ours, ReNoise (Garibi et al., 2024), and ExactDPM (Hong et al., 2024). Unfortunately,
the code for TurboEdit (Wu et al., 2024) was not available at the time of our evaluation. 100 images
were rated, 12 images were provided by the authors of (Mokady et al., 2023) and the rest were
randomly selected from COCO (Lin et al., 2014) and PieBench (Ju et al., 2023) benchmarks. Three
raters for each image were recruited through Amazon Mechanical Turk and were tasked to choose
the image that better applies the requested text edit while preserving most of the original image.
GNRI was preferred with 71.6% preference compared to ReNoise’s (Garibi et al., 2024) 15.9% and
ExactDPM (Hong et al., 2024) 12.5%.
Quantitative results. Following (Wallace et al., 2023; Huberman et al., 2023; Garibi et al., 2024),
we evaluate the results using two complementary metrics: LPIPS (Zhang et al., 2018) to quantify
the extent of structure preservation (lower is better) and a CLIP-based score to quantify how well
the generated images comply with the text prompt (higher is better). Metrics are averaged across
100 MS-COCO images. Figure 5(right) illustrates that editing with GNRI yields a superior CLIP
and LPIPS score, demonstrating the ability to perform state-of-the-art real image editing with supe-
rior fidelity. Following (Wu et al., 2024) we also evaluated our approach on the newly introduced
PieBench (Ju et al., 2023) dataset. Table 1 shows that our method more effectively follows the text
guidance while preserving the background, outperforming current SoTA techniques. These evalua-
tions further affirm the findings derived from the user study.
5.4 SEED INTERPOLATION AND RARE CONCEPT GENERATION
We evaluate the benefit of our inversion in a second task, of selecting latent seeds for image gen-
eration. It has been shown (Samuel et al., 2024; 2023) that text-to-image diffusion models poorly
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Table 3: Inversion Quality Impact on Rare Concept Generation: We assess image generation
using a pre-trained classifier’s accuracy, comparing NAO (Samuel et al., 2023) (with DDIM inver-
sion), ReNoise (Garibi et al., 2024), ExactDPM Zhang et al. (2023) and GNRI. We report average
per-class accuracy for Head (over 1M samples), Medium, and Tail (rare classes <10K samples).
GNRI enhances rare and medium concept accuracy without sacrificing overall performance.
ImageNet1k in LAION2B
Head Medium Tail Total Acc FID ˆ
TInit ˆ
TOpt
n=235 n=509 n=256 (sec) (sec)
Methods #>1M 1M>#>10K 10K>#
DDIM inversion 98.5 96.9 85.1 94.3 6.4 25 29
ExactDPM (Hong et al., 2024) 98.1 96.8 85.3 94.1 7.1 240 32
ReNoise (Garibi et al., 2024) 98.5 97.0 85.3 94.4 6.9 24 28
GNRI (ours)98.6 97.9 89.1 95.8 6.3 17 25
generated rare concepts, and this can be improved by selecting better noise latent zT. To address
this issue, SeedSelect (Samuel et al., 2024) takes a few images of a rare concept as input and uses a
diffusion inversion module to iteratively refine the obtained seeds. These refined seeds are then used
to generate new plausible images of the rare concept. NAO (Samuel et al., 2023) extends this by
introducing new paths and centroids for seed initialization. Both methods rely on DDIM Inversions,
crucial for initial seed evaluation. GNRI provides an alternative for precise inversion seeds, aiming
for improved image quality and semantic accuracy. It’s important to highlight that most inversion
techniques (Mokady et al., 2023; Wallace et al., 2023; Huberman et al., 2023; Brack et al., 2024) are
not applicable in this context as they necessitate extra parameters for image reconstruction, which
impedes the straightforward implementation of interpolation.
Interpolation and centroid finding: We evaluate GNRI by following the experimental protocol
of (Samuel et al., 2023) and compare images generated by four methods: DDIM, ReNoise (Garibi
et al., 2024), ExactDOM (Hong et al., 2024) and GNRI. Evaluation is conducted based on FID score
and classification accuracy (by a pre-trained classifier). Results are presented in Table 2. Notably,
initializing with GNRI seeds consistently results in higher-quality images both in interpolation paths
and seed centroids.
