Turbo-DDCM: Fast and Flexible Zero-Shot Diffusion-Based Image Compression
Authors: Amit Vaisman
Guy Ohayon
Hila Manor
Michael Elad
Tomer Michaeli
Venue: ICLR 2026 Poster (2026)
Keywords: image compression
diffusion models
diffusion-based image compression
zero-shot diffusion-based image compression
Primary area: generative models
TL;DR: We present Turbo-DDCM, a zero-shot diffusion-based image compression method up to an order of magnitude faster than state-of-the-art, while maintaining competitive compression quality. We also introduce prioritized regions compression for our method.

Abstract: While zero-shot diffusion-based compression methods have seen significant progress in recent years, they remain notoriously slow and computationally demanding. This paper presents an efficient zero-shot diffusion-based compression method that runs substantially faster than existing methods, while maintaining performance that is on par with the state-of-the-art techniques. Our method builds upon the recently proposed Denoising Diffusion Codebook Models (DDCMs) compression scheme. Specifically, DDCM compresses an image by sequentially choosing the diffusion noise vectors from reproducible random codebooks, guiding the denoiser’s output to reconstruct the target image. We modify this framework with *Turbo-DDCM*, which efficiently combines a large number of noise vectors at each denoising step, thereby significantly reducing the number of required denoising operations. This modification is also coupled with an improved encoding protocol. Furthermore, we introduce two flexible variants of Turbo-DDCM, a priority-aware variant that prioritizes user-specified regions and a distortion-controlled variant that compresses an image based on a target PSNR rather than a target BPP. Comprehensive experiments position Turbo-DDCM as a compelling, practical, and flexible image compression scheme.

Published as a conference paper at ICLR 2026
TURBO-DDCM: FAST AND FLEXIBLE ZERO-SHOT CAFUSION-BASBE IMAGE COMPRESSION
Amit Vaisman', Guy Ohayon', Hila Manor!, Michael Elad', Tomer Michaeli' Technion - Isracl Institute of Technology FFlatiron Institute, Simons Foundation amit. sman campus... technion. ac. 11, gohayon [hila www.mmaoooamaii....m eladêcs, tomer me e technion.ac.
ABSTRACT
While zero-shot diffusion-based compression methods have seen significant progress in recent years, they remain notoriously slow and computationally de- manding. This paper presents an efficient zero-shot diffusion-based compres- sion method that runs substantially faster than existing methods, while maintain- ing performance that is on par with the state-of-the-ar techniques. Our method builds upon the recently proposed Denoising Diffusion Codebook Models (DD- CMs) compression scheme. Specifically, DDCM compresses an image by se- quentially choosing the diffusion noise vectors from reproducible random code- books, guiding the denoiser's output to reconstruct the target image. We modify this framework with Turbo-DDCM, which efficiently combines large number of noise vectors at each denoising step, thereby significantly reducing the num- ber of required denoising operations. This modification also coupled with an improved encoding protocol. Furthermore, introduce two flexible variants of Turbo-DDCM, a priority-awar variant that prioritizes user-specified regions and distortion-controlles variant that compresses image based target PSNR rather than a target BPP. Comprehensive experiments position Turbo-DDCM as a compelling, practical, and flexible image compression scheme. Code is available on our project's webpage.
INTRODUCTION
The field of image compression has witnessed a shift towards neural-based approaches in recent years (Ballé et al., 2017; Toderici et al., 2017; Li & Ji, 2020), and more recently to methods that rely on diffusion models (Sohl-Dickstein et al., 2015; Ho et al., 2020; Song et al., 2020). In particular, diffusion models have been utilized for image compression by training dedicated models (Ghouse et al., 2023; Yang Mandt, 2023), by fine-tuning existing models (Careil et al., 2024), or by using them in zero-shot manner (Theis et al., 2022; Elata al., 2024; Ohayon et al., 2025; Vonderfecht & Liu, 2025). principle, zero-shot methods are appealing because they enable the same diffusion backbone to be shared across multiple tasks (such compression, restoration, editing, generation, etc.), thereby allowing all tasks to benefit simultaneously from improvements to the shared back- bone. However, existing zero-shot diffusion compression methods remain impractical due their high computational demands, which result in slow inference. Ranging from approximately 10 sec- onds (achieved using custom CUDA kernel (Vonderfecht & Liu, 2025)) several minutes (Elata et al., 2024) for compressing and decompressing a single image, these slow inference times make zero-shot diffusion compression methods less compelling compared training- maseed methods that operate much faster.
This work presents Turbo-DDCM, fast and practical zero-shot diffusion-based compression method. It achieves a round-trip mmmpression-decompresss time of 1.8 seconds per image without custom hardware-specific optimizations, while maintaining competitive performance to state-of art approaches. Our method extends Denoising Diffusion Codebook Model (DDCM) (Ohayon et al., 2025), a recently proposed zero-shot diffusion iiffusion-based compression method that demonstrated state- of of-the-and art results. Specifically, DDCM compresses target image by carefully selecting noise tors during the generative diffusion process, a manner that minimizes the denoising error between the target image and the denoiser's output each step. Importantly, each noise vector is picked

