PSC: Posterior Sampling-Based Compression
Authors: Noam Elata
Tomer Michaeli
Michael Elad
Venue: Accepted by TMLR ()

Abstract: Diffusion models have transformed the landscape of image generation and now show remarkable potential for image compression. Most of the recent diffusion-based compression methods require training and are tailored for a specific bit-rate. In this work, we propose Posterior Sampling-based Compression (PSC) -- a zero-shot compression method that leverages a pre-trained diffusion model as its sole neural network component, thus enabling the use of diverse, publicly available models without additional training. Our approach is inspired by transform coding methods, which encode the image in some pre-chosen transform domain. However, PSC constructs a transform that is adaptive to the image. This is done by employing a zero-shot diffusion-based posterior sampler so as to progressively construct the rows of the transform matrix. Each new chunk of rows is chosen to reduce the uncertainty about the image given the quantized measurements collected thus far. Importantly, the same adaptive scheme can be replicated at the decoder, thus avoiding the need to encode the transform itself. We demonstrate that even with basic quantization and entropy coding, PSC's performance is comparable to established training-based methods in terms of rate, distortion, and perceptual quality. This is while providing greater flexibility, allowing to choose at inference time any desired rate or distortion.

Published in Transactions on Machine Learning Research (09/2025)
PSC: Posterior Sampling-Based Compression
Noam Elata
Department of Electricol and Computer Engineering Technion Israel Institute of Technology
Tomer Michaeli
tomer, semeer.m@ee.eechtiin..
Department Electrical and Computer Engineering Technion Israel Institute of Technology
Michael Elad
Med@ecstechhion...
Department of Computer Science Technion Israel Institute of Technology
Reviewed OpenReview: https://openrevvien net/ forum? id= 1=ggU322224
Abstract
Diffusion models have transformed the landscape of image generation and now show re- markable potential for image compression. Most of the recent diffusion-basse compression methods require training and tailored for specific bit-rate. In this work, propose Posterior Sampling-basee Compression (PSC) zero-shot compression method that lever- ages a pre-trained diffusion model as its sole neural network component, thus enabling the use of diverse, publicly available models without additional training. Our approach is in- spired by transform coding methods, which encode the image in some pre-chosen transform domain. However, PSC constructs a transform that adaptive the image. This done by employing a zero-shot diffussin-based posterior sampler so as to progressively construct the rows of the transform matrix. Each new chunk of rows is chosen to reduce the uncer- tainty about the image given the quantized measurements collected thus far. Importantly, the same adaptive scheme can be replicated at the decoder, thus avoiding the need to encode the transform itself. We demonstrate that even with basic quantization and entropy coding, PSC's performance is comparable to established training-bassd methods in terms of rate, distortion, and perceptual quality. This while providing greater flexibility, allowing to choose at inference time any desired rate or distortion
1 Introduction
Diffusion models excel at generating high-quality images (Ho et al. 2020; Sool--Dickstein et al. 2015 Song
ct al. 2020
Dhariwal & Nichol 2021 Vahdat et al. 2021 Rombach et al.] 2022).
Their versatility has
enabled solutions for diverse tasks, including inverse problems (Saharia et al., 2021
2022 Chung et al.
2023
Kawar et al. 2021 2022a Song et al.] 2023), image editing (Meng et al. 2021
Brooks et al. 2023
Kawar et al. 2023
Huberman- Hubernaan-Spiegelllaa et al. 2023), and uncertainty quantification (Behaain et al. 2023
Horwitz Hoshen 2022). Conveniently, many of these applications can utilize pre-trained diffusion models
without requiring task-specific training.
Image compression is fundamental for efficient storage and transmission of visual data, attracting significant research attention over decades. Effective compression schemes preserve essential image information while discarding less critical components, establishing a lossy compression paradigm that balances image quality against file size. Traditional compression methods like JPEG (Wallace) 1991) and JPEG2000 (Skodras et al, 2001) achieve this through fixed whitening transforms and coefficient quantization, allocating bits based on
1 Code implementation for PSC available at

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Published in Transactions on Machine Learning Research (09/2025)
Original
MS-ILLM
PerCo
PSC (Ours)
Ultra-low Rates
0.008 BPP
0.004 BPP
0.004 BPP
Low Rates
0.050 BPP
0.033 BPP
0.033 BPP
Figure Images compressed with latent-PSC at low bit-rates. Latent-PSC leverages pre-trained latent diffusion models to deliver high perceptual quality any compression rate, indicated by the bits- per-pixel (BPP) for each decompressed result. Top: Example at ultra-low rates demonstrates that PSC maintains high image quality while preserving the original image composition. Bottom: Example at low rales with zoomed detail highlights PSC's capacily to maintain fine details, adapting seamlessly to any compression rate without training.
the cocfficients' importance and applying entropy coding for additional lossless compression. More recently, neural compression methods have demonstrated improved performance over their classical counterparts, by incorporating quantization and entropy-coding directly into their training objectives (Ballé et al. 2018 8018: Minnen et al. 20188: Cheng et al.] 22200; Ballé et al.) 2016)] Theis et al. 2017) Toderici et al. 2015). In this context, deep generative models, such as GANs (Mentzer et al. 2020 or diffusion models (ang & Mandt 2024), can improve the perceptual quality of decompressed images. While some approaches use generative modeling for post-hoc restoration of existing compression algorithms (Bahat & Michaeli, 2021 Kawar al.