Rare concept generation: We further show the effect of our seed inversions on the performance
of NAO centroids with SeedSelect for rare concept generation. Specifically, we compared images
generated by SeedSelect, initialized with NAO using DDIM inversion, ReNoise, ExactDPM, and
GNRI, as shown in Table 3). We followed the evaluation protocol of (Samuel et al., 2024; 2023)
on ImageNet1k classes arranged by their prevalence in the LAION2B dataset (Schuhmann et al.,
2022). The results, summarized in Table 3, demonstrate that our inversion method significantly
boosts performance, both in classification accuracy and FID, compared to other methods. Further-
more, our inversions yield a more precise and effective initialization point for SeedSelect (Samuel
et al., 2024), resulting in notably quicker convergence without compromising performance, in all
categories (head, medium, and tail) along with a high gap at tail.
6 SUMMARY
Image inversion in diffusion models is vital for various applications like image editing, semantic
augmentation, and generating rare concept images. Current methods often sacrifice inversion qual-
ity for computational efficiency, requiring significantly more compute resources for high-quality
results. This paper presents Guided Newton-Raphson Inversion (GNRI), a novel iterative approach
that balances rapid convergence with superior accuracy, execution time, and memory efficiency. Us-
ing GNRI opens the door for high-quality real-time image editing due to its efficiency and speed.
GNRI requires no model training, fine-tuning, prompt optimization, or additional parameters, and is
compatible with all pre-trained diffusion and flow-matching models with deterministic schedulers.
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ACKNOWLEDGMENTS
We would like to express our sincere gratitude to Prof. Nir Sochen for the intriguing discussion
during the course of this study.
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Appendix
A NEWTON METHOD FOR MULTIVARIABLE SCALAR FUNCTION
In this section, we present the formulation of Newton’s method for zero crossing of a multi-variable
scalar function. For a vector x∈RDand a function f(x) : RD→Rwe are looking for the roots of
the equation f(x)=0. Assuming that the function fis differentiable, we can use Taylor expansion:
f(x+δ) = f(x) + ∇f δT+o(||δ||2)(A1)
For every δ, x∈RD. The idea of Newton’s method in higher dimensions is very similar to the
one-dimensional scalar function; Given an iterate xk, we define the next iterate xk+1 by linearizing
the equation f(xk)=0around xkas above, and solving the linearized equation f(xk+δ)=0.
Dropping the higher orders we then solve the remaining linear equation for δ. In fact, in the scalar
case, the solution for δis not unique, with each solution potentially determining a different direction
of propagation of the iterate xkin the high-dimensional input space. The optimal direction cannot
be known in advance, and some have proposed selecting the propagation direction by imposing
constraints, such as minimizing δ(Polyak & Tremba, 2020). We adopt a simple, non-sparse, yet
effective solution, that allows the scheme flexibility in deriving the direction of propagation:
δ=−1
D"1
∂f
∂x1
,1
∂f
∂x2
, ..., 1
∂f
∂xD#f(xk)(A2)
where xiindicates the i-th component of vector x. The above can be easily proven as a solution by
substituting δinto Eq. A1, dropping the higher orders setting it equal to zero. Using the relation,
δ=xk+1 −xkwe get the final iterative scheme:
xk+1
i=xk
i−1
D
f(xk)
∂f
∂xi(xk)(A3)
Note that this equation is component-wise i.e. each component is updated separately, facilitating the
solution.
B DISCUSSION ON THE NEWTON-RAPHSON METHOD FOR FUNCTIONS
WITHOUT ZERO CROSSINGS
Note that our objective function in Eq. 9 is a non-negative function. When the target function F ≥ 0
and does not have zero crossings,
the NR procedure may converge to a (non-zero) minima. A common example is the function f(x) =
x2+ 1 that has no real roots, but NR converges to its minimum. Note that while the Newton-
Raphson method is typically used to find zero crossings of a function, our approach applies it to
drive convergence toward local minima of the objective function (being locally convex around this
point). The analysis of this type of convergence within the Newton-Raphson framework is left for
future numerical analysis research.
C GNRI SCHEME CONTRACTION MAPPING
Fixed-point iterations are guaranteed to converge if the operator is contractive in the region of inter-
est. Formally, a mapping Tis contractive on its domain if there exists ρ < 1(also called Liphshitz
constant) such that ∥T(x)−T(y)∥ ≤ ρ∥x−y∥,∀(x, y)∈X, where ∥ · ∥ denotes a norm. In the
following we will demonstrate empirically that our GNRI scheme introduces contraction mapping,
a property needed for convergence of the scheme. Contractive mappings ensure that each iteration
moves closer to the limit, with the distance shrinking at a predictable rate. The rate of contraction
(the Lipschitz constant) can be used to give bounds on how fast the error decreases, helping to as-
sess the efficiency of the scheme. Next, we show empirically that, the mapping is contractive in our
region of interest.