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Original
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see
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Figure I: Turbo-DDCM: Our method provides reconstructions with equal or better fidelity com- pared to previous methods, while being much faster. At the same BPP and runtime, the priority- aware variant (bottom-right) better serves key regions of choice.
from reproducible Gaussian codebook, implying that the final generated image can be efficiently stored/transmitted by storing/transmiting the indices of the selected noise vectors. While such a simple compression mechanism works surprisingly well, it requires hundreds of denoising steps to achieve sufficient reconstruction quality, which results in an average round-trip compression- decompression time of 65 seconds. Our proposed Turbo-DDCM compression method accelerates this process by significantly reducing the required number of denoising steps to just few dozen. In particular, Turbo-DDCM combines a large number of noise vectors at each DDCM step by solv- ing sparse least-squares optimization problem in closed form, leveraging the vear-orthogonalityy of Gaussian codebook vectors high-dimensional spaces. While Ohayon et al. (2025) proposed seemingly similar approach that utilizes matching pursuit (MP) strategy (Mallat & Zhang, 1993), their method relies on a greedy iterative process based on convex combinations and an exhaustive search. As result, the scalability of this approach is limited due to runtime constraints. In contrast, our solution for combining codebook noise vectors is significantly faster and more computation- ally efficient. Specifically, it achieves orders of magnitude faster runtime compared to the method proposed by Ohayon et al. (2025), while producing equivalent results (see App. D for theoretical justifications and empirical evaluations). Indeed, show that the high scalability of our noise combination strategy enables a 92% reduction in the number of required diffusion steps. Beyond efficiency, we also propose new bit-coding protocol for effective encoding of the indices of the selected noise vectors. These contributions establish Turbo-DDCM as competitive with existing zero-shot methods in terms of reconstruction quality, while achieving dramatically lower runtime (see example in Fig. 1).
Finally, we introduce two flexible variants of Turbo-DDCM. The first supports priority-awart com- pression (Li et al., 2023; Xu et al., 2025), which allows allocating more bits to arbitrarily shaped user-specified regions in the target image to improve reconstruction quality in those regions (see Fig. 1 for an example). The second variant targets a user-specified PSNR rather than fixed bitrate. This is useful since, at a fixed bitrate, Turbo-DDCM and alternative zero-shot methods yield highly variable distortion across images. To the best of our knowledge, our work is the first to incorporate such capabilities into a zero-shot diffusion- based compression method.
To summarize, this paper introduces Turbo-DDCM novel and highly efficient diffusion- image compression algorithm, with the following features:
Zero-shot: Turbo-DDCM relies pre-trained latent diffusion generator, without any need for further training or fine-tuning As such, the backbone diffusion model can be replaced flexibly to allow improved future versions.
Performance: Turbo-DDCM has a competitive performance with the current state-of-ther of-the-art methods in terms of the attediisortioonperrepiii tradeoff.
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Speed: Turbo-DDCM is the fastest zero-shot method, achieving nearly an order of magnitude speedup over the fastest existing approach. Our method operates without any custom hardware- specific acceleration, maintaining nearly constant runtime across bitrates. This is achieved via a better noise sampling mechanism, which in turn allows using a shallower diffusion process.
Coupled with new bitstream protocol, performance is not compromised.
Perfect bitrate control: Our method provides a predictable and constant bitrate across images, which can be finely controlled via a single hyperparameter across wide range of bitrates. Priority-aware: We introduce a variant of Turbo-DDCM that enables enhanced reconstruction fidelity in user-selected regions of the image, with controllable prioritization levels.
Distortion control: We present a distortion-geared Turbo-DDee variant that targets a specific PSNR for each image (instead of target bitrate), addressing the variable distortion in zero-shot methods at fixed bitrate.
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RELATED WORK
Non-Zero-Shot Diffusion-based Image Compression. Recent advances in eeffusion-baseed com- pression have demonstrated impressive wwwdssoottoopeerepppie
performance by training models from scratch (Yang& & Mandt, 2023; Ghouse et al., 2023; Iwai et al., 2024) or fine-tuning existing diffusion models (Körber al., 2024; Careil et al., 2024). More recently, several one-step meth- ods (Park et al., 2025; Xue et al., 2025) have tried to bypass the computational cost of iterative denoising by directly learning a mapping from the latent code the clean signal in a single re- verse step. However, all these approaches share the drawback of requiring training or fine-tuning tailored for compression. In contrast, zero-shot methods preserve the diffusion model as a multi- purpose backbone, which can also serve for generation (Ho et al., 2020; Song et al., 2020), restora- tion (Kadkhodaie & Simoncelli, 2021; Kawar et al., 2022; Raphaeli et al., 2025; Man et al., 2025), editing (Manor & Michaeli, 2024; Cohen et al., 2024), etc.
Zero-shot Diffusion-based Image Compression. Rather than training models or fine-tuning ex- isting models, some recent methods use pretrained diffusion models in a zero-shot manner for image compression. IPIC (Xu et al., 2024) adopts a compression method based on posterior- sampling. PSC (Elata et al., 2024) and DifIC (Theis et al., 2022) harness ideas from compressed sensing (Donoho, 2006) and reverse channel coding (RCC) (Theis & Yosri, 2022). respectively. DDCM (Ohayon et al., 2025) changes the standard DDPM process (Ho et al.. 2020) by sampling from a quantized Gaussian space, offering a simpler approach. However, all existing methods suffer from prohibitive computational demands, often requiring hundreds or even thousands of diffusion steps to compress a single image, making them unsuitable for practical usage. Recently, the RCC protocol used by DiffCC was implemented an optimized CUDA kernel (Vonderfecht & Liu, 2025), which alleviates much of the computational demands. However, this method remains limited by custom hardware-specins sseeifef accelerations, large deviations from target bitrate across different input images, and substantial runtime variation across different compression bitrates. In contrast, our pro- posed method is the fastest by wide margin, without custom hardware-dependen optimizations, nearly constant runtime across all bitrates and a constant bitrate between different images given the same target bitrate. At the same time, DifIC, DDCM, and our Turbo-DDCM share fundamental concepts in their underlying design, but extend it in different directions, as detailed in App. H.
ROI (priority-aware) compression methods. Region-of-interest (ROI) compression (Li et al., 2023; Jin et al., 2025) prioritizes user-specified regions of an image by allocating to them a larger portion of the bits, resulting in higher fidelity in those regions the expense of others. This paradigm can be useful in medical imaging (Srivastava & Fujii, 2025), video conference calls and more. Recently, it was demonstrated in diffusion- based compression (Xu al., 2025). To the best of our knowledge, we are the first to apply ROI compression to a zero-shot diffusion method. We do so in general way, enabling per- per-pixel prioritization, which we refer to as priority- aware compression.
Concurrent with our work, Su & Kasai (2025) investigate one of our main ideas, multiple choice from reproducible codebook, primarily in the context of inverse problems.
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3 BACKGROUND
3.1 DENOISING DIFFUSION PROBABILISTIC MODELS (DDPM)
Diffusion models (Sohl-Dickstein et al., 2015; Ho al., 2020; Song et al., 2020) generate samples from data distribution Po by learning to reverse forward diffusion process. Specifically, for t (I...., T, the forward process gradually corrupts the data Xp ~ Po with noise via
X -a + v1 CrE,, e, e (0,,O,
where a......, or O are time-dependent constants controlling the signal-to-noise to-soise ratio. In DDPM (Ho et al., 2020), the reverse diffusion process generates samples from the data distribu- tion by gradually denoising random noise sample xT (0,, (0,1) I) via
x [4 + o.Ze
N(O, I),
where d; vI - de. and pe (Xx) is the conditional mean of x given xt. (xx) can be expressed in terms of the minimum mean-squared-error (MMSE) estimator Xajp of xo given Xt.
Vāi-
ax) Sofe=
ā(-1)
(x,))
where ā IT ag. The MMSE estimator Xoo, plays central role in the rest of this paper.
3.2 DENOISING DIFFUSION CODEBOOK MODELS (DDCM)
DDCM (Ohayon et al., 2025) modifies the reverse process of DDPM (eq. (2)) by replacing the ran- dom Gaussian noise sampling with selection of noises from reproducible codebooks C. Specif- ically, each codebook C₁ is an ordered set filled with K i.idd white Gaussian noise vectors, which we refer to atoms,
C. 21 (1) (2)
(K)
1= +
(4)
where, as in DDPM, no noise is added at l = 1. The DDCM generation step then becomes
x = (x,) + (k.),
(S)
where K, ltd Unif([1,.... K)). This modification yields discrete yet highly expressive generated distribution, as the number of possible distinct output samples grows exponentially with the number of diffusion steps.
The primary property of DDCM is its ability to act as a zero-shot image compression algorithm, achieved by creating all the codebooks once and keeping them constant for all subsequent applica- tions of the model (e.g., by using shared random sced). Specifically, a target image is compressed by selecting, at each diffusion step, the fixed codebook atom that best matches the target image. For- mally, to compress target image Xp. Ohayon al. (2025) compute the denoising residual between Xy and the MMSE estimation Xnjz at each timestep t, and select the codebook entry that maximizes the inner product with this residual:
K arg max (C.(k), - -Role) kE(I....K)
(6)
where is the selected codebook entry timestep This sampling process results in an ordered sequence of chosen indices (kz)T=2, whose binary representation serves as the compressed form of the image. Decompression then follows eq. (5), where instead of randomly sampling from the codebooks, the stored indices are re-selected deterministically. Consequently, the bits-per-pixel (BPP) of DDCM can easily be computed via
(T -) 1)- [K) number of pixels
BPPDDCM
While this strategy leads to good results, it is practically limited only to the regime of extremely low bitrates. Indeed, even when using T 1000 diffusion steps and codebooks with K 16,384 atoms,
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Compression
Decompression
H
Sa
Original Image
Closed foru
Cu Tersph
Combline
Enoade
Decced
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Recoasteusted Image
Seand
socsoved tadiece
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Figure 2: Turbo-DDCM overview: Building DDCM, replace its random noise sampling with an effective and efficient closed-form selection rule that can quickly combine an arbitrary number of noise vectors, enabling significantly fewer diffusion steps. 'he selected indices encoded using our new bit transmission protocol, which achieves substantially higher encoding efficiency than DDCM's protocol. The decoder reconstructs the image by running the generative diffusion process while re-selecting the codebook noise vectors that correspond to the decoded indices. This results zero-shot compression method that is both highly efficient and competitive performance.
the bitrate for 768 x 768 image is only about 0.024 BPP. Increasing 7 applies the denoiser more times, which is computationally expensive, while increasing K increases the bitrate logarithmically but makes searching for the correct noise much more demanding. To enable higher bitrates, the authors propose a refinement strategy for noise selection based on matching pursuit (MP) (Mallat & Zhang, 1993). Specifically, each step I, the chosen noise is constructed tion of M elements from C, selected greedily to maximize correlation with the residual X Xoji (as in eq. (6)). This combination involves A - quantized scalar coefficients, each drawn from a set of 2 values within [0, 1] (where C is the number of bits needed to communicate each coef- ficient). Transmitting the M selected noise indices requires [log, [K)]M bits per timestep, along with C(M - 1) bits for the quantized coefficients. When using this approach, the BPP becomes
convex combina-
(T number of pixels
C(M
BPPDDCM
(8)
This MP strategy widens the bitrate range DDCM. In practice, however, incurs extremely high runtime due to its iterative nature, as MP process can take more than 0.1 seconds and must be performed after each diffusion step, resulting greedy design, increasing M alone provides only limited gains in correlation with the residual: C must also be increased, while runtime grows exponentially with C, which further limits scalability. See Apps. and D for theoretical justifications and empirical demonstrations.
total cost multiplied by T. Moreover, due to its
4
METHOD
We now turn to introduce Turbo-DDCM. This includes a new and highly efficient approach for com- bining many codebook atoms at each of DDCM's denoising steps. Our approach yields additional advantages across multiple aspects of compression beyond the acceleration of DDCM's matching pursuit. We complement our new noise construction method with novel encoding protocol. An overview of approach is shown in Fig. 2 and pseudo-code is provided in App.
4.1 EFFICIENT BULTI-ATON SELECTION
We approximate the residual vector Xg X with a linear combination of exactly M atoms having nonzero quantized coefficients from fixed ordered set V. Formally, optimization problem for timestep is a constrained least squares of the form
s = arg min C,s, (Xo - 20/e)11 s.t. ||s/llo = M, Vi VU (0).
(9)
s, K
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where (St); denotes the i-th entry of the vector st. Using the solution s?, define
C
zi
(10)
(ts()
Finally, the Turbo-DDCM sampling process is defined as
X (e 0.z..
(11)
To solve the optimization problem in eq. (9), sight of our approach that Gaussian random codebooks are nearly orthogonal in high-dimensional spaces (see App. B for how this approximate orthogonality affects performance). Under this as- sumption, the thresholding algorithm (Elad, 2010) provides closed-form solution for sparse least squares (eq. (9) without the quantization constraint):
efficient closed-form solution. The key in-
(s = { (u.)./llz, (8) 11a. 10,
e TopM((uu)) (ux); otherwise
(2) xo
So1e) i= 1, 1...,, K, (12)
where z,") is the i-th column of C, and T(pl([ul) denotes the indices of the M largest entries of ju.. We extend this solution to incorporate the quantization constraint. We then adapt it to our specific setting of Gaussian i.i.d. codebooks and our characteristie configurations which share all == 1-1,,, resulting in the following algorithm:
(st): { (iin((u))) i TopM([uul) otherwise
(u:); = (z." Xo -oop); i= 1....., K. (13)
0,
See App. C for the derivation and App. for the rationale behind the chosen V.
Our approach fundamentally differs from DDCM's MP strategy in four key aspects, leading to enhanced capabilities and desirable properties.
Noise Construction Efficiency. Our closed-form algorithm is orders of magnitude faster than DDCM MP, which relies on an iterative search with exhaustive evaluations. Consequently, we con- struct the noise at each diffusion step much more efficiently.
Number of Required Diffusion Steps. Unlike DDCM, our method maintains a nearly constant runtime as M increases (App. D). Thus, we can scale M to hundreds, whereas DDCM MP is prac- tically limited to very small values. This enables a major reduction in diffusion steps, selecting many atoms per step leads to stronger residual estimations. Consequently, few diffusion steps with strong estimations can replace many steps with weak ones. Overall, the number of diffusion steps is reduced by more than 92% for comparable compression quality.
Possible Quantization Levels. While DDCM's MP is restricted to non-negative quantization lev- els due to its reliance on convex combinations, our approach allows both positive and negative coefficients. This effectively doubles the representational capacity, as allowing negative coefficients enables pointing in opposite directions, thereby increasing the number of directions in latent space available to approximate the residual and improving the solution the optimization problem.
Hyperparameters. Both DDCM and Turbo-DDCM rely on four hyperparameters that influence bitrate: T, K, M, and C. Controlling bitrate via T' increases expensive denoiser calls; varying K slows optimization in both methods; and varying C' alone yields only marginal gains. In our thresholding- based approach, increasing M enhances representational power with negligible run- time cost and allows fine-grained bitrate control. Consequently, Turbo-DDCM can adjust bitrate using M alone, ensuring runtime stability across bitrates and avoiding inefficient hyperparameter combinations. DDCM, however, cannot benefit from increasing M in isolation and must simulta- neously increase C. As is not computationally efficient in both, it must also increase K and T', resulting in significant runtime variation across bitrates. Moreover, DDCM is highly sensitive to inefficient hyperparameter combinations, which can further degrade performance. Detailed justifi- cations and demonstrations provided in Apps. C, D and E.
Due to the large reduction in T described above, we replace the synthesized noise z in the final steps with DDIM sampling to improve perceptual quality low bitrates. The number of DDIM

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steps, N, is determined heuristically and decreases with increasing bitrate. Specifically, for T- steps scheduler, the encoder transmits z for the first T N steps, which the decoder reconstructs, followed by N DDIM steps executed only at the decoder. See App. A for exact details.
4.2 EFFICIENT BIT PROTOCOL FOR LARGE-M COMBINATIONS
When large M values are employed, using the DDCM's bit protocol leads to poor compression due redundancies. Specifically, DDCM encodes atom selections with ( bits per diffusion step, preserving the order in which the atoms were selected, which is crucial for the noise constric- tion on the decoder. However, in our thresholding- based approach, atom ordering is semantically meaningless and only identity matters. Thus, naive encoding of M indices creates M! equivalent representations per step, yielding (M!))=1 identical compressed representations. For extremely modest parameters of M 5 and T = 30, this results in 12029 = 2200 equivalent representations, underscoring the need for a more efficient encoding protocol.
Each diffusion step requires communicating combination of M indices from codebook of size K (without repetition and order-invariant along with quantized coefficients (C bits each). The number of distinct choices is ()) (29)M, requiring
((x)
K (2 ((9))M)]
(())
K M
loga
+ MC
(14)
bits per step. This gives the worst-case lower bound on the bits needed to encode this information.
We propose an encoding protocol that achieves this bound. Our protocol transmits the lexico- graphical index of the selected M-atom combination from within the set {I.... (Mr) j of possi- ble indices, followed by the selected M quantized coefficients in canonical order. This approach eliminates the observed factorial redundancy while transmitting effectively the same information. Consequently, Turbo-DDCM's BPP is
}
T - - 1) [[08g2
(())
+ MC)
BPPTuub-DDDM
(15)
number of pixels
As shown in App. F, our protocol reduces BPP by ~ 40% for typical Turbo-DDCM configurations.
5 EXPERIMENTS
We evaluate our compression method on the Kodak24 (Franzen, 1999) and DIV2K (Agustsson & Timofte, 2017) datasets, center-cropping 512 512. We compare to existing zero-shot diffusion- based methods, including PSC (Elata et al., 2024), DDCM (Ohayon et al., 2025), and DiffC (Theis al., 2022), using the custom CUDA kernel implementation of DiffC (Vonderfecht Liu, 2025). Additionally, we compare to non-neural, fine-tuning- based and training-based approaches, including BPG (Bellard, 2018), PerCo (SD) (Körber al., 2024; Careil et al., 2024), ILLM (Muckley et al., 2023), two CRDR (Iwai al., 2024) configurations, HiFiC (Mentzer al., 2020), DiffEIC (Li et al., 2025) and StableCodec (Zhang et al., 2025). All zero-shot methods use the same pre-trained diffusion model, SD 2.1 Base. For Turbo-DDCM M from 45 to 300 to control the bitrate. Distortion is measured using PSNR and LPIPS (Zhang al., 2018), while perceptual quality is evaluated with FID (Birikowski al., 2018), computed on 64 x 64 patches following Mentzer et al. (2020). Runtime is measured based on process time for round-trip compression-eccoppeesse decompression on an NVIDIA A40 GPU.
use T = 30, K 16,384, C and vary
Compression Quality. As shown in Figs. 3 and 4, Turbo-DDCM achieves competitive results against both zero-shot and non-zero-shot methods. Among zero-shot approaches, Turbo-DDCM surpasses PSC both in terms of distortion and perceptual quality. Compared DDCM, Turbo- DDCM achieves equal or better distortion and perceptual quality. At low bitrates, DiffC yields better perceptual quality than Turbo-DDCM, with equal distortion. At high bitrates, DiffC and Turbo- DDCM present nearly the same distortion and perceptual quality. Compared to the other methods (non-neural, fine-tuning-basee and waining-based approaches), Turbo-DDCM surpasses all prior
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Figure 3: Qualitative results: The presented images are taken from the Kodak24 (512 x 512) dataset. Our method produces highly realistic reconstructions while achieving over 5x speedup compared to previous approaches, depending on the bitrate.
methods on the deeddiiottooopereepptte plane (Blau & Michaeli, 2019), except for StableCodec, still achieves
which specialized for each individual bitrate. Yet, low bitrates, approaches, such as PerCo (SD) and
better distortion compared to other perceptual-qualiy-orreee DifEEIC, despite being zero-shot method. However, for high bitrates, our method underperforms in distortion due to the encoder-decoder distortion bound imposed by SD 2.1. When using latent diffusion model such as SD, compression is applied in the latent representation space rather than in the image pixel space. Since the encoder-decoder already introduces distortion, the maximum attainable quality of any latent-based method bounded by this reconstruction error, forming natural upper limit (Körber et al., 2024; Elata al., 2024). Accordingly, Fig. 4 reports this bound. See App. A for additional evaluations.
Runtime Performance. As shown in Figs. 3 and 4, among zero-shot methods, Turbo-DDCM achieves state-of-the-art runtime by significant margin. outperforms DDCM by more than an order of magnitude, achieving over x4x speedup at high bitrates. Turbo-DDCM also outperforms DiffC, with 3x acceleration at low bitrates and nearly an order of magnitude at high bitrates. Importantly, this performance advantage is achieved even though DiffC employs custom CUDA kernel. As runtime might be aapllementation-deeenddde function-evalluations (NFEs), which correspond to denoiser activations in this case. Even though NFE is implementation independent, it is imperfect, since it ignores operations performed between denoiser activations, which might also be computationally demanding. Nevertheless, the trends and differences in NFEs closely follow those observed for runtime, as detailed in App. A, along with additional evaluations. Among other methods, Turbo- Rarbo-DDCMIII is faster than HiFiC, DiffEIC, CRDR, and PerCo (SD). However, it is slower than BPG (non- ILLM (non- tan---ffusio--baaeee basedd, and StableCodec (non-zero-shot).
we also compare the number of neural-
TURBO-DDCM VARIANTS
While traditional diffusion-based methods allocate bits uniformly across the image, some applica- tions (c.g. medical imaging) benefit from prioritizing important regions. This paradigm, commonly compression (Li et al., 2023; Srivastava Fujii, 2025), im-
referred to as ROI proves fidelity in specified areas at the expense of others by non-uniform bit allocation. We introduce a variant TTrbboDDCM that supports ROI compression through per-pixel prioritization, which we term priority- -ware compression.
Our adaptation is based on a latent priority mask w E RC, where each entry specifies the relative weight of the corresponding latent coordinate, obtained by down-sampling pixel-space prioritiza-
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Bits per pixel
Figure 4: Quantitative evaluation of wwweddiioortoo-peereeeeee and runtime performance: We compare Turbo-DDCM against zero-shot Liffusion-baser compression methods (top two rows) and other methods (bottom two rows), by evaluating distortion (PSNR or LPIPS), perceptual quality (FID), and runtime (round-trip compression cumpressioo-decomprssiioo time, in seconds). PSC's runtime is omitted due to its extreme complexity (>300 seconds/image). Overall, Turbo-DDCM achieves perior or competitive rate-distortion-pert petiiiptionccepionnnnonoo performance compared to previous zero-shot meth- ods, but with significantly faster runtime (nearly an order of magnitude faster more high bitrates). The dashed vertical line in each subplot corresponds to the encoder-decoder distortion bound imposed SD 2.1, attained by passing the clean images through this encoder-decoder with- out any compression. Since all the compared zero-shot methods and PerCo (SD) rely on SD 2.1, they all suffer from this distortion bound.
tion map. We then extend the optimization problem in eq. (9) to
:: = arg min ||Crs; - w @ (xo x s.t. ||s: = M, Vi (s:), VU (0).
(16)
S.ERK
Here, the residual vector (xo X is weighted by w, scaling each emror according to its corre- sponding pixel priority. The M codebook atoms and their quantized coefficients are then chosen accordingly. Importantly,
is not transmitted the decoder, leaving both the encoding protocol and the BPP unchanged. Additionally, this modification has a negligible impact on runtime. As demonstrated in App. A, this adaptation generalizes naturally both DDCM and DiffC methods.
We evaluate our variant on the Kodak24 (512x 5112) dataset and compare to the other zero-shot meth- ods, including the baseline Turbo-DDCM Figure 5 shows that, unlike regular zero-shot methods,