2022b; Saharia et al.) 2022; Man al.) 20233 Song et al., 2023: Ghouse al. 2023 Xu al. 2024), their
performance gains remain limited as they do not modify the encoder. Alternative methods that integrate
neural compression with diffusion model-basod decoding (Carcil et al. 2023 Yang & Mandt 2024 Relic
et al. 2024) achieve impressive results but require rate-specific dilfusion model training for a single modality, leading to reduced flexibility.
In this paper, we introduce lossy compression method that uses pro-trained diffusion model. This allows leveraging publicly available models without requiring additional training, and thus enables lossy compression of any data type which diffusion model has been trained. Our paradigm is very different
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from recent neural compression literature, and can be considered adaptive version of classical transform coding techniques. Specifically, our work draws inspiration from AdaSense (Elata et al. 2024b), which utilizes a pre-trained diffusion-model to identify an image-specific linear transform, from which the image can be roconstructed with near-minimal error. Here, we propose to use the same approach but for constructing an speefii compression transform. A key challenge in doing so, that in addition to encoding the transformed image, this approach scemingly requires encoding also the transform itself, which is completely impractical. However, our key observation is that the communication of the transform can be bypassed altogether. This allows method to perform well at extremely low bit rates, as illustrate in Fig. L
Our compression scheme, which we coin Posterior Sampling-based Compression (PSC), uses diffusion-based posterior sampler to progressively transform and quantize the given image. In each step, the next rows of the transform matrix are chosen in a way that minimizes the uncertainty that remains about the image, given the code constructed so far. The decoder replicates these calculations (fixing the same sced) such that both the encoder and the decoder reproduce exactly the same image-adaptive transform, climinating the need for transmitting side-information beyond the quantized coefficients of the image in the transform domain.
PSC can be applied any rate or distortion level prescribed by the user at inference time, and enables decompression at high perceptual quality. We evaluate PSC's effectiveness against established compression methods on the ImageNet dataset. (Deng et al. 2009), comparing both distortion and image quality. We also explore the compression of general images using offate-of-the-rre (SOTA) text-to to-tttggeeeaaaee latent diffusson models (Rombach et al.] 2022), incorporating textual descriptions within the compressed representation. We evaluate this latent-PSS PSC variant against nigh-perceptual -uality compression algorithms (Careil et al. 2023 Muckley et al., 2023) the CLIC Toderici et al.] 2020) and DIV2K (Agustsson & Timofte 2017] datasets. Our experiments demonstrate that PSC is competitive with established methods, despite using pre-trained diffusion model as its sole neural network component. While our preliminary implementation
employs simplified quantization, lacks tailored entropy coding and has high computational complexity, the results underscore the potential of our approach for ficxible compression applications. Future advances in diffusion-based posterior samplers, combined with our training- free compression framework, have the potential to yield significant improvements in compression of images well as other signals of interest.
To summarize, PSC offers the following advantages:
It provides precise instance-level control over rate and distortion. This is achieved by accumulating measurements until reaching the desired rate or distortion level.
For the same compressed code, decoding can aim for either high-quality or low-distortion. This is done by appropriately choosing the final restoration algorithm.
As zero-shot approach, PSC generalizes to any data lype supported by diffusion models, extending beyond image-specific applications.
Our method will inherently benefit from future advances in generative modeling and posterior sam- pling, without requiring modifications or re-training.
2 Background
2.1
Posterior Sampling for Linear Inverse Problems
Linear inverse problems are tasks in which a signal x needs to be recovered from linear measurements y = Hx, where H E RdxD is a known matrix. One approach to obtaining plausible reconstructions, is to draw samples from the posterior distribution p(xly). Recent research demonstrates that pre-trained diffusion models, which were originally trained to sample from the prior distribution p(x), can be adopted in a zero- shot manner to approximately sample from the posterior distribution (Kawar al.] 2022a Chung et al., 2023 Song al.] 2023). This can be done for any vector of measurements y and any measurement matrix H, which are provided to the sampler at inference time.
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2.2 Adaptive Compressed Sensing
In several imporiant problems, such as single pixel cameras and MRI, there is flexibility in designing the operator H. This gives rise to compressed sensing problem (Donoho) 2006), in which the question is which matrix H (of predefined dimensions) allows reconstructing the signals of interest with minimal error. Recently, Elata et al. (2024b) introduced AdaSense, a method that utilizes posterior samplers to progressively construct the sensing matrix H so as to optimally represent the input image.
The algorithm works as follows. At stage k; we have the currently held matrix Ho. and measurements Yo:k H The selection of the next row is done by generating samples from the posterior p(x|yo:* Hosk) using any posterior sampler and applying principal component analysis (PCA) to identify the principal direction of the uncertainty that remains in x given the current Yo.k- This direction is chosen as the next row in H, which is used to acquire a new measurement
x. More generally, instead of selecting one new measurement at a time, it is possible to add r new measurements in each iteration This selection of the new rows of H is optimal in the sense that allows achicving the minimal possible mcan squared error (MSE) that can be obtained with a linear decoder (even though more sophisticated reconstruction method is eventually used).