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Figure C1: Contraction Mapping. Contraction mapping for two fast diffusion models are shown
(in log-scale), at each time-step. The scheme converges in 2-3 iterations with a notable contraction
occurring in the first iteration, assisting the rapid convergence. t= 0 is close to the image side and
t= 3 close to seed.
According to Eq. 10 the GNRI scheme for the solution F(z)=0(defined in Eq. 9), at each
diffusion time-step, is given by:
zk+1
i=zk
i−1
DF(zk)
gi(zk)(C1)
where gi:= ∂F
∂ziis the partial-derivative of Fwith respect to the variable zi, while i∈[0,1, ..., D]
indicates z’s components. We can rewrite the NR iteration as the fixed-point iteration ˜
f(z) = zby
setting ˜
f(z)as:
˜
fi(zk) := zk
i−1
DF(zk)
gi(zk)(C2)
Note that the fixed point of the newly introduced ˜
fis the solution of F(z)=0.
Let us now define a new residual function:
˜r(zk) := ||˜
f(zk)−zk|| (C3)
By substitution we get:
˜r(zk+1) = || ˜
f(zk+1)−zk+1)|| =||f(zk+1)−˜
f(zk)|| (C4)
˜r(zk) = ||˜
f(zk)−zk|| =||zk+1 −zk||
Therefore contraction mapping requirement for ˜
f:||˜
f(zk+1)−˜
f(zk)|| ≤ ρ||zk+1 −zk|| can be
written as:
˜r(zk+1)≤ρ˜r(zk)(C5)
and the contraction mapping is satisfied if ˜rfollows an exponential decay (r(zk)≤ρkr(z0)), with
some ρ < 1. Note that ˜r(zk)given in Eq. C3 can be computed at each iteration step. In Fig. C1 we
plot ˜r(zk), tested on 5,000 image caption pairs from the COCO dataset (the same as used in Sec.
5.1) showing that ˜r(zk)indeed decays exponentially (linearly in log-scale), till convergence. This
behaviour therefore implies that GNRI iteration is a contraction mapping. Note that our contraction
mapping does not converge to zero, namely the fixed point, since our objective function Fmay not
have an exact solution. Computing contraction rate ρfor GNRI shows ρ≈0.50 (at the first iteration)
while ρ≈0.90 for FPI indicating the faster convergence of GNRI.
Note that we further show in the main paper the convergence of the equation residual ˆr=||f(zt)−
zt|| (EQ. 7) as an indicator for convergence toward the inversion solution.
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Figure D1: Failure cases: GNRI fails to converge where the prompt and image do not align.
Figure D2: The influence of λon reconstruction performance. We observe that employing no reg-
ularization (λ= 0) leads to poor reconstruction, while λ= 0.1typically yields the highest recon-
struction accuracy. As λincreases, reconstruction accuracy declines, possibly because assigning
excessive weight to the prior undermines the root-finding objective.
D FAILURE CASES
Here we provide information about an analysis to find failure cases for convergence. We ran in-
version and reconstruction, in scale, on COCO2017 (118k caption-image pairs) and found that in
95.4% of cases, GNRI successfully converged to a solution. Specifically, residuals went down from
∼1(for DDIM) to <10−4indicating convergence, and the PSNR was >25.7indicating good
solutions. The remaining 4.6% were samples with incorrect captions, see Fig. SD1. These results
imply that lack of convergence may indicate text and image miss-alignment which we consider for
future work.
E PRIOR TRADE-OFF PARAMETER
Figure D2 shows the impact of the weight parameter λon the reconstruction accuracy. We observe
that using no regularization (λ= 0) results in poor reconstruction, whereas setting λ= 0.1achieves
the highest reconstruction accuracy, underscoring the importance of the prior in the objective func-
tion. There is a gradual decrease with larger λvalues, where at λ= 1 the PSNR starts to decline
faster, likely because placing too much emphasis on the prior compromises the residual root-finding
objective.
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Figure E1: (Left) Inversion Results: Mean reconstruction quality (y-axis, PSNR) and runtime
(x-axis, seconds) on the COCO2017 validation set. Our method achieves high PSNR while reduc-
ing inversion-reconstruction time by a factor of ×4to ×14.(Right) Evaluation of editing perfor-
mance: GNRI achieves superior CLIP and LPIPS scores, indicating better compliance with text
prompts and higher structure preservation.