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Published as a conference paper at ICLR 2026
Original
DDCM
DifIC
Turbo DDCM
Turbo-DDCM (PA)
0.0057 BPP
0.0036 BPP
0.0034 BPT
0.0034 BPP
Priclie Lovel
riid
0.0057 BPP
0.0068 BPP
0.0056 BPP
0.0056 BPP
Welcame To LISBON
8:0 E OZS
PouEa NSBON up Tameigh
POLIE MO
Welcome LISBON
ANOME Labu
18BBON SANEEUN GRSTTE
LUC INCE PDP
MAKE MMG 3641
Figure 5: Qualitative results of the priority- (PA) variant: Regular methods fail to recon- struct key regions, whereas our PA variant reconstructs them faithfully according to the prioritization mask. In the second row, the first two lines of the sign that are highly prioritized, are fully recon- structed, while the third line, medium prioritized, only partially reconstructed. These results are better viewed when zoomed in.
our priority-aware variant successfully reconstructs regions that would otherwise be poorly recov- ered, adapting fidelity according the prioritization mask while keeping the same BPP. Additional details and results can be found in App. A.
Our second variant of Turbo-DDCM addresses the significant distortion variation across images fixed target bitrates see Fig. $19. We present a simple and efficient method to address this problem, substantially reducing this variation while targeting given distortion level. See App. G for more details on this variant of the algorithm.
7 CONCLUSION AND DISCUSSION
This paper introduces Turbo-DDCM, an efficient and flexible zero-shot diffusion-based compression method. It achieves state-of satte-of-the-ane -ht--ar runtime, reducing round-trip compresion-deccompession time by nearly an order of magnitude compared to the fastest prior zero-shot method, while maintaining competitive compression quality compared to state-of-the-art techniques. also offers favorable properties, such as constant bitrate across images for a given target bitrate. Moreover, we extend Turbo-DDCM with two variants: the first supports priority-aware compression for spatially-varying fidelity, and the second is eestortion-tareeter mode that fixes PSNR instead of bitrate.
While our method significantly advances zero-shot compression speed, training-based methods can achieve similar reconstruction quality in single forward pass. A one-step zero-shot method could provide significant additional speedup while preserving zero-shot flexibility. Moreover, some trade-off compared to
non-zero-shot methods demonstrate superior disttotiinn-peeeeppiii method, suggesting potential room for improvement. Finally, establishing a comprehensive theory for DDCM-based compression remains open problem that could guide future improvements.
ACKNOWLEDGMENTS
This research partially supported by the Israel Science Foundation (ISF) under Grants 951/24, 409/24, and 2318/22, as well as by the Council for Higher Education - Planning and Budgeting Committee. G.O. gratefully acknowledges the Viterbi Fellowship from the Faculty of Electrical and Computer Engineering at the Technion.
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APPENDIX
A EXPERIMENTAL CONFIGURATIONS AND ADDITIONAL EVALUATIONS
All distortion and perceptual quality metries computed using Torch Metrics, which is built on Torch Fidelity (Obukhov et al., 2020).
A.1
CONFIGURATIONS
The following outlines the experimental configurations used for the evaluations in Section 5.
Zero-Shot Methods.
For all methods we use Stable Diffusion 2.1 Base!, based on the official hablittyilssabb-ddittiio-------- 1--base checkpoint from Hugging Face, using float16 precision. The remaining hyperparameters are determined as follows:
For Turbo-DDCM use 7 = 30, K 16,384, == and M values in the range [45, 300]. determine N, we initially assume
and calculate a preliminary value BPp, using eq. (15). Then we partition the interval [0.01, 0.15] into 70 logarithmically spaced bins and set
N max bin(H 1,T 2).0),
(S1)
where bin(BPPo) denotes the index of the logarithmic bin containing BPP. The scheduler we use is based the optimized scheduler from Vonderfecht & Liu (2025), adapted our setting by selecting evenly spaced indices from the timestep list for our T. See App. E for the rationale behind the chosen hyperparameters.
For PSC we use the hyperparameters that the author described (Elata et al., 2024), setting the number of measurements - for
O, D.... 8.
For DDCM we use E {500, 1000), K E {64, C E (2,3) which aligns with the spirit of the hyperparameter configurations described by the authors (Ohayon et al., 2025).
M E (1,2. 6} and
For DiffC authors (Vonderfecht & Liu, 2025).
the schedulers, DEL values and reconstruction timesteps suggested by the
Non-Zero-Shot Methods.
The hyperparameters for the non-zero-shot methods are as follows:
For CRDR-R and CRDR-D we use the quality factors of (0, 1, 2, 4), where CRDR-D uses
8 = 0 and CRDR-R uses 3 = 3.84, as recommended by the authors (Iwai et al., 2024).
For ILLM use the MS-ILLM pre-trained models available in the Official GitHub repository. We use ms i www.quuaiitt.aaa.mmmmm for X 2, 3 and ms www.limmmmallt.y.......
for Y = 1,2.
For BPG use quality factors g 50, 48, 46, 42, 40, 29, 36, 32)
For PerCo (SD) we use the three publicly available Stabe Diffusson 2.1 fine-tuned checkpoints from the Official GitHub repository, with the default hyperparameters.
For HiFiC we test the low quality regime, using the checkpoint available in the official GitHub repository.
For StableCodec we use the checkpoints stablecoded ftx for 2, 4, 8, 16, 32.
For DiffEIC we test the 1.2.X pre-trained weights for X = 1, 2, 8, 16.
Turbo-DDCM Prierity-Aware Variant Configuration. To achieve extremely low bitrates,
modify the Turbo-DDCM configuration above by setting T = 20. In addition, we use a linear scheduler.
Recent models such as FLUX are trained using optimal transport based flow matching (FM) (Lipman al., 2023). To apply Turbo-DDCM, we translate between DDPM and OT flow model parameterizations, following approach similar to Vonderfecht & Liu (2025). This extension available in code.
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Original
PSC
DDCM
DifCC
Turbo-DDCM
0.066 BPP
300 sec
0.149 BPP
98 p91d
0.134 BPP
19 Sel0
0.148 BPP
2.6 sec
0.097
16
BPP
0.085 BPP
300 sec
0.091 BPP
96 sec
0.091 BPP
16 sec
0.085 BPP
2.2 sec
0.095 BPP
300 spc
0.076 HPP
72 500
0.058 BPP 12 500
0.058 BPP
2.0 sec
0.049 BPP
0.030 HPT
72
0.027 BPP 7 scc
0.027 BPP
1.6
0.018
0.0134 BPP
300 sec
0.0133 BPP
36 Sec
0.0131 BPP
99C
0.0123 BPP 1.4 sec
The images taken from the Kodak24 dataset, center-cropped to 512 x 512 pixels. Our compression method generates highly realistic reconstructions, matching surpassing prior approaches in fidelity to the original images, while consistently offering significant runtime improvements.
Figure S1: Qualitative results compared to zero-shot methods:
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Original
ILLM
BPG
PerCo (SD)
Turbo-DD DDCM
0.111 BPP
0.131 BPP
0.125 BPP
0.117 BPP
0.043 BPP
0.120
0.125
0.117 BPP
0.074 BPP
0.125 BPP
0.125 BPP
0.117 BPP
0.1 BPP
0.142 BPP
0.125 EPP
0.117 BPP
BPP
0.035 BPP
0.031 BPP
0.012 BPP
0.012 HSP
0.000
0.031
HPP
BPP
0.060 SPP
0.031 BPP
0.012 BPP
Figure S2: Qualitative results compared to non-zero-shot methods: The images taken from the Kodak24 and DIV2K datasets, center-cropped to 512 x 512 pixels. Our compression method produces highly realistic reconstructions and preserves better fidelity to the original images com- pared to previous methods.
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A.2 ADDITIONAL EFFICIENCY EVALUATION
Figure S3 decomposes the round-trip time results from Fig. 4 into compression and decompression components. The results demonstrate that method's runtime advantage arises from balanced improvements in both processes, yielding faster performance for both the encoder and the decoder.
As discussed in Section runtime measurements can be biased by implementation details. We therefore compare the number of neural function evaluations (NFEs) (Fig. S4), corresponding to denoiser activations, across the zero-shot methods. While NFEs are iuplementaaioonindeeann they do not capture costs from other components, such as the RCC in DiffC, the MP process in DDCM and the thresholding based process in Turbo-DDCM. The alignment between NFEs and runtime trends suggest that our efficiency is not attributable to implementation details.
A.3 ADDITIONAL RECONSTRUCTION QUALITY EVALUATION
Figures S1 and S2 provide additional qualitative comparisons on the Kodak24 (512 x 512) and DIV2K (512 512) datasets, against both zero-shot and non-zero-shot methods. Figure S5 provides additional quantitative results. Tables 1, 2, and report the results presented in Fig. 4. Tables 5, and report BD-PSNR (Bjøntegaard, 2001).
A.4 ADDITIONAL EVALUATIONS FOR THE FRIORITY-AWARY VARIANT
Figure S6 illustrates how the priority-aware variant improves the fidelity of prioritized regions as prioritization level increases. Figures S7 and highlight advantage priority-aware com- pression in reconstructing complex image regions extremely low bitrates. Depending the prioritization level, our method successfully reconstructs these regions, while other methods fail to reconstruct them at all. In addition, priority-aware compression method can also be applied to DDCM and DiffC, owing to the shared foundations of these approaches (see App. H). Figure $9 illustrates this generalization.
A.S GPU MEMORY CONSIDERATIONS
At first glance, Turbo-DDCM may appear to be GPU-memory-bound algorithm. However, the only substantial memory overhead beyond the diffusion model itself comes from storing the code- books. Using float16 6 precision, Stable Diffusion 2.1-Base occupies approximately 2.5 GB of GPU memory. Turbo-DDCM requires only single codebook to be resident memory at any given time. Each codebook contains 16k atoms, each of dimensionality 16k (SD 2. 1.1-Base latent space dimensionality), stored in float16:
codebook memory 16k 16k 2 bytes 22 bytes 0.5 GB.
Thus, the total expected peak memory for Turbo-DDCM
2.5 GB (model) 0.5 GB (codebook) 3.0 GB.
This matches our empirical measurements, which show a peak memory usage of approximately 3.05 GB. In practice, Turbo-DDCM introduces only about a 20% memory overhead relative the diffusion model alonc.
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PSNR
LPIPS
FID
Roundtrip Time (sec)
method
bpp
DDCM
0.010
19.31
0.46
60.17
35.89
0.013
20.46
0.36
48.84
35.74
0,019
21.38
0.28
38.53
36.50
0.025
21.92
0.23
33.53
35.92
0.034
22.33
0.20
30.67
71.20
0.046
22.84
0.17
26.87
73.37
0.080
23.23
0.15
25.35
75.48
0.114
23.48
0.14
25.21
74.27
0.126
23.70
0.13
23.67
75.45
0.149
24.04
0.12
22.59
87.95
0.263
24.36
0.12
22.43
86.66
DifIC
0.007
18.66
0.41
40.49
3.57
0.012
20.19
0.32
36.67
4.52
0.019
21.26
0.25
32.98
5.58
0.029
22.42
0.20
29.87
7.18
0.050
23.73
0.15
26.69
10.19
0.053
23.92
0.14
25.96
10.80
0.057
24.08
0.13
26.39
11.23
0.061
24.27
0.13
25.97
11.91
0.066
24.44
0.12
25.46
12.43
0.073
24.67
0.12
24.56
13.15
0,081
24.89
0.11
24.00
14.38
0.092
25.11
0.10
23.45
15.63
0.109
25.42
0.09
22.69
17.09
0.141
25.81
0.08
22.06
19.38
PSC
0.025
18.52
0.47
47.34
0.048
20.08
0.37
40.70
0.095
21.68
0.27
35.32
Turbo-DDCM
0,007
19.01
0.42
45.92
1.26
0.012
20.16
0.33
38.92
1.36
0.018
21.04
0.28
36.62
1.43
0.031
22.33
0.21
30.83
1.63
0.044
23.14
0.17
27.41
1.78
0.058
23.82
0.14
25.75
1.97
0.071
24.21
0.13
24.19
2.01
0.085
24.58
0.12
23.15
2.19
0.117
25.19
0.10
22.44
2.34
0.148
25.55
0.09
22.07
2.53
Table 1: Quantitative comparison on Kodak24512 dataset between zero-shot methods.
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PSNR
LPIPS
FID
Roundtrip Time (sec)
method
bpp
DDCM
0.010
17.09
0.45
64.94
36.62
0.013
18.01
0.37
52.43
35.96
0.019
19.02
0.30
42.25
36.23
0.025
19.64
0.25
36.97
36.86
0.034
20.11
0.22
34.19
70.66
0.046
20.71
0.19
31.61
73.59
0.080
21.13
0.17
30.06
75.01
0.114
21.41
0.16
29.54
77.24
0.126
21.68
0.15
29.02
78.45
0.149
22.10
0.13
28.26
87.17
0,263
22.47
0.12
27.67
85.15
DifiC
0.008
16.68
0.39
43.84
3.52
0.013
17.95
0.31
38.56
4.52
0.020
19.07
0.26
35.86
5.57
0.031
20.25
0.21
33.20
7.15
0.053
21.76
0.15
29.58
10.21
0.056
21.92
0.15
29.52
10.69
0.060
22.12
0.14
28.73
11.22
0.065
22.32
0.14
28.70
11.79
0.070
22.54
0.13
28.24
12.39
0.077
22.78
0.12
27.51
13.22
0,086
23.05
0.12
27.23
14.24
0.097
23.35
0.11
26.62
15.62
0.115
23.71
0.10
25.92
17.12
0.148
24.17
0.09
24.95
19.36
PSC
0.008
13.66
0.59
56.50
0.013
14.91
0.53
51.51
0.025
15.87
0.47
48.36
0.048
17.47
0.39
44.27
0.095
19.22
0.28
38.41
Hurbo-DDCMN
0.007
16.70
0.42
50.95
1.26
0.012
17.83
0.34
44.41
1.34
0.018
18.69
0.30
40.23
1.45
0.031
20.10
0.23
36.22
1.65
0.044
20.96
0.19
33.04
1.82
0.065
21.96
0.15
29.54
2.03
0.085
22.63
0.13
28.06
2.21
0.117
23.33
0.11
26.68
2.42
0.148
23.81
0.10
25.97
2.62
0.194
24.11
0.09
24.98
2.66
0.272
24.35
0.08
24.43
2.81
Table Quantitative comparison on DIV2Ks12 dataset between zero-shot methods.
19