A single iteration of the method is detailed in Alg. [ The process repeats until H reaches the desired dimensions. Tt is important to note that AdaSense produces an smage-specifel sensing matriz H and corresponding measure- ments y. These can be used for obtaining candidate reconstruction & by leveraging the final posterior, p(x|y, H), where H is the final matrix (obtained at the last step). This final reconstruction may employ a different, more accurate (and possibly more computational demanding) posterior sampler, as it executes only once. Please see (Elata et al. 2024b) for further details.
Algorithm 1 A single iterative step of row selection Denoted as SelectNewRows Yo:k.)
Require: Previous sensing rows Hu.k, corresponding mea-
surements Yo:k, number of new measurements r
1: {xi]i=ı p(x Ho.k)
2: {xi + (x - ビ X
3: H + Append top r singular vectors of (x1....,x,,
4: return H
2.3 Transform Coding
Image compression algorithms based on the transform coding paradigm, like the widely used JPEG (Wallace, 1991), apply a pre-chosen, fixed and orthonorma transform on the input image, x RD,, obtaining its representation coefficients. These coefficients go through a quantization stage, in which portions of the transform coefficients are discarded entirely, and other portions are replaced by finite precision versions, with bit-allocation that depends on their importance for the image being compressed. As some of the transform coefficients are discarded, this scheme can be effectively described as using partial transform matrix H E R with orthogonal rows, and applying the quantization function Q(-) to each of elements of the remaining measurements y = Hx. Image compression algorithms include an entropy coding stage that takes the created bit-stream and passes it through a lossless coding block (e.g. Huffman coding, arithmetic coding, etc.) for further gain in the resulting file-size.
The decoder has knowledge of the transform used, H. Therefore, given the encoded signal, Q(y), the decoder generate reconstructed image e.g. by using H Hy)),, where H is the Moore Penrose pseudo-inverse of H. In practice, more sophisticated restoration methods are often used, some of which make use of neural networks.
When a compression algorithm said to be progressive, this means that the elements of y are sorted based on their importance, and transmitted in their quantized form sequentially, enabling decompression of the image any stage based on the received coefficients so far. Progressive compression algorithms are highly
IIn our notations, the subscript (0 k) implics that k elements available, from index 0 to index k 1.
TThis algorithm presents strategy of choosing the r leading cigenvectors of the PCA at every stage instcad of a single one, getting a substautial spcedup in the measurements' collection process at minimal cost to adaptability.
"Having orthogonal rows has two desirable effects easy-inversion and whitening effect. Using biorthogonal system as in JPF:2000 (Skodras et. al. 2001 has similar benefits.
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Algorithm 2 PSC Encoder
Algorithm 3 PSC Decoder
Require: Image X, number of steps N, number of
Require: compressed representation y, number of
measurements per step
sleps N, number of measurements per step
1: initialize Vo.a, Ho:0 as an empty vector matrix
1: initialize Yo:Nr + Entropy Decode(y)
2: for T. E {0: N - 1 do
2: initialize Ho.0 as an empty matrix
3: Hurmrr+ < SeloctNewRows Hu:rr No:n,; r)
3: for n E {0: N - do
Yomrtr < Append [yuur, ((nrarttx)))
4: Harartr +- Newsss (Homrs Yours r)
Hourtr + Append [Hurr Harsertl
Homrtr & Append [Hourr Hurmetel
end for return Entropy Encode(yo:Nr)
6: end for
return x= f(yo.Nr, Ho:Nr)
desirable, since they induce a low latency in decompressing the image. Note that the progressive strategy effectively implics that the rows of H have been sorted well based on their importance, each row gives birth to the corresponding element in y. Adopting this view, at step we consider the sorted portions of and y, denoted by Hos E R and Yock = Ho E Rt. the decoder gets Q(yo.), may produce H o:k Q(yox) as temporary output image. It is important to note that in this paradigm H is fixed, and therefore the sorting of its rows is determined only once. This chosen order used for compressing every image x.
3 Method
Posterior Mean
In this section, present how our proposed com-- pression scheme builds upon the framework of transform coding by leveraging the learned prior of diffusion models to determine an mnage-specific transform. By adapting the compressed sensing al- gorithm detailed in Sec. 2.1 to compression, PSC implements progressive approach to select the most informative partial measurements, effectively reducing reconstruction error by progressively in- creasing the bit-stream length. We solve the co- mundrum created by using an image-specific trans- form, by ratongt that both the encoder and the decoder can synchronize the transform without any use of side-information.
Samples from Posterior p y Haa)
Diffusion Model
Yo:k
Ho:k
Previous Measurements
PCA
and Rows
First Principal Component
Input Image
During each step of the compression phase, our system dynamically estimates the posterior prob- ability distribution p(x Hox), which is con- ditioned on the previously extracted Ho.k and the corresponding quantized partial measurements Yo.k- This estimation utilizes samples generated by a posterior sampler. Importantly, the zero-shot methods listed in Sec. 2.1 can solve any inverse problem of the form utilization of pre-trained diffusion models without training. In practice, we use posterior samplers de- signed for lincar inverse problems (without quan- tization). This allows using efficient samplers and leads to sufficiently accurate results.