F SEED EXPLORATION & RARE CONCEPT GENERATION
Figure F1: Generating rare concepts based on a few examples with the method of (Samuel et al.,
2023) that heavily depends on the diffusion-inversion quality. In our comparison, we evaluate GNRI
alongside ReNoise (refer to the discussion in the main paper). ReNoise frequently struggles to
produce a realistic representation of certain objects (such as Oxygen-mask or Patas Monkey) or an
accurate depiction of specific concepts (like Tiger-cat or Pay-phone). However, the use of GNRI
rectifies these issues in the results. For a detailed quantitative comparison, please refer to the main
paper. See the main paper for a quantitative comparison.
Figure SF1 further displays results for the rare-concept generation task introduced in (Samuel et al.,
2024; 2023). The objective is to enable the diffusion model to generate concepts rarely seen in its
training set by using a few images of that concept. Both methods in (Samuel et al., 2024; 2023)
utilize diffusion inversion for this purpose. In the main paper, we presented experiments showcasing
the impact of our new inversion process on the outcomes of (Samuel et al., 2024; 2023).
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Figure F2: Qualitative comparison for image editing on the PIE-benchmark. Illustrates how al-
ternative approaches may struggle to preserve the original structure or fail to edit the image, while
GNRI succeeds in editing the image properly.
We provide qualitative results based on NAO (Samuel et al., 2023) centroid computation when
utilizing GNRI, contrasting them with those obtained through DDIM inversions. The illustrations
demonstrate that GNRI is capable of identifying high-quality centroids with correct semantic content
compared to centroids found by DDIM.
G ADDITIONAL QUALITATIVE RESULTS ON PIE-BENCHMARK
Additional quantitative results on the PIE-Benchmark. Figure F2 provides quantitative results
on the PIE-Benchmark using Flux.1. It highlights how alternative methods often fail to maintain
the original structure or miss key elements specified in the target prompt, whereas GNRI effectively
achieves accurate and proper image editing.
Quantitative results with Stable Diffusion 2.1. We present a quantitative comparison between
GNRI and baseline methods, utilizing latent diffusion SD2.1 (Rombach et al., 2022). Figure E1(a)
illustrates the image inversion-reconstruction performance, while Figure E1(b) highlights the editing
performance, evaluated using LPIPS and CLIP-score metrics. The results demonstrate that GNRI
surpasses all other inversion methods in terms of reconstruction quality, which subsequently im-
proves editing performance.
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Figure F3: Qualitative comparison for image editing: Illustrates how alternative approaches may
struggle to preserve the original structure or overlook crucial components specified in the target
prompt, while GNRI succeeds in editing the image properly.
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Figure F4: Various editing with same input: Note the GNRI capability in both subtle and extensive
changes as one would expect from the particular prompt change.
Table H1: PSNR vs. NFE results using SDXL Turbo on the COCO validation set. Our method
achieves the highest PSNR with the fewest NFEs, compared to other methods.
PSNR NFE
ReNoise Garibi et al. (2024) 18.1 36
ExactDPM Hong et al. (2024) 20.0 40
TurboEdit Wu et al. (2024) 22 8
GNRI (Ours) 23.9 6
Table H2: Inversion comparison with Edit Friendly on SDXL Turbo (COCO validation set). While
DDPM achieves higher PSNR through stochastic inversion, our deterministic approach (GNRI) pro-
vides competitive results with significantly faster inversion time (0.521s vs 32.3s).
PSNR Inv Time
EditFriendly Huberman et al. (2023) 26.1 32.3
GNRI (Ours) 23.9 0.521
H ADDITIONAL QUALITATIVE AND QUANTITATIVE RESULTS -COMPARISON
TO BASELINES
In this section, we present additional qualitative comparisons involving GNRI and baseline methods.
Figures F3 provide further comparisons for real-image editing, using SD2.1. These figures illustrate
how alternative approaches may struggle to preserve the original structure or overlook crucial com-
ponents specified in the target prompt. For example, n the first row of Figure F3, GNRI correctly
transforms the pizza into bread, while other methods generate a bad looking bread. Row three shows
an example of GNRI success (bananas to oranges), where other alternatives totally fail.
Figure F4 shows the outcomes of various edits on the same image, providing additional confirmation
that inversion with GNRI yields modification of the pertinent parts in the image while maintaining
the original structure.
Table H1 provides PSNR vs NFE (Neural Function Evaluations) results using SDXL Turbo on the
COCO validation set. Our method requires 6 NFEs, calculated as 4 steps with an average of 1.5
NR iterations per step (some steps needing 1 iteration, others 2). As shown in the table below, our
approach achieves the highest PSNR while using the fewest NFEs compared to other methods.