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Published as a conference paper at ICLR 2026
PSNR
LPIPS
FID
Roundtrip Time (sec)
method
bpp
BPG
0.037
24.21
0.54
148.31
0.16
0.044
24.64
0.51
141.58
0.17
0.062
25.54
0.46
128.09
0.18
0.088
26.49
0.41
114.26
0.19
0.121
27.38
0.36
104.29
0.21
0.167
28.35
0.31
92.42
0.22
0.227
29.36
0.26
82.18
0.24
CRDR-D
0.114
27.99
0.26
94.50
3.88
0.210
30.07
0.17
76.04
3.89
CRDR-R
0.114
27.31
0.09
35.69
3.89
0.210
29.37
0.06
28.40
3.89
DIREIC
0.023
18.83
0.34
41.68
5.25
0.043
20.27
0.25
35.61
5.25
0.067
22.01
0.18
30.52
5.26
0.098
23.63
0.13
26.54
5.26
0.130
23.40
0.11
24.11
5.27
HiFIC
0.191
27.38
0.07
31.71
19.99
ILLM
0.009
20.27
0.50
128.40
0.32
0.014
21.43
0.40
93.67
0.32
0.100
25.68
0.11
36.08
0.32
0.182
27.30
0.07
28.56
0.32
PerCo (SD)
0.031
19.02
0.31
37.02
2.68
0.125
22.32
0.14
26.42
2.76
StableCodec
0.008
19.94
0.32
43.36
0.37
0.013
20.98
0.25
37.91
0.37
0.020
21.71
0.21
34.93
0.37
0.029
22.34
0.18
32.91
0.37
0.038
22.69
0.17
31.94
0.37
Turbo-DDCM
0.007
19.01
0.42
45.92
1.26
0.012
20.16
0.33
38.92
1.36
0.018
21.04
0.28
36.62
1.43
0.031
22.33
0.21
30.83
1.63
0.044
23.14
0.17
27.41
1.78
0.058
23.82
0.14
25.75
1.97
0.071
24.21
0.13
24.19
2.01
0.085
24.58
0.12
23.15
2.19
0.117
25.19
0.10
22.44
2.34
0.148
25.55
0.09
22.07
2.53
Table 3: Quantitative comparison Kodak24512 dataset between non-zero-shot methods.
20

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Published as a conference paper at ICLR 2026
PSNR
LPIPS
FID
Roundtrip Time (sec)
method
bpp
BPG
0.058
22.79
0.49
152.62
0.19
0.068
23.22
0.46
146.22
0.19
0.096
24.12
0.41
134.03
0.20
0.134
25.09
0.35
122.90
0.22
0.181
26.03
0.29
110.13
0.23
0.245
27.01
0.24
98.93
0.25
CRDR-D
0.153
26.62
0.20
89.78
3,86
0.274
28.76
0.12
69.48
3.85
CRDR-R
0.153
26.11
0.08
39.30
3.84
0.274
28.27
0.05
31.43
3.85
DIfIEIC
0.023
16.75
0.33
42.77
5.21
0.043
18.43
0.24
38.23
5,21
0.067
20.26
0.18
33.03
5.23
0.098
21.94
0.13
28.88
5.21
0.130
21.84
0.11
27.68
5.19
HiFiC
0.226
26.14
0.07
39.83
20.26
ILLM
0.009
18.56
0.49
119.83
0.30
0.014
19.74
0.38
96.94
0.30
0.100
24.58
0.11
42.59
0.30
0.182
26.21
0.07
34.10
0.30
PerCo (SD)
0.031
16.52
0.33
40.95
2.69
0.125
20.48
0.16
29.52
2.71
StableCodec
0.008
17.95
0.32
45.98
0.35
0.013
18.97
0.26
39.85
0.35
0.020
19.70
0.22
36.72
0.35
0.029
20.33
0.20
35.05
0.35
0.038
20.72
0.18
33.95
0.35
Turbo-DDCM
0.007
16.70
0.42
50.95
1.26
0.012
17.83
0.34
44.41
1.34
0.018
18.69
0.30
40.23
1.45
0,031
20.10
0.23
36.22
1.65
0.044
20.96
0.19
33.04
1.82
0.065
21.96
0.15
29.54
2.03
0.085
22.63
0.13
28.06
2.21
0.117
23.33
0.11
26.68
2.42
0.148
23.81
0.10
25.97
2.62
Table 4: Quantitative comparison DIV2Ks12 dataset between non-zero-shot methods.
21

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A
DDCM
DiffC
PSC
Turbo-DDCM
B
DDCM
0,00
-0.98
2.69
-0.76
DitIC
0.98
0.00
3,61
0.07
PSC
-2.69
-3.61
0.00
-3.35
Turbo-DDCM
0.76
-0.07
3.35
CRDR- D
CRDR- R
PerCo (SD)
Stable- Codec
Turbo-
A
BPG
DiAFIC
HiFiC
ILL.M
DDCM
B
BPG
0.00
-0.99
-0.22
3.75
1.67
1.02
4.95
1.58
1.76
CRDR-D
0.99
0.00
0.76
4.66
2.70
2.12
5.93
3.51
3.06
CRDR-R
0.22
-0.76
1.96
1.43
5.25
3.03
2.37
DIMIEIC
-3.75
-466
-3,98
0.00
-4.64
-3.15
0.91
-3.30
-2.36
HiFIC
-1.67
-2.70
-1.96
4.64
0.00
-0.03
4.54
8,66
1.56
ILLM
-1.02
-2.12
-1.43
3.15
0.03
0.00
4.05
0.52
0.86
PerCo (SD)
-4,95
-5.93
-5.25
-0,91
-4.54
-4.05
0.00
-3.56
-3.16
StableCodec
-3.51
-3.03
3.30
-8.66
-0.52
3.56
0.00
0.46
Turho-DDCM
-1.76
-3.06
-2.37
2.36
-1.56
-0.86
3.16
-0.46
0.00
Table 5: BD-PSNR evaluation on Kodak24512 dataset
A
DDCM
DifCC
PSC
Turbo-DDCM
B
DDCM
0.00
-0.85
3.24
-0.84
DiffC
0.85
0.00
3.41
0.27
PSC
-3.24
-3,41
0.00
-3.53
Turbo-DDCM
0.84
3.53
0.00
CRDR- D
CRDR- R
PerCo (SD)
Stable- Codec
Turbo-
A
BPG
DiffEIC
HiFiC
ILLM
DDCM
B
BPG
0.00
-1.41
-0.88
2.60
NaN
-0.33
3.81
1.33
1.25
CRDR-D
1.41
0.00
0.52
4.62
NaN
0.96
5.79
3.46
2.72
CRDR-R
-0.52
0.00
NaN
0.46
5.28
2.97
2.22
DifEEI
-2.00
-4.22
-4.12
0.00
-13998
-3.67
0.85
-3.26
-2077
HiFiC
NaN
NaN
NaN
13.98
NaN
2.71
15.00
44.03
8.28
ILLM
0.33
-0.96
-0.46
3.67
-2.71
0.00
4.34
0.92
1.62
PerCo (SD)
-3.81
-5.79
-5.28
-0.85
-15.00
-4.34
0.00
-3.57
-2.76
StableCodec
-1.33
-3.46
-2.97
3.26
-44.03
-0.92
3.57
0.00
0.77
Turbo-DDMM
-1.25
-2.72
-2.22
2.07
-8.28
-1.62
2.76
-0.77
0.00
Table 6: BD-PSNR evaluation DIV2K 552 dataset
22