Y/k
Figure 2: A diagram of how PSC zeros in on the input image by progressively tightening the posterior. The diagram shows a single step, where the new rows and matching measurements are com- puted based on the direction of largest uncertainty the postcrior distribution. The posterior mean is shown visualize the information captured by previ- ous iterations.
Q(Hx), enabling the
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Compression
Decompression
x
Select New Rows
y
Select New Rows
X
H
H
Figure 3: PSC diagram: Both encoder and decoder construct an image-specific transform through an adaptive compressod sensing algorithm, progressivcly adding rows based on posterior sample covariance. The transmission of quantized measurements y ensures identical inputs each progressive step, while a shared random seed guarantees deterministic outputs both sides. Together, these factors enable the construction of identical transforms on both sides eliminating the need to transmit the transform side information.
The selection of the next of H, denoted as h& RIxD is determined by identifying the eigenvector corresponding to the largest eigenvalue of the posterior covariance. This method ensures the projection of x occurs along the most informative direction, maximizing the value of incremental information gathered. = Q(h,x), is then appended to the previous compressed representation Youk
The resulting measurement, to form Yo.++1- This process effectively reduces the uncertainty of candidate images within the posterior distribution p(x|yo.k; Ho.)) in a nearly optimal manner. Interestingly, as a by-product of the algorithm, the obtained sensing matrix H has orthogonal rows, disentangling the measurements, as expected from a compression algorithm. A single step of this process is described in Fig. 2
This approach might appear counterintuitive for transform coding, it raises questions about the de- coder's ability to determine the appropriate transform for image recovery. The naive approach of directly communicating the transform would be impractical, as it would require more bits than a lossless transmission of the image itself (the transform can be any matrix in RdxD). However, we present an elegant solution that circunvents this challenge through our progressive compression structure, which eliminates the need to communicate the transform entirely.
More specifically, PSC maintains a synchronized and identical state between encoder and decoder throughout its operation. The system relies an agreed-upon seed, ensuring all random sampling operations produce deterministic and reprodueible outputs. PSC initiates both encoder and decoder algorithms from the same empty matrix Ho.0 and empty vector of previous quantized projections Vo.0- Assuming that the previous steps were completed successfully - i.e. the accumulated matrix Ho.k and quantized measurements Youk are identical in both the encoder and decoder, we proceed to construct the next row of Ho.k- During this computation, all posterior samples {x.}i= p(x|yok; Hoa) are identical in both encoder and decoder, ensuring the synchronization of the newly computed row hg- The encoder then evaluates and quantizes the new measurements ys Q(hxx), incorporating them into the compressed representation transmitted to the decoder. Using the compressed representation, the decoder can utilize all measurements Vo.++1 directly in subsequent steps without requiring access to the input image. This ensures that the inputs to the next iteration, Ho and Yo.4+1, remain synchronized. This novel approach to synchronized transform roconstruction illustrated in Fig. 3 The complete procodures for compression and decompression with PSC, including the optimization of selecting rows from matrix H for improved efficiency, are detailed in Alg. and Alg. respectively.

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Original
BPG
HiFIC
PSC Distortion
PSC Perception
0.057 BPP
25.68 dB
0.052 BPP
25.46 dB
0.052 BPP
25.78 dB
0.052 BPP
23.55 dB
0.077 BPP
25.49 dB
0.071 BPP
24.39 dB
0.071 BPP
26.22 dB
0.071 BPP
24.23 dB
0.038 BPP
27.10 dB
0.038 BPP
26.46 dB
0.038 BPP
27.74 dB
0.038 BPP
26.60
0.087 BPP
25.39 dB
0.089 BPP
15.29 dB
0.089 BPP
30.16 dB
0.089 BPP
27.73
Figure 4: Qualitative examples for compression with PSC, compared to other compression algorithms. BPP and PSNR are reported per example. Our method can be used for both low-distortion or high perceptual quality using the same compressed representation.
3.1 Implementation Choices
We use DDRM Kawar et al. 2022a as a zero-shot posterior sampler for the selection of H, due to it's relative low computational complexity. Due to the repeated sampling from different posteriors, PSC retains a high computational complexity, requiring approximately 10,000 NFEs for both compression and decompression (see runtime details in App. A.2. Nevertheless, we expect advances in diffusion models and posterior sampling to significantly expedite future versions. While the matrix Ho.1 used in the first step can be optimized globally using images from the dataset, keep the first step identical to the following steps described above for simplicity. In our implementation we focus on unsophisticated quantization approach, reducing the precision of y from floa132 to float8 (Micikevicius et al. 2022). We employ Range Encoding implemented using (Bamler 2022) as an entropy coding on the quantized measurements. The quantization, the posterior sampler and the entropy coding could all be improved, posing promising dircctions for future work. Finally, after reproducing H on the decoder side, PSC may use a different final posterior sampler during decompression, in attempt to further boost perceptual quality for the very same measurements y.