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Table I1: Comparison of Anderson Acceleration and the Guidance term for out-of-distribution
COCO samples. A higher likelihood is better.
mean likelihood q(zt|zt−1) PSNR Inv Time
Anderson Acceleration 0.34 18.3 Inf
Guidance Regularizer (Ours) 0.82 25.8 0.4 s
Table J1: Memory usage and convergence time for different methods on A100 and RTX 3090Ti.
A100 (VRAM 40GB) RTX 3090Ti (VRAM 24GB)
Memory Inv Time Memory Inv Time
AIDI Pan et al. (2023) 15GB 5 sec 16 GB 13 sec
ExactDPM Hong et al. (2024) 30GB 17 sec 20 GB 25 sec
GNRI (Ours) 28GB 0.4 sec 19 GB 1 sec
Table H2 compares inversion performance with Edit Friendly Huberman et al. (2023) using SDXL
Turbo on the COCO validation set. Edit Friendly achieves the maximum PSNR possible given the
VAE distortion, because it does a stochastic DDPM inversion, saving additional noise matrices at
every step and “overfitting” the inverted image. As a result, it requires extensive inversion time
(more than 30 seconds), whereas our GNRI reaches a relatively high PSNR in under a second. Our
approach solves deterministic inversion (DDIM or Euler) making it suitable for applications like
interpolation and rare concept generation, where DDPM is not feasible.
I COMPARISON TO ANDERSON ACCELERATION
The guiding term introduced in Sec 4.2 might appear similar to Anderson acceleration used in Pan
et al. (2023), which aims to allow more gradual changes from previous estimates. However, One key
difference is that our guidance term introduced in Eq.(9) does not pull zttoward zt−1but towards the
mean µt. By that, it directs the Newton-Raphson method toward solutions having a high likelihood,
using “side-information” about the noise. In contrast, Anderson acceleration relies on previous
values of the implicit function f(zi)and residuals but lacks awareness of the latent distribution (see
for example, line 13 in Algorithm 1 of (Pan et al., 2023)).
In GNRI, keeping ztclose to µ, encourages solutions that are more “in-distribution” and aligned
with the diffusion model. In other words, if zt−1starts far out-of-distribution, keeping ztclose to
zt−1is likely to yield worse solutions compared to guiding zttoward inputs that the model expects
to receive.
We illustrate this effect in table I1. We analyzed the inversion of 300 COCO images that the model
would consider to be non-typical by selecting the samples with the lowest likelihood under q(z0)
(Eq.(1)). The table shows that GNRI drives the latents toward significantly higher likelihood solu-
tions (mean q(zt|zt−1)), leading to substantially better reconstructions (higher PSNR) than Ander-
son acceleration.
More broadly, our guidance term could potentially be applied to other methods, such as fixed-point
iteration approaches like those proposed by Pan et al. It would also be interesting to find methods
that can include more domain knowledge into the inversion process.
J MEMORY USAGE
We compared the memory usage of our approach, with AIDI Pan et al. (2023) and ExactDPM
(Zhang et al. (2023)) on a A100 GPU (40 GB VRAM) and a RTX 3090Ti GPU (24GB VRAM).
Results are given in table J1. Our approach consumes about the same GPU memory as ExactDPM,
however, it converges faster about x43 times than ExactDPM on an A100 GPU, and x25 faster on
an RTX 3090 GPU.
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Published as a conference paper at ICLR 2025
K MULTI OBJECT EDITING
We conducted several qualitative experiments to evaluate the capabilities of our method in editing
multiple objects simultaneously. Our results demonstrate that the method can effectively handle
complex scenes, allowing for the independent manipulation of several objects without compromising
the quality of individual edits. As illustrated in Figure K1, our GNRI model successfully performs
multi-object transformations while maintaining scene coherence and natural composition - from
converting multiple dogs to cats while preserving the scene layout, to simultaneously transforming
different food items (steak to apple, eggs to pancakes) on a plate. These results underscore GNRI’s
robustness in handling multiple concurrent edits while maintaining high visual quality and semantic
coherence across the transformed scenes.
Figure K1: Multi-object editing capabilities of GNRI. Top: Simultaneous transformation of multiple
dogs into cats. Bottom: Concurrent food item conversion on a plate (steak→apple, eggs→pancakes),
demonstrating preservation of scene composition and context.
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