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DDCM
Dift
Turbo DDCM
Compression Time
Decompression Time
Round Trip Time (snc)
10a
Kodak24gp
10a
10
DIV2K
10
101
10a
10
10
10
10
Bits per pixel
Bita per pixel
Biss per pixel
CRDR R.
ILLM
StubleCudec
DUDIIC
CRDR D
BPG
PerCo (SD)
Turbo DDCM
Compression Time (sec)
Decompression Time (sec)
Round Trip Time (sec)
Kodak2d512
100
10
10a
DIV2K
10a
10a
10
10
10
10
10
10
Bits per pixel
Bits per
Bits per pixel
Figure S3: Compression & Decompression runtime comparison.
23

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Published as a conference paper at ICLR 2026
Round Trip NFEs
DDCM
DiffC
Turbo DDCM
10
102
10 2
10 10-1
Bits per pixel
Figure S4: Round-trip cunpresion-decompressii NFEs comparison: Our method maintains its advantage over others, with margins similar to those observed in runtime.
PSC
DDCM
DIHO
+ Turbo DDCM
SD 2.1 Encoder Decoder Bound
PSNR
LPIPS
FID
10a
Round Trip Time (sne)
CLIC2020gaz
0.5
16
24
0.3
10
21
18-
4
10a
10
10
10
10
10
10
10
10
Bita per pixel
per pixel
Bits per
Bits per pixel
CRDR It
ILLM
StableCodec
DifEII HIFIC
Turbo DDCM
CRDR
BPG
PerCo (SD)
SD Encoder
Decoder Bound
PSNR f
FID
Trip (sec)
CLIC2020ar
30
0.4
100
10
75
24
0.2
10"
0.1
18
10
10 Bits per pixeel
10
10
10
10 Bits per pixel
10
10
135t per pixel
Bits per pixe!
Figure S5: Additional Quantitative Results.
24

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Published as a conference paper at ICLR 2026
A
DDCM
DifIC
PSC
Turbo-DDMM
B
DDCM
0,00
-0.84
3.71
-0.84
DifIC
0.84
0.00
4.07
0.14
-3.71
-4.07
0.00
-3.88
Turbo-DDCM
0.84
-0.14
3.88
0.00
CRDR- D
CRDR- R
PerCo (SD)
Stable- Codec
Turbo-
A
BPG
DiffEIC
HiFIC
ILLM
DDCM
B
BPG
0.00
-1.53
-0.87
3.60
NaN
-0.08
5.08
1.27
1.40
CRDR-D
1.53
0.00
0.66
NaN
1.36
6.83
3.37
3.04
CRDR-R
0.87
-0.66
0.00
4.83
NaN
0.76
6.24
3.02
DiffEIC
-3.60
-5.42
-4.83
0.00
-11.59
-4.35
1.35
-4.14
-2.84
HiFiC
NaN
NaN
NaN
11.59
NaN
2.10
10.78
33.29
3.93
ILLM
0.08
-1.36
-0.76
4.35
-2.10
0.00
5.32
0.91
1.55
PerCo (SD)
-5.08
-6.83
-6.24
-1.35
-10.78
-5.32
0.00
-3.86
StableCodec
-1.27
-3.37
-3.02
4.14
-33.29
-0.91
4.68
0.00
0.76
Turbo-DDCM
-1.40
-3.04
-2.44
2.84
-3.93
-1.55
3.86
-0.76
0.00
Table BD-PSNR evaluation on CLIC2020G12
Original
LISBON
p
p= 0=1
p 0.2
p =
P 0.8
PURE No
CBR
Weicoge LISBON
IBBON
NSBDN
LISBON
LISBON
Figure S6: Priority-Aware results: stands for the prioritization level, such that the values in w (Section 6) are for the deprioritized pixels and + p for the prioritized ones. Reconstruction the prioritized regions shows better fidelity to the original image as the prioritization level increases.
25

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Published as a conference paper at ICLR 2026
PSC
DDCM
DINC
0.025 BPP
0.021 BPP
0.020 BPF
Original
0.020 BPP
0.020 BPP
0.020 BPP
Turbo-DDCM
Turbo-DDCM (PA)
Turbo-DDCH (PA)
Low Prioritization
High Prioritization
PSC
DDCM
DITI
0.025 BPP
0.019 BPP
0.019 BPP
Original
0.020 BPP
0.015 BPP
0.015 BPP
TDrMo-DDCM
Turbo-DDCM (PA) Low Prioritization
Turbo Turbo-DDCM (PA) High Prioritization
Figure S7: Priority-Aware results:
With our priority-aware (PA) variant, specific objects in the image can be reconstructed at extremely low BPPs, with fidelity depending on the prioritization level. These objects are reconstructed by other methods at the same BPP.
26

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Published as a conference paper at ICLR 2026
DOCCN
PSC
DifIC
0.025 B3P2
0.01O BIP
0.008 BPF
Onigitai
0.008 D BPP
0.008 BPP
0.008 BPP
Turbo DDDDDDC (PA)
Turbo-DDCM
ThrrboDDCMM
Low Apprrtiizatti
Turbo Turbo-DDCM ( High Prioritization
DDCM D
PSC
Dirt
0.013 BIPP
0011 BPP
0.012 BPP
Orfiaal
0,011 EPP
0L011 BPP
0LOTE BPP
Turbo Turbo-Drri  ) High Aoootiiaaaooo
Turbo-Dui DDCM (PA) Low Dirittizaiinn
T S8: Pitority-Ahhuue results:
With our priority-aware (PA) variant, specific objects in the image can be drronstructed at extremely low BPPs, with fidelity depending on the pesoriizzzaiii
speciin
evel. These objects are barely deteeneeeee if at all, by other methods the same Bpp.
27

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Published as a conference paper at ICLR 2026
Original
Mask
No gler
DDCM
DiffC
Turbo-DDCM
0.0076 BPP 37 sec
0.0075 BPP
80C
0:0075 BPP
1.3
Vanilla
0.0076 BPP
37 sec
0.0075 BPP
sec
0,0075 BPP
1.3
Priority-Aware Version
No gla
No gglerrr
No No-gler
Original
Mask
Welcoma To LISBON
DDCM
DifIC
Turbo-DDCM
0.0057 BPP
30
0.0058 BPP
3.4 sec
0.0056 BPP
sec
WOO
IW tnatrat N8BON Newiigh
POLIEE Mo
Vanilla
AN 20 eit
118BON
0.0057 BPP 30 sec
0.0058 BPP
3.4 sec
0.0056 BPP
1.4 sec.
Priority-Awant Version
Welceiee LISBON SREA SECVIZO
LISLON
LISBON
KEWT MIKE SK
Figure S9: Priority-Aware results in DDCM and DiffC: Our method for priority- can be extended to DDCM and DiffC. Turbo-DDCM preserves its superiority in runtime.
28

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Published as a conference paper at ICLR 2026
26
Unmodified
with Gram-Schmidt
PSNR +
22
20
0.01
0.1
Bits per pixel
Figure S10: Effect of the orthogonality assumption: The codebook size used is 16k x 16k. Ap- plying Gram-Schmidt orthogonalization to the codebook does not improve rate-distortion compared to the unmodified version, which does not apply Gram-Schmidt.
B CODEBOOKS NEAR- ORTHOOOOOGGNALTTY
As described Section 4, we assume that the codehook in each diffusion step C, is orthogonal to build on the efficient and closed- form thresholding algorithm. However, since the codebook consists of i.i.d. Gaussian noise vectors, it is not necessarily orthogonal. Thus, in this short appendix, we evaluate how much this approximation degrades the quality of the solution. We do by applying Gram-Schmidt (GS) orthogonalization to all the codebooks and comparing the results to the base- line, which does not use GS. Notably, if GS performed in the encoder, it should be done in the decoder as well. On the one hand, GS requires substantial computation, since we may use large codebooks with more than K = 16k atoms, this results codebooks larger than 16%: x 16k in the SD-2. 1-Base latent space. On the other hand, GS makes the orthogonality assumption valid and might yield better solutions that could enable better compression capabilities.
Figure S10 shows that for our chosen codebook size of K 16,384 atoms, the rate-distortion without GS is almost identical rate-distortion with GS.
29