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Distoiisto
Sate-Perception
JPEG
JPEG2000
BPG
30.0
MS-ILLM
10a
ELIC
27.5
IPIC
PSNR
FIID
PSC- Distortion
25.0
PSC Perception
20.0
17.5
10
10
10
10
10
BPP
BPP
Figure 5: Sate-Distootiin (left) and Rate- Pate-Perceetion (right) curves for ImageNet256 compres- sion. Distortion is measured as average PSNR of images for the same desired rate or specified compression quality, while Percoption (photorealism) mcasured by FID.
4
Experiments
We begin with an evaluation of PSC on 256 x 256 color images from the ImageNet (Deng et al. 2009 dataset, using the unconditional diffusion models from (Dhariwal & Nichol (021] as an image prior. We compare distortion (PSNR) and bits-per-pixel (BPP) averaged subset of validation images, using
image from each of the 1000 classes, following (Pan et al. 2021 We apply PSC to progressively decode higher rates, as detailed in App.At A
A key advantage of PSC is its ability to prioritize perceptual quality during decompression by changing the final reconstruction algorithm. However, this flexibility comes with a caveat: using a high-quality roconstruction algorithm will inevitably lead higher distortion (Blau & Michaeli, 2019). Despite this, using PSC, the same compressed representation can be decoded using either a oow-disortion or high perceptual quality approach with minimal additional computational cost. Specifically, 2023 produces images with highest photorealism, while DDRM (Kawar et al. 2022a leads to the lowest distortion. We present both restoration solutions as PSC Perception and PSC Distortion accordingly.
find that ITGDM (Song al.
Figure 5 presents the rate-distortion and rate-perception curves of PSC compared to several established methods: classic compression techniques like JPEG (Wallace 1991). JPEG2000 (Skodras et al.
2001 and
BPG (Bellard 2018 We also compare neural compression methods, such ELIC (He al. 2022 and
its diffusion-based derivative IPIC (Xu al. 2024), as well as HiFiC (Mentzer al. 20220), prominent GAN-based neural compression method. Distortion is measured by averaging the PSNR across different algorithms for given compression rate. Image quality is quantified using FID (Heusel el al. 2017 estimated on 50 random 128x 128 crops from each image (inspired by the evaluation in (Mentzer et al. 2020 and compared to the same set of basclincs. The graphs demonstrate that PSC achieves comparable performance, particularly at low BPP regimes, when considering both distortion and image quality. Figure ! showcases qualitative image samples compressed using different. algorithms at the same rate, further supporting our findings. Notably, PSC achieves exceptional image quality despite the fact that does not require any compression-specffic training.
4.1 Latent PSC
Latent Text-to-Image diffusion models have gained popularity due their casc-of-use and low computational requirements. These models employ VAE (Kingma & Welling 2013) to conduct the diffusion process in

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CLIC
DIV2K
Rate-Distortion
Rate-Perception
Rate- Distortion
Rate-Percee Perception
27.5
BPG
MS-ILLM
25.0
PerCo
PSC Perception
22
22.5
20
20.0
10-2
17.5
14
12
10
10
10-2
10
10"2
10"0
10-2
10
BPP
BPP
BPP
BPF
Figure 6: Rate-Distortion and Pate-Perception curves demonstrating PSC with latent- compared to similar methods. Left: CLJC dataset, Right: DIV2K dataset. Distortion is measured as average PSNR, while Perception (photorcalism) is mcasured by KID.
a lower-dinensional latent space (Vahdat et al. 2021 Rombach et al. 2022 the integration of PSC with Stable Diffusion [Rombach al.) 2022]. a publicly available latent Text-to- Image diffuusio model. This variant, named latent-PSC, operates in the latent space of the diffusion model. Both compression and decompression occur within this latent space, leveraging the model's VAE decoder to reconstruct the image from the decompressed latent representation. Additionally, we condition all posterior sampling steps on textual description, which must be given along with the original image or inferred using an image captioning module (Vinyals et al. 2016 Li et al.) 2022 2023). The text prompt must be added to the compressed representation to avoid side-information. A detailed diagram latent-PSC presented in App.
this work we also explore
Due to the use of the VAE decoder, we expect significant drop in PSNR. Thus, develop latent-PSC extension of PSC Perception, maintaining high perceptual quality at low bit-rates. We find that the posterior sampler outlined in Nested Diffusion (Elata et al.) 2024a) works best in this setting. We use images from the CLIC (Toderici et al. 2020 and DIV2K (Agusssson & Timofte 2017) to compare Latent-PSC to PerCo (Careil et al. 2023 a recent work which also utilizes latent diffusion for low-rate image compression. Using the same base diffusion model, image captioning model, and text compression as PerCo, we demonstrate in Fig. and Fig. that we are comparable in terms of both distortion (PSNR) and photorcalism (KID (Bińkowski et al. 2018)) all bit-rates despite not adding any training. We also compare to MS-ILLM (Muckley et al., 2023), another compression method that focuses quality, well as BPG, as classical baseline. While the results of MS-ILLM do not suffer from the VAE- induced drop in PSNR, they do not reach the image quality of PerCo or Latent-PSCC, especially at very low rates.