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Published as a conference paper at ICLR 2026
C THRESHOLDING-BASED STRATEGY CORRECTNESS
As explained in Section 4, Turbo-DDCLn employs a fundamentally different approach to combin- ing codebook atoms compared to DDCM. Our method builds the thresholding algorithm (Elad, 2010), which solves sparse least squares, with modifications tailored to our problem, such as the quantization constraint. To present considerations clearly, derive the solution from seratch. We also compare our approach to DDCM MP.
C.I PROBLEM SETUP
Inputs. For diffusion timestep
Original image: Xo
Prediction the original image: Xoj=
Codebook of iid. Gaussian atoms: C2 E dx where d is the dimensionality and K is the codebook size
Sparsity parameter: M
Quantization ordered set: = [40: ... (20) (communication cost is loga | = bits).
We define the residual at timestep as
X0
Suje-
(S2)
Objective: Find a linear combination of codebook atoms that best approximates the residual, subject to sparsity constraint and quantization constraint. Formally, the optimization problem is
s arg min |Css:
rell2 s.t. ||s:|lo = M, vi (s:) E VU {0}.
(S3)
s, ERR
Assumption: C₁ is netroy-ort See App. B for the impact of this assumption.
C.2 APPROXIMATED CLOSED-FORM DERIVATION
Let proj, be the orthogonal projection of r, onto the column space of Ct. By the Pythagorean theorem,
|C,s rell3 [Css: proj, 112 + ||proj, rel13.
(S4)
Since ||proj, rellă is independent of st, the objective reduces to
arg min | proj, 1
(S5)
subject the same constraints.
Because proj, lies the column space of C₁ there exists Sprof such that proj, = CtSproj- yielding
arg min || Cs Spraj l12-
(S6)
8,
Under the near-orthogonalliy assumption
Spmj.
(S7)
12
where z is the i-th column of C, Since the atoms are high-dimensional i.i.d. Gaussian vectors, their norms are approximately equal. Hence, the optimization approximated by
K
arg min
Σ (SL,
(z(0) (r)))
(S8)
Using the craoooothognnality and the Pythagorean theorem the problem reduces to
K
K
arg min
(St - (z) rx)
zu arg min Σ (S1. - (2 rr))
(S9)
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Published as a conference paper at ICLR 2026
Sparsity only constraint. If we ignore quantization constraint and enforce only the sparsity straint, then for any support S c {l....,Kt } with |S| = M the optimal coefficients are
aj (2) re). i
$1,1
(S10)
0,
The corresponding error
E(S) = Σ of.
(S11)
iES
Thus, the best support is obtained by selecting the M indices with the largest values of a².
Adding the quantization constraint. Now coefficients must in the finite set V. For a fixed index i, the best quantized value is the nearest element of V to az- Thus, we define
q :=
arg min 4 - arl. PEV
(S12)
If we select index and quantize to q,, the error contribution of index becomes
Equant
(g] - -a,)²
(S13)
Compared to leaving index i out (which yields error of a²), the net reduction error by selecting and-quantizing i is
A at (g) az)
(S14)
As a result, the best support in that case is obtained by selecting the M indices with the largest values of (aî -0- a.
Turbo-DDCM Characteristic Quantization Levels. In Turbo-DDCM we use the quantization set V = [-1, corresponding C' (see App. for the rationale). Thus, for each atom, the nearest quantized value is of (a: yielding net error reduction
A a
21 r()) 1.
(S15)
Thus, the support can be chosen simply by selecting the M indices with the largest (x .r)) values with correspondence quantized coefficients of sign ((2 (z(()) r.)).
C.3 APPROXIMATION QUALITY AND HYPERPARAMETER: TURBO-DDCM VS. DDCM MP
Both DDCM MP and thresholding- based strategy aim to combine codebook atoms improve the approximation of the residual vector. Although their approaches fundamentally differ, their underlying goal is the same. This becomes evident when evaluating the final constructed noise z" from each method within their respective optimization problems for M = 1, assuming z" is the selected noise. In DDCM, the objective reduces to maximizing the inner product between the noise and the residual vector, while in Turbo-DDCM reduces to minimizing the L2 norm of their difference (eq. (6) and eq. (9)). Importantly, ||2"| ll is approximately constant across both methods, due to normalization to unit standard deviation and the approximate zero mean of z". Under this condition, the objectives are closely related:
arg min ||z
r112 = arg min (||2*
112
||r| 2(z",r)) r))
(S16)
arg max r).
(S17)
Moreover, since (x", r) = ||z |||||/1122 cos 0, with E [0, π| denoting the unsigned angle between
the vectors, we obtain
arg max(z" r) = arg max 1|z || cos
(S18)
arg min
||2||||] const 0).
(S19)
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method
DDCM
C
90
(dleg]
24
60
50
22
.85
PSNR
30
20
90
20
24
23
24
M
M
M
Figure S11: Effect of hyperparameters on Turbo-DDCM Thresholding and DDCM MP: Met- rics are shown for compression of the Kodak24 (512 512) dataset using DDCM and Turbo-DDCM with T = 100 and K = 1024, while varying M and C. Turbo-DDCM consistently approximates the residual least as well as DDCM MP and continues improve the approximation with increased M, whereas DDCM MP does not improve the approximation beyond certain point if C' is fixed, which results in constant distortion and perceptual performance. Notably, Turbo-DDCM does not scale with C; see App. E for details. The C' values used differ from our typical value of 1, since DDCM performs MP with 2 2.
The left plot in Fig. S11 measures 0 during image compression with both methods. It confirms our derivation and shows that Turbo-DDCM consistently provides a solution at least as good DDCM MP. Moreover, while Turbo-DDCM scales with M and continues to improve the approximation as M increases within the presented range, DDCM MP does not benefit from increasing M alone be- yond certain point; it also requires increasing C. This hyperparameter interdependency in DDCM MP can lead to suboptimal configurations and limits fine-grained control over the bitrate, since both hyperparameters must be adjusted simultaneously. In addition, negatively affects runtime efficiency, as discussed in App. D.
The middle and right plots in Fig. S11 further confirm that the ability to produce z" with small angle to the residual translates into improved compression performance, both in terms of distortion and perceptual quality. The lack of improvement in the DDCM MP angle is reflected in constant distortion and perceptual quality.
C.4 INJECTED NOISE DISTRIBUTION
The noise x that we inject into the denoiser computed using the method described above. this subsection, we provide characterization of this random variable.
First, z has zero mean, since
C
E
2
(S20)
st,((C,s*)
E[C₁s*]
(S21)
std std(Cis)))
E
Σ zi (s,);
(S22)
sts((Cisf)
(B))
0,
(S23)
(ts(( 1=0
where 2 is the i-th column of Ct.
Second, estimate the covariance matrix of z². Figure S12 shows several patches extracted from this matrix for M E [10, 150]. We observe that the entries within these patches are uncorrelated, and each entry exhibits unit standard deviation.
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10
1822:1922
18155:15259
10086: 16186
M MC150 7307
1491
Figure S12: Patches of the covariance matrix of zz: Each subplot shows the empirical covariance of a patch, with the bounds indicated in its subtitle. All entries have unit standard deviation, and different entries appear be uncorrelated.
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D THRESHOLDING-BASED STRATEGY EFFICIENCY
This appendix quantifies the computational efficiency of Turbo-DDCM's thresholding strategy rel- ative DDCM's matching pursuit (MP). As described in Sections and 4, both strategies combine multiple atoms from the codebook to obtain improved solutions to the optimization problems. We provide both theoretical complexity analysis and empirical results. Importantly, both procedures are performed after each diffusion step (except the last one). As result, in image compression, the total runtime of these algorithms corresponds to the runtime presented this appendix multiplied by the number of diffusion steps minus one.
D.1 THEORETICAL COMPLEXITY COMPARISON
Given a codebook, the MP strategy of DDCM employs a greedy iterative search over M iterations, starting by selecting the atom with the maximum inner product with the residual vector (2no foje)- This step requires exhaustive search over all K atoms, with computational cost of ((K where d the latent space dimensionality. In each of the subsequent M - iterations, the algorithm searches for additional atom and quantized coefficient that, together with the current combi- nation, form a convex combination most correlated with the residual. This search is performed via exhaustive search, and after selecting the atom and coefficient, the combination is normalized to unit standard deviation. The process incurs an additional cost of @(M - 1)2 Kd). Therefore, DDCM's MP complexity is
@(M2 Kd).
(S24)
In contrast, our approach solves approximate least squares problem under sparsity and quantiza- tion constraints (see App. C for the mathematical foundations). We begin by computing the inner products between all atoms and the residual vector, which requires computational cost of O d). Next, we efficiently select the top-M most correlated atoms, which can be implemented using a heap-based selection algorithm with cost of O(K log M). Finally, quantization performed using the previously computed inner products by finding the nearest quantized coefficient for each of the M selected atoms, with complexity of ( M)) Hence, the overall complexity of our method is
@(Kd + K log M + 2 M) & @(Kd),
(S25)
since M K and in our typical configurations M < and C 1.
Our algorithm eliminates the dependency on M and C' presented in DDCM MP, allowing large values of these parameters be used without significant additional computational cost. As explained in Section 4, the ability to increase M is critical in our approach for achieving substantial reduction in the number of diffusion steps, as well as for tuning the bitrate using a single hyperparameter.
D.2 EMPIRICAL RUNTIME COMPARISON
To quantify the difference between the algorithms and assess the impact of the constants hidden in the notation, we measure the runtime of both algorithms while varying one parameter at a time among K, M, and C' (with d fixed). Figure S13 confirms theory and supplies glimpse for the overall speedup, which passes two orders of magnitude.
Figure S14 shows the acceleration achieved across different combinations of K and M. In the figurations that characterize Turbo-DDCM, our thresholding approach achieves two to four orders of magnitude runtime speedup over DDCM approach.
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16-1
Vary K
M C-
Vary 512 C-
K 512, M
3.0
DDCM MP
runtine (s0d)
2.0
1.5
1.0
0.5
Tarbo DDCM Thresholding
5.1
rustate (60c)
5.0
2"
215
2
212
215
279
2
2
25
20
Figure S13: Impact of hyperparameters on the efficiency of DDCM MP vs. Turbo-DDCM thresholding: While DDCM MP scales linearly with K and M and exponentially with C, our method scales linearly with K and remains nearly constant in M and C, achieving over two orders of magnitude speedup.
-10
2
DDCM
22
100
23
22
Sp preediu
M
Turbo- DDCM
25
10
26
2
10
29
200
2/1
2/2
2
2
K
Figure S14: Relative speedup of Turbo-DDCM thresholding over DDCM MP: The heatmap shows the speedup using C' = 2 for both methods, DDCM MP does not support C = 1. The ange box shows DDCM's typical configurations, and the green box shows Turbo-DDCM's. Our method achieves up four orders of magnitude speedup in the configurations used by Turbo- DDCM, highlighting the difficulty of using DDCM MP in these regions.
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Turbo DDCM T-
Turbo DDCM T-
Turbo DDCM T
LPISS
Ronad Trip (sed)
Kordak211 222
21-
20-
10"3
10-1
10"4
10
10"2
20
1012
10"1
Bize piom
Bita pise
Bita
Bibe plan)
Figure S15: impact on Turbo-DDCM: There is a trade-off between rale-distorttion-perrepioo and runtime. T =3 30 gives minimum runtime without sacrificing performance.
E HYPERPARAMETERS
Turbo-DDCM, has five hyperparameters:
T: number of diffusion steps.
K: codebook size at each diffusion step.
M: number of selected atoms from the codebook each step (M S K).
C: number bits per quantization coefficient, yielding 2c quantization levels.
N: number of DDIM steps performed at the end without requiring bits.
In this appendix, we discuss the trade-offss between these parameters and shed light on our choice for the base configuration: T 30, 16,384, = 1, varying M to control bitrate and N ranging from T - 2 to 0 depending on the bitrate (see App. A).
We found that T Fig. $15. We set K- 16,384 because this value is large enough to span substantial subspace and, in Stable Diffusion 2.1 Base, the entire latent space. the same time, this K remains small enough to avoid overcompleteness,, ensuring reasonable approximation of orthogonality (sce App. B). With and fixed, the bitrate determined primarily by M and C.
provides the best trade-off off between performance and runtime, as presented in
The hyperparameters M and C' directly affect ability to obtain high-quality solution to the optimization problem in eq. (9). To understand their marginal impact, we analyze the sources of approximation error in reconstructing the target residual (Xo- & The approximation error
I|z" (xo - x
(S26)
can be decomposed into several components. First, setting constraints aside momentarily, the code- book span may not cover the entire space. Consequently, the best achievable solution is the projec- tion onto the codebook span. If the codebook spans the whole space, this error becomes zero under the assumption that the codebook atoms are linearly independent. Second, require sparse solu- tion, so we cannot use the full projection but must find sparse approximation, which increases the error. Finally, we cannot this sparse projection directly, but must quantize it, further increasing the approximation error.
Figure S16 illustrates our solutions to the objective with and without the quantization constraint, comparing the sparse projection to the quantized sparse projection with C = 1. Notably, C = 1, corresponding to quantization coefficients of 1,, does not introduce traditional quantization levels. Instead, it allows selection of either the codebook noise vector or its opposite, effectively doubling the codebook size. Using C This behavior can be explained by the fact that the real coefficients are similar in magnitude, making quantization exact values unnecessary. As result, we set C to our base configuration.
achieve solutions very close those of the sparse projection.
Finally, we use DDIM steps at low bitrates to improve perceptual quality, but at high bitrates where perceptual quality is already good enough, additional DDIM steps may damage distortion. As result, N decreases with bitrate. See App. A for exact details on N.
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Z(z' r) [deg]
L
quantised sparse proj. r)
L(z sparse proj.
r)
[deg]
sparse proj.
86
quantized sparse proj.
0.08
81
82
80
0.04
78
70
0.02
74
72
125
M
Figure S16: Quantization impact on objective approximation: The figure illustrates the dif- ference in approximating our per-diffusion-stey objective defined in eq. (9) with and without the quantization constraint. Since we normalize our solutions (eq. (10)), the angle between z" and the residual is proportional to the norm of their difference. The quantized projection is computed with = and we observe that yields nearly the same solution as the sparse projection, which corresponds to the solution obtained without the quantization constraint.
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F BITSTREAM PROTOCOL
As described in Sec. 4, we propose an alternative protocol for bitstream transmission, distinct from that used in DDCM. In this appendix. primarily show that our protocol achieves relative bit savings exceeding 40% and affects our distortion-pereepeeee for both protocols are given in eq. (8) and eq. (15), with the differences arising from how the selected M atom indices are encoded.
performance. The BPP formulas
The analyses below performed for single diffusion step. Since bits are encoded identically for each step in both protocols, the relative differences similarly apply to the total bit count.
Relative Bit Saving. Let Bola and Bnew denote the number of bits required per diffusion step for the original DDCM protocol and our proposed protocol, respectively. Thus,
)
Bold = M [log2 K] + MC
and Basw =
log2
+ MC.
(S27)