high perceptual
5 Related Work
Diffusion models have enhanced classical compression algorithms by providing data-driven decompression for high-perceptual quality reconstruction (Ghouse et al., 2023 Saharia et al. 2022). Several approaches implement zero-shot diffusion- based reconstruction (Kawar et al. 2022b Song al. 2023 offering training-
free decompression, but remain constrained to specific compression algorithms, which may be found lacking, Notably, recent work by Xu el. al. (2024) attempts to ut utilize general diffusion-based posterior samplers ro increase the image quality using a leading neural compression method. While this work employs pre-trained diffusion-basse basod postcrior samplers similar to our method, they focus on traversing the RDP trado-off (Blau & Michaeli 2019) of existing neural compression schemes rather than developing a comprehensive compression solution.
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Recent developments integrate neural compression with diffusion models for decompression. Some approaches employ separale (Hoogeboom et al. 2023) or joint (Yang & Mandi 2024) neural compression and diffusion training to create compact representations with conditional diffusion models for high-quality decompression. Specifically, Carcil et al. (2023); Relic et al. (2024) utilize latent diffusion (Rombach et al. 2022) and text- conditioned models for efficient training. Despite their promise, these methods require complex rale-specific training. limiting flexibility.. While work by Gao al. (2022) addresses this through training-free post-hoc rate reconfiguration, they incur high computational costs and performance penalties.
The concept of leveraging pre-trained diffusion models for compression originated in the DDPM publica- tion (Ho et al. 2020 though it focused on theoretical compression limits rather than practical implementa- tion. Similarly, Theis et al. (2022) analyzes theoretical limits using reverse channel coding techniques (Li & Gamal 2018), but their implementation's high computational complexity and lack public code prevents direct comparison with our approach.
6 Limitation, Discussion and Conclusion
While PSC introduces a novel approach to generative model-based compression, several limitations warrant discussion. The method's primary constraint its substantial computational overhead due to iterative diffu- sion model sampling. This computational burden is intrinsically linked the zero-shot posterior sampler's quality, though ongoing advances in diffusion models and posterior sampling techniques may significantly reduce this limitation. The current. implementation's 's simplified quantization strategy for measurements presents another constraint. Implementation of more sophisticated quantization methods could yield signif- icant improvements in compression rates. Furthermore, PSC's restriction to linear measurements, imposed by both existing posterior sampler capabilities and the complexity of non-linear measurement optimization, indicates potential for enhancement through the exploration of non-linear measurements and correspond- ing inverse problem solvers. Notwithstanding these limitations, PSC represents a significant advancement in zero-shot diffusion-based image compression through several distinet advantages. The method progres- sively acquires informative measurements to create compressed representations, with decompression faith- fully reconstructing the original image by replicating the compression algorithm's steps. Its implementation simplicity, independence from training data, and cross-domain flexibility underscore its potential impact. Future developments promise to further advance this approach to both image compression and compression in general.
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Acknowledgments
This research was partially supported by the Israel Science Foundation (ISF) under Grants 951/24, 409/24 and 2318/22, and by the Council for Higher Education Planming and Budgeting Committee. This research was also partially supported by by a gift from Elbit Systems, and by the Ollendorff Minerva Center, ECE faculty, Technion. We would like thank Hila Manor for her help running evaluations, and Matan Kleiner and Sean Man for their helpful discussions and ideas.
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14


Reviews:
[{"review_id": "awwvun1X7b", "reviewer": "Reviewer_RYVp", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n- The paper is clear and well written, using a reasonable approach to including diffusion models in compression and decompression.\n- Multiple datasets, resolutions, and baselines are considered, demonstrating better or comparable results. \n- The inclusion of a latent diffusion-based version utilizing text-to-image models is interesting, where the image description acts as part of the compressed representation.\n\nWeaknesses:\n- The proposed approach is not well motivated, especially considering the high computational cost involved in the compression and decompression process.\n- The compression approach appears to be largely semantic and layout in nature, resulting in specific loss of details as shown in the qualitative examples.\n- While the compression and decompression outer-loops are well described, the incorporation with the diffusion model is not.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper proposes an image compression method which utilizes a diffusion model to generate the linear encoding matrix. During encoding, the diffusion model is used to build this matrix by focusing on the principal components, thereby achieving a compressed representation through component weights, which can then be quantized and entropy encoded. During decompression, the compressed representation along with the initial diffusion seed can be used to reconstruct this matrix and subsequently a form of the original image. Additionally, the diffusion networks are zero-shot, establishing a training-free approach, and result in a more generalizable approach that prior works. The authors demonstrate strong results on ImageNet samples compared to baselines, and on both CLIC and DIV2K for their latent diffusion-based version.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Changes:\n\n- Could the authors add a discussion on how the diffusion model is incorporated into the posterior sampling loop? In the pseudocode, what does `posterior_sampler ( noise , H , y)` look like? Most networks operate on only the noise and label (integer class or text), which is different from the compressed vector `y`. \n\n- Sampling configuration and sensitivity to sampling hyperparameters is also necessary to understand the evaluations and for reproducibility. As it stands, this part of the method is described as a black-box. Additionally, are the results sensitive to the ODE solver, sampling timesteps, network / network size, etc. \n\n- A clearer discussion on how the encoder and decoder networks are linked would also be helpful. Can these be different networks? If so, then that adds another level of generality, whereas if not, then the network description would also be needed for reconstruction.\n\n- Are there any limitations with image resolution? Most diffusion models have trouble generating at resolutions OOD from the training cases. \n\nQuestions:\n\n- For the latent diffusion version, is the text description included in the BPC calculation, since this information must also be transmitted? And is the latent diffusion version sensitive to the quality and length of the text description? \n\n- Could the authors provide some motivation as to why this problem is interesting from a practical perspective? Despite the efficiency gains in diffusion models, the computational cost is likely not worth the small quality increase when compared with BPG and JPEG2000. \n\n- Does the compressed version `y` contain semantic information similar to a CLIP embedding, independent of the compression process? In such a case, a dedicated diffusion model could be trained to decode `y` directly, without the expectation of strong perceptual similarity but instead focusing on semantic similarity.", "broader_impact_concerns": "No concern.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "VpM4tdKqCz", "reviewer": "Reviewer_n8gb", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "*Strengths*\n* The proposed encoding method provides a very straightforward and elegant way to extend AdaSense to an image compression method by seeding posterior sampling in the same way both during encoding and decoding, which allows image reconstruction from only the measurement code (at the expense of re-performing computationally intensive diffusion during decoding).\n* The overall goal of the paper is interesting and novel. As the authors note, image compression has been discussed even in very early work on diffusion modeling, but this method (to my knowledge) provides the most concrete and convincing practical demonstrating of diffusion-based compression.\n* The experiments show impressive results in terms of low-BPP reconstruction using both distortion (PSNR) metrics based on the DDRM algorithm and perceptual quality based on the $\\Pi$GDM algorithm. \n\n*Weaknesses*\n* The primary weakness of the proposed algorithm is the high computational cost of the algorithm. Thousands of NFEs with large diffusion models are needed to encode and reconstruct a single image. While the aim of this work seems to be more of a proof of concept than a practical tool, it is still a major limitation. The cost is only discussed briefly in the paper and a thorough breakdown of NFEs and runtimes for different situations would provide important context for the reader.\n* The method is limited in its reconstruction abilities when the diffusion model is a latent space model. It is well-known that even the most advanced autoencoders used in latent diffusion introduce significant reconstruction error for small details and high frequency patterns. Since autoencoder reconstruction quality provides the upper bound for reconstruction from the proposed method when the diffusion model is latent, the proposed method is not suitable for low-distortion encoding when performed in the latent space. Given that low-distortion encoding is probably the most important aspect of compression, the fact the most recent diffusion models are in the latent space, and the extreme cost of pixel space diffusion for high-resolution images, there are a lot of practical obstacles for this method to achieve low-distortion encoding with off-the-shelf diffusion models.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper investigates the use of pretrained diffusion models for the purpose of image compression. The work builds on the recent AdaSense method, which provides a paradigm for using zero-shot posterior diffusion sampling for linear inverse problems with pretrained unconditional diffusion models. This method iteratively builds encoding coefficients $y$ and linear encoding transform $H$ for an observed image $x$ by drawing several samples from $p(x | y)$ under the assumption that $y = Hx$, taking the PCA of these samples, and adding the top PCA coefficients to $y$ and the corresponding PCA vectors to $H$. However, AdaSense cannot be used directly for compression because it requires the matrix $H$ to decode $y$, and storing $H$ requires a large amount of memory. This work provides a method for reconstructing $x$ using only the compressed measurements $y$, thereby enabling image compression. This is done by fixing the random seed of the diffusion model during both encoding and decoding and re-calculating the $H$ matrix iteratively during the decoding using parallel posterior diffusion samples with the same seed. Once $H$ is obtained from $y$, the user is able to select diffusion zero-shot posterior sampling algorithms to get the final reconstruction. Experiments apply the proposed method to reconstruct ImageNet 256x256 samples using an unconditional pixel space diffusion and reconstruction using a latent space text-conditioned diffusion. The ImageNet experiments present two versions that use different zero-shot posterior sampling: one with low distortion at low BPP compared to related methods, and one with high perceptual quality at low BPP compared to related methods. The latent diffusion experiments cannot provide low distortion due to VAE reconstruction, but can demonstrate high perceptual quality at low BPP compared to related methods.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "My main requested change is that a thorough report on NFE and runtime (and perhaps other computational requirements like GPU memory use) of the method is added. This provides important context and also provides a baseline for future work on diffusion-based compression to compare against.\n\nI have a few questions that would clarify the work.\n\n* Can you elaborate on how $y$ and $H$ are selected at the very beginning of the compression stage when they are designated as empty? Does this mean that unconditional samples are drawn from the diffusion model $p(x)$ and used to provide initial PCA directions? It seems like this very first step does not use any information from the input image, is that right? Can this step be \"skipped\" by just memorizing $H$ from the PCA of unconditional samples?