M
The relative saving ratio therefore
Bold Brew
(S28)
Bold
Using the Stirling approximation
K M
K M
log2
~ M log2
O(M).
(S29)
Assuming C is small (see App. E), we express the saving ratio as
M logg K
M logz
M log, M
log, M
(S30)
M log, K
M log, K
log, K
Thus, the relative savings depend logarithmically on the ratio of M to K, becoming more significant as M increases relative to K. For example, with K 16,384 and M 100, which yiclds a BPP of 0.01 in the new protocol for T' 30, N = 0, = 1, and an image resolution of 512 x 512, the relative reduction is approximately
log2 100
= 47%.
(S31)
log, 16384
Empirical Evaluation We evaluate the relative bit savings by focusing on the transmission of the selected indices, which constitutes the dominant portion of the rate when C is small. As shown in Fig. S17, the empirical results align with the theoretical analysis, demonstrating a substantial reduction in rate (>40%). Moreover, Fig. S18 shows that without the new bit protocol, Turbo- DDCM underperforms in deteditttioo-peecpppioo perception metrics compared to DDCM, whereas with the protocol it outperforms DDCM.
Lexicographical Combination Encoding and Decoding. Each combination c drawn from (O...., K 1} can uniquely represented by its lexicographical rank:
[er, CM.
M
K -
1)
rank(c) = Σ
with co = -1
M
+=c-1++
This provides mapping between combinations and integers in [0, (K))
Decoding is performed by iteratively subtracting binomial coefficients:
K x -111 M - - rank, rank + rank (K= ==1 t- x +1
K
while
M (M-1-1)
which recovers each element c; in order. This yields an efficient and reversible mapping between combinations and their lexicographical indices.
Implementation Details. The lexicographic index of each combination is computed efficiently by precomputing binomial coefficients and summing the relevant terms during runtime.
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200
70
175
60
150
125
% Bits Saved
100
30
75
20
50
25
0
4
6
8
10
12
14
16
K (x 10²)
Figure S17: Relative bit saving: Percentage of bits saved when transmitting the selected atom indices using our protocol compared to the original DDCM protocol. To illustrate a continuous trend, the plot omits the ceiling operator in the bitrate expressions, which does not affect the asymptotic behavior. For the Turbo-DDCM configuration with = 16,384, bitrate savings can exceed 40%.
DDCM
Turbo DDCM with DDCM Bit. Protocol
Turbo - DDCM
PSNR 1
LPIPS 4
FID J
0.50
0.45
0.40
0.30
0.25
0.20
0.10
10-2
10-2
Bits per Pixel
Bits per Pixel
Bits per Pixel
Figure S18: Impact of bitstream protocol on rate-distotiionpeerepti:::: The plot evaluates DDCM, Turbo-DDCM with DDCM protocol, and Turbo-DDCM,, which employs proto- col, on the Kodak24 dataset. While Turbo-DDCM with the original protocol underperforms relative DDCM, the new protocol allows outperform DDCM.
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A PSN Raro (image) PSN (imagr)) PSNRare
PSC
z2 0.1 BPP
PSNR 90% Prediction Iaterval
DDCM
PSNRar (image) with PSC
= 0.01 BPP
225
10
Tarbo
DDCM
225
22
-6-
10
10
10
0
10
Bits Per Pixel
A PSNaaro(image) with Turbo-DDCM
Figure S19: Distortion variance between images at a fixed bitrate: All zero-shot methods exhibit high distortion variability across images when evaluated at the same bitrate. In addition, the same images tend to have similar deviations from the mean under both PSC and Turbo-DDCM, despite the fundamental differences between the two methods. Both plots use the DIV2K (512x512) dataset.
Quality
60
80
PSC
DDCM
DRRC
Turbo DDCM
251
(31
18
100 200
20
40
40 JPEG
00
size (KB)
(KD)
(KB)
(KB)
Figure $20: Correlation between JPEG file size and distortion in zero-shot compression: Linear regressions are shown between JPEG file size (at different quality levels) and PSNR obtained by each method, for BPPs in the range 0.04-0.07. All methods exhibit strong inverse correlation. Experiments are conducted on the DIV2K dataset, center-cropped to 512 x 512 images.
G TURBO-DDCM DISTORTION VARIANT
Current diffusion-based image compression algorithms generally take an image and a target bitrate, specified via hyperparameters, input. However, for fixed bitrate, the resulting distortion vary significantly across images. The left plot in Fig. S19 illustrates this for zero-shot diffusion- based methods, showing that PSNR values at a given bitrate can deviate from the mean by more than 2 dB. To improve the predictability of the outputs, it may therefore be preferable to target distortion rather than bitrate.
In this appendix, we propose an efficient method based on Turbo-Due DDCM, which can also be adapted other methods, that takes an image and target distortion as input and predicts the appropriate bitrate to achieve it. We observe that, for given image, its PSNR deviation from the dataset mean at a fixed bitrate is highly correlated across different methods. For example, the right plot in Fig. S19 demonstrates a strong correlation between PSC and Turbo-DDCM, despite their fundamentally dif- ferent designs. This observation motivates us to investigate correlations with simple, non-neural methods such JPEG, which offer ultra-fast compression.
In Fig. S20, we compress images using JPEG at various quality levels and compared the resulting file sizes to PSNR values obtained with zero-shot diffusion- based methods at specific bitrate. A strong correlation observed in all quality levels, which may reflect common compression challenges across all methods, such the difficulty of compressing images with many objects.
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Naive Approach
Naive Approach Our Approach
Our Approach
26
Target
PSNR RMSE
24
PSNR
22
20
18
21.0
21.5
22.0
22.5
23.0
23.5
24.0
24.5
25.0
21.0
21.5
22.0
22.5
23.0
23.5
24.0
24.5
25.0
Target PSNR
Target PSNR
Figure S21: Distortion control evaluation: Our method brings the actual distortion much closer to the target, reducing RMSE by over 40% for most target PSNRs. Results in both plots are reported on the test set.
Leveraging this observation, we propose method for PSNR control with Turbo-DDCM, First, given training set, compress all images using high-quality JPEG. Next, compress the same images with Turbo-DDCM at various bitrates and learn the correlation between JPEG file size and Turbo-DDCM PSNR for each bitrate via linear regression. To compress new image target PSNR, first compress it with JPEG and, based on its JPEG file size, predict its Turbo-DDCM PSNR at each bitrate using the learned linear regressions. Finally, we select the bitrate whose predicted PSNR closest to, but not below, the target. If no such bitrate exists, we choose the highest available bitrate.
To evaluate our approach, we use a large dataset CLIC2020 (Toderici et al., 2020), with images center-cropped to 512 x 512. We first filter out highly difficult images whose JPEG file size at quality 100 exceeds 300 KB, which constitute less than 4% of the dataset. These images are excluded because achieving high PSNR values on them is difficult, almost regardless of the used bitrate. The remaining dataset split into training and test sets, with 80% of the images used for training and 20% for testing. Both sets are then compressed with JPEG at quality 100. We train a linear regression model for each bitrate on the training set. Finally, for each image in the test set and target PSNR, we determine the bitrate via the above method and evaluate the actual PSNR. The naive approach compare against selects, for each image, the bitrate whose mean PSNR closest to the target PSNR. As shown in Fig. $21, our method achieves over 40% RMSE reduction the test across most target PSNR target values compared to the naive approach.
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H DDCM AND TURBO-DDCM VS. DIFFC
DDCM, Turbo-DDCM, and DiffC are all state-of-the-art zero-shot compression methods, achiev- ing comparable compression quality (Fig. 4). While DiffC is based on the reverse-channel-codnng (RCC) principle introduced by Theis & Yosri (2022), Turbo-DDCM builds on DDCM (Ohayon al., 2025), which is not motivated from a solid theoretical foundation. Interestingly, both DDCM- based methods and DiffC optimize the same core objective, yet extend it in fundamentally different ways. In this appendix, we first illustrate DiffC and its underlying motivation, and then highlight its similarities and differences from DDCM and Turbo-DDCN
H.1 SHARED CORE OPTIMIZATION OBJECTIVE
All three methods are based on solving optimization problems. The optimization problem of DDCM is presented in Section 3, that of Turbo-DDCM in Section 4, and now turn to the optimization process of DiffC which is based on RCC. In each diffusion step, DiffC aims to communicate the forward diffusion distribution q(x,11 Xo. Xc) the decoder, assuming both can sample from the reverse distribution po (x xz). This communication is performed only for a specific number of initial diffusion steps, which depends on the target bitrate, similar Turbo-DDCM. The broadcasted
information is then used to steer the diffusion process toward the target image via a strategically chosen diffusion noise vector, similar the approach in Turbo-DDCM.
Vonderfecht & Liu (2025) implement DifIC by applying RCC using the Poisson-Functional- Representation (PFR) approach presented by Theis & YoSri (2022). In their implementation. the PFR algorithm iteratively samples i.i.d. Gaussian noise vectors, selecting the noise z; that mini- mizes po (z:)//(z.) Exploiting the isotropy of both distributions, they simplify this deviation to
h4 := exp (- (HU
T zi
(S32)
Ope
where Hy and Hpu are the means of and pe, respectively, and dpo is the standard deviation of pe. The iterations for searching the best noise are prioritized, favoring early iterations through an increasing multiplicative weight w, = Σラ= ej for the i-th iteration, where ~ exp(1) are i..dd exponential random variables. The noise with the minimum weighted score, computed as the product of w, and h,, replaces the randomly sampled noise in the DDPM reverse process (eq. (2)).
Temporarily ignoring prioritization, DiffC optimization can be formulated as
(Hg
Mpp )T Zi
arg min exp
arg max( pbp)) )T 21.
(S33)
Ops
Placing the values of the means, it simplifies to
arg max((((1x) + o2x1) - (c Sojs + +2xx))) 2,) arg max Xy - xofo)
(S34)
2;
where e₁ and 02 are time-dependent constants. This objective is actually the original DDCM objec- tive for the case of M = 1, meaning no matching pursuit is performed (eq. (6)). Since ||xo S l| is constant regardless of z,, and || || la2 is approximately constant in high dimensions, eq. (S34) can be written
arg minliz; (xo - x
(S35)
which equivalent to Turbo- DDCM's objective for the case of M (eq. (9)). Thus, all three methods steer the diffusion process towards the target image based on the same core objective.
H.2 DIFFERENCES BETWEEN METHODS
Although these methods share the same core objective, they differ in several key aspects.
Sampled Noise Prioritization. As mentioned above, DiffC weights the sampled noises by their sampling iteration number, whereas DDCM and Turbo-DDMM treat all noises equally, without pri- oritization. While noise prioritization can improve compression average using variable-length
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Fimal
(Mean BPP)
300 (0.020)
0.8
200 (0.031)
(0.060)
0.6
30 (0.097)
Density
0.4
0.2
0.0
0.4
0.6
0.8
1.0
1.2
1.4
Actual BPP
Mean BPP
Figure S22: Actual BPP variance in DiffC across images: DiffC exhibits variable BPP, which can deviate from the mean more than 25% under the same BPP target. Limi is the final timestep up to which the encoder performs RCC and communicates the result to the decoder. This hyperparameter controls the target BPP.
encoding such as Zipf coding used by DifIC, DDCM and Turbo-DDCM provide a constant and pre- dictable bitrate across images. Figure $22 illustrates that DifIC's bitrate varies significantly between images, with deviations exceeding 25% from the mean, even when using the same target bitrate hyperparameters.
Increase of the Effective Search Space Turbo-DDCM and DiffC employ different strategies to effectively explore a large space of sampled noise vectors. DiffC achieves this by partitioning both 2, and f4g pbp into chunks and independently solving each optimization problem via exhaustive search. the search is performed over x iterations per chunk across e independent chunks, this effectively explores zf possible noise maps with only X eexauustive search iterations. In contrast, Turbo-DDCN performs effective multiple-atom selection. This explores (#r 2MxC combina- tions, where the codebook size, M the number of chosen atoms, and 2 denotes the number of possible non-zero quantization coefficients.
Search Space Size along Diffusion Steps. Supported by theoretical justifications, DiffC progres- sively increases both the number of chunks and the number of search iterations the reverse dif- fusion process advances. In contrast, DDCM and Turbo-DDCM maintain a fixed codebook size and fixed number selected atoms across all diffusion steps. Importantly, while DifIC requires custom CUDA kernel due to performing 2 65,536 evaluations per chunk across more than 400 chunks in later diffusion steps, Turbo-DDCC DDDM achieves multiple atom selection through an efficient closed-fom foorm solution without requiring custom hardware-specific acceleration. The progressively increasing search complexity in DiffC is major factor behind its growing runtime with bitrate, as shown in Figure 4. As the bitrate increases, the encoder performs more intensive optimization across a greater number diffusion steps.
H.3 TURBO-DDCM Vs. ACCELERATED DIFFC
Vonderfecht Liu (2025) mention the option to reduce DiffC runtime by decreasing the number of inference steps. To evaluate both methods under comparable runtimes, create a faster variant of DiffC using this approach. Since DiffC's runtime varies significantly across bitrates, we reduce the number of diffusion steps to approximately match Turbo-DDCMM runtime DiffC's minimum runtime. This results in just a few encoding steps for DiffC at low bitrates, increasing up to 10 steps at high bitrates. We refer this new configuration Fast-DiffC.
Figure S23 shows that bitrates, but its perceptual quality is notably inferior to both DiffC and Turbo-DDCM except the
maintains comparable distortion to the original DiffC across all
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DifIC
Fast. DiffC
+
Turbo DDCM
Round Time (sec)
0.5
100
24
LPIPS
0.4
10a
80
PSNR
22
0.3
60
0.2
40
10"
10
10"
Bits per Pixel
Bits Pixel
Bits per Pixel
Bits per Pixel
Figure S23: Fast-DiffC evaluation: Fast-DiffCC maintains the equivalent distortion to DiffC. How- it has much worse perception. The evaluation uses the Kodak24 (512 x 512) dataset.
highest bitrate. One possible explanation for this phenomenon is that RCC is computationally de- manding due to the large number of evaluations required, even with custom CUDA kernel. Thus, Fast-DiffC is forced to perform fewer diffusion steps than Turbo-DDCM, whose inter-step mecha- nism is more efficient, in order to achieve comparable runtime.
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I TURBO-DDCM PSEUDO-CODE
Algorithm S1 Turbo-DDCM- Compression
1: Input: Image to compress Xg. T, K, M, C.
2: Output: Compressed representation (xr))
3: Calculate N.
Simple thresholds for N described in App. A. Initialize the compressed representation XT generation. The random seed s shared with decoder
4: & ++0
5: X; rand normal)s
6: for t = T,, ......N + do
7:
Xojt f D(x,,t) t)
Denoiser activation codebook sampling with K i..d. gaussian latent vectors Solving eq. (9) optimization with eq. (13) closed-form
8:
C. t rand normal(s tt, K).
9:
ii - Opt(C,, No; & M.C)
z + Cis)/std(Cisp)
eq. (10)
11: calculate X
DDPM step
encoded, + pack(s;) t Eleleodco,,,,,
Lexicographic index & quantized coefficients encoding; App. > Concatenate step encoding to the compressed representation
13:
14: end for
15: return {(xo)
Algorithm S2 Turbo-DDCM Decompression
1: Input: Compressed representation E(x)), T, K, M, C.
2: Output: decompressed image Xo
3: Calculate N.
Simple thresholds for N described in App. A > Sampling Xy. Identical to the sampled Xy in the encoder
4: X; < (ormall))
5: for t .....,N N
do
6:
Xalt D(x,,
Denoiser activation D codebook sampling. Identical to the encoder codebook
7:
C. < raarranddooen normal(s + 1, K).
8:
St + (E)
9:
z, + C,s / Sts())
b eq. (10) DDPM step
10: calculate X;-1
11: end for
12: perform N + DDIM steps from Xx
13: return Xo
See App. A for typical hyperparameters.
45

---

Published as a conference paper at ICLR 2026
J LLM USAGE
Large language models (LLMs) were used for minor text polishing and readability improvements.
46


Reviews:
[{"review_id": "ybBF5b3qi7", "reviewer": "Reviewer_4dvB", "summary": "The paper introduces a zero-shot algorithm based on a pre-trained diffusion model to achieve image compression at extremely low bit rates. In essence, this method represents an efficient enhancement of the DDCM approach, transforming the original MP method into MULTI-ATOM and proposing a new bit protocol to further reduce the redundancy in the bitstream generated by the MULTI-ATOM method. The paper presents a plethora of experiments and evidence to validate the effectiveness and reliability of the algorithm. The experiments demonstrate that this approach achieves excellent performance metrics in zero-shot diffusion-based schemes.", "questions": "1. The article's overview of the overall encoding and decoding process is somewhat vague. It would be beneficial to include a pseudocode  to provide readers with a clearer understanding of the algorithm's encoding and decoding processes.\n2. The use of ROI in the article for flexible bitrate allocation is commendable. However, the paper lacks details on the application of this technology. For instance, is ROI specific to this algorithm only? Can it be integrated with DDCM or other zero-shot schemes? What is the specific process of implementing ROI? Does ROI introduce additional inference latency? These aspects should be further elaborated.\n3. The article showcases the Round Trip Time. What does this specifically refer to? In a compression algorithm, it's essential to separately compare encoding and decoding times.\n4. The article employs a 512 central crop for the Kodak dataset, which is relatively uncommon in the compression field where full-size Kodak testing is more prevalent. Is there a specific reason for this approach? Is it related to high GPU memory usage by the algorithm?\n5. Testing FID on the Kodak dataset may not be appropriate as Kodak comprises only 24 images, and even when divided into 64-pixel patches, reliable FID metrics may not be guaranteed.\n6. CLIC20 is a commonly used dataset in image compression. It would enhance the algorithm's reliability to include CLIC20 in the main experiments.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "1. The paper is well-written, with clear expression and concise yet precise explanations of the motivation and methodology.\n2. The theoretical explanations are solid, providing a high level of theoretical underpinning for the approach.\n3. The experiments are comprehensive, comparing all zero-shot diffusion-based image compression baselines and achieving satisfactory performance even with a several-fold acceleration", "weaknesses": "1. Some modules lack sufficient explanations, especially those borrowed from other articles. Providing necessary explanations can help readers better understand the operational mechanisms of the entire algorithm.\n2. The lack of striking innovativeness in the algorithm may be noted, as the entire solution builds upon the pipeline of DDCM and does not surpass DiffC in terms of performance.\n3. I believe confining the baselines to the zero-shot domain is inappropriate. While zero-shot algorithms show promise and are worth researching in diffusion-based image compression schemes, all zero-shot algorithms fundamentally sacrifice rapid inference to reduce or eliminate training costs, whereas compression tasks are sensitive to inference latency. Recently, some solutions based on few-step pre-trained diffusion models [1,2] have achieved outstanding performance with minimal latency. Overall, I suggest that the method should be compared against some non-zero-shot diffusion baselines or explore the potential application of this algorithm in fine-tuning diffusion priors, which could enhance the practical contributions and persuasiveness of the paper.\n\n[1] [TCSVT] RDEIC: Accelerating Diffusion-Based Extreme Image Compression with Relay Residual Diffusion\n\n[2] [ICCV 2025] StableCodec: Taming One-Step Diffusion for Extreme Image Compression", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "983BRqKNVp", "reviewer": "Reviewer_4uEv", "summary": "This paper proposes a fast and flexible zero-shot diffusion-based image compression method (i.e., Turbo-DDCM), which reduces the number of required denoising operations and maintains the performance with an improved encoding protocol. Moreover, Turbo-DDCM presents a priority-aware variant that prioritizes regions of interest and a distortion-controlled variant that compresses an image based on a target PSNR. Experiments are performed on Kodak and DIV2K datasets to investigate the effectiveness of the proposed method.", "questions": "1.\tWhat is the meaning of the symbol C in Eq. (8)?\n2.\tThe author should provide a detailed explanation of the encoding and decoding process in Figure 2.\n3.\tWhat is the meaning of log2(K M) in Eq. (14)?\n4.\tIt is difficult to distinguish the differences among the decoded images in the first row of Figure 1.\n5.\tIn Figure 4, when comparing with other methods, the authors should also provide the results on the DIV2K dataset.\n6.\tThe proposed method should be compared with GAN-based algorithms.\n7.\tWhen comparing computational complexity, the authors should also provide GPU memory usage.\n8.\tThe author should analyze the impact of the values of hyperparameters T, K, and C on performance.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "Turbo-DDCM has a competitive performance with recent methods in terms of the rate-distortion-perception tradeoff, and it achieves up to an order of magnitude speedup over existing methods.", "weaknesses": "1.\tThe experimental section lacks comprehensive quantitative results, such as BD-rate or BD-PSNR.\n2.\tThe workflow description of the proposed method is not concise enough.\n3.\tAlthough the proposed method is faster than the comparison algorithm, it does not offer a performance advantage.\n4.\tThe paper does not analyze the advantages of diffusion-based image compression methods compared to other types of image compression models, such as GAN, CNN, and RNN.\n5.\tNo results tables are provided for better indicating its superiorities over other methods.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "9Dya6kz5wr", "reviewer": "Reviewer_NNvr", "summary": "Turbo-DDCM proposes a new approach to zero-shot diffusion-based compression. In the original Denoising Diffusion Codebook Models (DDCM) approach, at each denoising timestep, the compression algorithm selects the next noise vector to add to the image from a codebook of K noise vectors, y selecting the one which moves the noisy image closest to the target image. In Turbo-DDCM, the authors instead encode a noise vector by selecting a subset of M of those K random vectors, and taking a linear combination of them, with coefficients either -1 or 1. This effectively allows the authors to select from a combinatorially larger set of noise vectors, getting closer to the target image with each step. With this improved guidance, they can steer the diffusion model to produce the target image in many fewer steps. They empirically show that this method allows for zero-shot image compression using diffusion models which is multiple times faster than prior approaches.", "questions": "The other available zero-shot diffusion compression methods (DDCM, and DiffC) have hyperparameters for speeding up their runtime by trading off against their rate/distortion performance. Primarily this means the number of denoising steps performed. It would be very interesting to see how these methods fare as you decrease the number of denoising steps to match Turbo-DDCM.\n\nIt's not obvious to me that the z_t* vectors selected by turbo-DDCM should yield x_{t-1} vectors which are in the same distribution that the diffusion model was trained on? Like the diffusion model was trained to expect specific linear combinations of real images + gaussian noise, at different ratios, for each time step. But when you generate z_t* according to this fancy process, does it still have the same statistics that random noise does, from the perspective of the diffusion model? Like you are selecting these vectors to be correlated with the target image, so I would naively expect them to have different statistics from random noise. But I'm not confident in this assessment.", "limitations": "", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "This is a clever idea for improving the computational efficiency of noise-vector selection in zero-shot DDPM-based compression. It clearly works quite well.", "weaknesses": "I consider all of these zero-shot methods (DiffC, DDCM, Turbo-DDCM) to be modifications of Theis et al's original DiffC proposal. They all, to various degrees, trade off theoretical elegance/rigor for real-world usability. In the original 2022 algorithm, there's a precisely defined relationship between the diffusion model's log probability of an image and the number of bits needed to compress that image to a certain noise level. Turbo-DDCM achieves state-of-the-art real-world performance, but trades away these theoretical guarantees.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "pSLKnL6HhQ", "reviewer": "Reviewer_QvxK", "summary": "The paper proposes an efficient zero-shot diffusion-based image compression method, which is based on the Denoising Diffusion Codebook Models (DDCMs) compression scheme. The paper modifies DDCM with Turbo-DDCM and introduces two flexible variants of Turbo-DDCM.", "questions": "1. What are the backbones of all zero-shot diffusion-based methods? For a fair comparison of speed, the proposed method should have the same backbone as these methods.\n2. Does the author use Turbo-Lora to accelerate Stable Diffusion 2.1?\n3. What is the speed of non-diffusion-based methods? The author should also compare with them.\n4. How to process higher resolutions?\n\nPlease reply to the Weaknesses and Questions. Based on the author's response, I will adjust my rating.", "limitations": "", "rating": 2, "confidence": 5, "soundness": 3, "presentation": 1, "contribution": 2, "strengths": "1. The paper is easy to read.\n2. The paper proposes a method which has a faster speed than existing zero-shot diffusion-based image compression methods.", "weaknesses": "1. The novelty and contribution are weak. The author just modified the DDCM, but there is no ablation study to analyze the proposed components.\n2. The presentation is incomplete. There is a lack of quantitative comparison and ablation study. And there are no tables in the whole paper.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Y6sPj1cgHa", "reviewer": "Reviewer_f616", "summary": "This paper addresses the issues of slow speed and high computational resource requirements of DiffC by proposing the Turbo-DDCM method. As a continuation of DiffC methods based on the RCC theory, TurboDDCM well inherits advantages such as zero-shot capability and achieves improvements in speed and performance.", "questions": "See weaknesses.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "1. The motivation is reasonably elaborated and well-supported in the subsequent methods and experiments. The time issue is a key concern in the field of image diffusion research based on diffusion architectures, and the authors have properly proposed a new noise reconstruction method to tackle this.\n2. The structure of the paper is clear and well-written.", "weaknesses": "1. The authors only conducted time comparisons within the RCC field. It would be valuable to know the speed comparison with diffusion compression methods based on condition introduction and fine-tuning. Specifically, whether RCC-based image compression has time advantages over fine-tuning-diffusion-based image compression, especially given the emergence of many one-step diffusion image compression methods (e.g., StableCodec).\n2. Following the first point, for fewer time steps (e.g., 5 steps or even a single step), does the performance of the proposed method degrade significantly?\n3. The performance improvement of the final results seems not particularly significant, and the comparisons are insufficient. The baselines selected by the authors appear to be consistent with those of DiffC, but DiffC is a work from ICLR25. It is suggested that the authors include more comparisons with recent works from the past year, such as DiffEIC and StableCodec.\n---\nref: \n\n[1] Li Z, Zhou Y, Wei H, et al. Towards extreme image compression with latent feature guidance and diffusion prior[J]. IEEE Transactions on Circuits and Systems for Video Technology, 2024.\n\n[2] Zhang T, Luo X, Li L, et al. StableCodec: Taming One-Step Diffusion for Extreme Image Compression[J]. arXiv preprint arXiv:2506.21977, 2025. (ICCV25 accepted)", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)