\n* Can you elaborate about the practical use of encoding with high perceptual quality? Are there situations where this is important?", "broader_impact_concerns": "Broader impacts are not discussed, but that does not impact my evaluation of the paper.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "hIDU5JwIh5", "reviewer": "Reviewer_rszy", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:   \n1The method's primary strength is its zero-shot nature, leveraging publicly available, pre-trained diffusion models without any additional training for the compression task.   \n2PSC provides precise, instance-level control over the compression rate and allows the user to decode for either low distortion or high perceptual quality from a single compressed representation.   \n3Despite its training-free approach, PSC achieves rate-distortion and rate-perception performance comparable to established training-based methods like HiFiC, particularly in low-bitrate scenarios.   \nWeaknesses:   \n1The most significant limitation is the substantial computational overhead. The method requires an order of 10,000 NFEs for both compression and decompression of a single image, making it impractical for many real-world applications. This cost was not adequately quantified or discussed in the main paper.   \n2The approach is a clever integration of existing technologies—namely diffusion-based posterior samplers (e.g., DDRM) and the AdaSense algorithm—which led some reviewers to question its fundamental novelty.   \n3The paper's reliance on the relatively obscure AdaSense algorithm made the methodology difficult to follow for readers unfamiliar with it.    \n4The evaluation was missing direct comparisons to some relevant state-of-the-art flexible compression methods. Furthermore, the lack of analysis on encoding/decoding time was a major omission.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "Summary Of Contributions\nThe paper introduces Posterior Sampling-based Compression (PSC), a zero-shot image compression framework that utilizes a pre-trained diffusion model as its sole neural network component, eliminating the need for task-specific training. The method is inspired by transform coding but uniquely constructs an image-specific transform matrix progressively. The core innovation is a synchronized process where the decoder can independently reconstruct the exact same adaptive transform as the encoder by leveraging the transmitted quantized measurements and a shared random seed.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1The paper must include a clear, quantitative analysis of the computational complexity in the main text. This should include metrics like encoding/decoding time on specific hardware and the number of function evaluations (NFEs) required at different rates, directly comparing these figures with the baseline methods.   \n2The authors should revise the methodology section to be more self-contained. This involves providing a higher-level intuition behind the AdaSense algorithm and explicitly explaining why minimizing the posterior covariance (i.e., uncertainty) is an effective proxy for optimizing rate-distortion performance in this context.   \n3The experimental section should be expanded to include more comparisons with other relevant and state-of-the-art methods.", "broader_impact_concerns": "none", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "ccl55KFSEs", "reviewer": "Reviewer_kacb", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n\n1. Strong empirical results: The proposed algorithm yields higher-fidelity reconstructions with fewer bits per pixel for pixel diffusion priors, outperforming strong contemporary baselines.\n2. Simple, elegant implementation: The algorithm is easy to implement given adequate computational resources, and the authors provide in-depth implementation details in Section 3.1.\n\nWeaknesses:\n\n1. Aspects of the writing:\n   a. In “To summarize, PSC offers the following advantages,” the last two bullet points merely reflect the use of a diffusion model as a prior, rather than novel contributions. Generative models as priors for inverse problems predate this work.\n   b. In Figure 2, “H” is not labeled, and it is difficult to understand the added benefit of this diagram since Algorithm 1 already explains the concept clearly.\n   c. The computational requirements should be specified in the Experimental Details section.\n   d. In Figure 5 (Rate–Perception), it is hard to distinguish the exact performance difference between MS-ILLM and the proposed method.\n2. Latent PSC evaluation: In the Latent PSC section, there appears to be no clear benefit of the proposed method over Perco, but is interesting that proposed alogrithm works for both pixel and latent diffusion models. \n3. Code availability: The manuscript does not mention plans to publicly release the code or include it in the supplementary materials.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The authors propose an algorithm that leverages diffusion as a prior to sample the posterior of a compressed image, which they coin Posterior Sampling–based Compression (PSC). Their work is inspired by AdaSense (an adaptive compressed sensing algorithm), but focuses on image-specific compression transformations instead of linear transformations. They introduce two main algorithms— the PSC encoder (Algorithm 1) and the PSC decoder (Algorithm 2) both of which leverage the posterior distribution. The encoder progressively expands the sensing matrix to encode compressed measurements y, and the decoder then reconstructs the true signal x from those measurements. To guarantee deterministic outputs when sampling from the posterior in both algorithms, a fixed random seed must be used. The authors demonstrate their method using both pixel-diffusion priors and latent-diffusion techniques with established posterior-sampling algorithms. Across a wide range of bits-per-pixel (BPP) settings, PSC outperforms strong contemporary baselines in both latent and pixel diffusion scenarios. The main contribhution of this work is strong experimental results.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1. In the Implementation section, add a link to the publicly available code repository and list the necessary computational requirements.\n2. Replace the “advantages of using the proposed method” heading with “novelty of the work.”\n3. Revise or remove Figure 2—Algorithm 1 is sufficient. If you keep it, add a sentence in the figure caption or main text explaining how Algorithm 1 differs from AdaSense (e.g. by introducing an additional sensing matrix H in the first few lines for conditional sensing).", "broader_impact_concerns": "Not Available", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)