Diffusion-OAMP for Joint Image Compression and Wireless Transmission Wentao Hou, Yimin Bai, Zelei Luo, Jiadong Hong, Lei Liu
arXiv:2604.27952v1 [eess.IV] 30 Apr 2026
College of Information Science and Electronic Engineering, Zhejiang University, China Email: {wentao010, yimin.bai, zeleiluo, jiadong5, lei liu}@zju.edu.cn
Abstract—Joint image compression and wireless transmission remain relatively underexplored compared to generic image restoration, despite its importance in practical communication systems. We formulate this problem under an equivalent linear model, and propose Diffusion-OAMP, a training-free reconstruction framework that embeds a pre-trained diffusion model into the OAMP algorithm. In Diffusion-OAMP, the OAMP linear estimator produces pseudo-AWGN observations, while the diffusion model serves as a nonlinear estimator under an SNRmatching rule. This framework offers a way to incorporate multiple generative priors into OAMP. Experiments with varying compression ratios and noise levels show that Diffusion-OAMP performs favorably against classic methods in the evaluated settings. Index Terms—Diffusion Models, Orthogonal Approximate Message Passing, Wireless Transmission, Image Compression, Flow Matching
I. I NTRODUCTION This paper considers the problem of joint image compression and wireless transmission, which is relatively underexplored compared to generic image restoration, despite its relevance to practical and emerging intelligent communication systems [1]. The joint process can be described by the equivalent linear model: y = Ax + n,
(1)
where y ∈ RM denotes the received signal vector, x ∈ RN denotes the transmitted signal, A ∈ RM ×N is the equivalent matrix representing the joint effect of modulation, compression, and transmission, and n ∼ N (0, σ 2 I) is additive white Gaussian noise (AWGN). The recovery performance is therefore determined not only by the conditioning of H and the noise level of n, but also by how accurately the prior underlying image can be incorporated into the receiver. Approximate message passing (AMP) algorithms [2], [3] provide an attractive route to solve the linear recovery problem in (1). In particular, Orthogonal AMP (OAMP) [4] and Memory AMP [5] can achieve Replica-optimal performance. The linear / nonlinear decoupling structure in the AMPtype algorithm is especially appealing for joint compression and transmission, and previous work has already shown that classical denoisers such as BM3D [6] can be incorporated into this framework [7]. However, the optimality of the AMP-type algorithm relies on having an accurate prior model for x such as Bernoulli-Gaussian, while high-dimensional signals such as natural images do not admit a simple analytically tractable
distribution. Once the assumed prior is mismatched to the true image distribution, the performance of OAMP becomes suboptimal. Recent progress in generative AI offers a practical way to address this prior-modeling bottleneck. Diffusion models [8]–[11] can capture rich image distributions far beyond the hand-crafted analytical prior distribution. This capability has motivated a series of diffusion-based solvers for linear inverse problems [12]–[14]. However, most of these diffusion-based methods are designed for generic image restoration rather than the joint image compression and wireless transmission scenario considered here. Among recent advances, Score-Based Turbo Message Passing (STMP) [15] is particularly relevant, demonstrating the potential of the modern generative model for plug-and-play compressive image recovery. Different from STMP [15], we focus on joint image compression and wireless transmission with channel-induced ill-conditioning, and develop a diffusion-assisted OAMP receiver. Our framework can also be instantiated with different diffusion models, such as DDIM [9] and Flow Matching [11]. The main contributions of this paper are summarized as follows: • We propose Diffusion-OAMP, a training-free framework for joint image compression and wireless transmission that embeds a diffusion model into the OAMP algorithm. • We show that the proposed framework is compatible with multiple diffusion priors. In this paper, we instantiate the nonlinear estimator with both DDIM and Flow Matching models and use an SNR-matching rule to select the diffusion time step at each OAMP iteration. • Experiments on the CelebA dataset under multiple compression ratios and noise levels show that the proposed approach compares favorably with OAMP-BM3D and DDRM in the evaluated settings. II. P RELIMINARIES A. Linear System Model for Joint Image Compression and Wireless Transmission Modulation and compression of the original signal bits can be modeled as a linear process from the source image vector s ∈ RN to the transmitted signal: x = Fs,
(2)
where F is the joint modulation and compression operator. The source image vector is assumed to be drawn from an
image prior distribution Ps , denoted by s ∼ Ps . The concrete construction of F, based on random multiplexing (RM) [16], is described in Section II-C. Image transmission over the wireless channel can also be represented as a linear process: y = Ax + n,
(3)
where y ∈ RM denotes the received signal vector, A is the channel matrix, and n ∼ N (0, σ 2 I) is AWGN. This paper views joint image compression and wireless transmission as an integrated linear inverse problem by combining the two linear stages: y = A (Fs) +n = Ax + n, |{z}
(4)
x
or equivalently y = (AF)s + n. From this point of view, the receiver recovers the source image s from y under the operator AF, while still exploiting the explicit intermediate variable x to separate channel estimation in the transmission domain from the image reconstruction in the source domain. B. AMP Algorithms for Linear System AMP algorithms [2], [3] are a class of effective iterative methods for linear inverse problems, such as compressed sensing. By passing messages between a linear measurement module and a nonlinear estimation module, AMP-type algorithms turn a large coupled recovery problem into a sequence of simpler denoising and linear estimation steps. OAMP [4] and MAMP [5] further improve this framework by introducing an orthogonalization mechanism between the linear and nonlinear estimators. Compared with conventional AMP, OAMP is better suited to sensing matrices beyond the i.i.d. Gaussian case, admits rigorous state-evolution analyses, and can achieve Replica-optimal performance in the largesystem limit for right-unitarily invariant matrices. In this work, OAMP serves as the backbone algorithm for solving the integrated joint compression-and-transmission inverse problem in Eq. (4). The OAMP algorithm is performed in the transmission domain x: its Linear Minimal Mean Square Error (LMMSE) estimator enforces consistency with the known channel model and the noisy observation, while the orthogonalized output is subsequently mapped to the sourceimage domain for diffusion-based nonlinear estimation. Specifically, given the pseudo-Gaussian prior estimate mmse (xmmse pri , vpri ), the OAMP LMMSE performs an update under y = Ax + n. The posterior mean and covariance are mmse T mmse xpost = xmmse pri + vpri A C(y − Axpri ), −1 mmse where C ≜ σ 2 I + vpri AAT . mmse mmse 2 T mmse Vpost = vpri I−(vpri ) A σ 2 I + vpri AAT
−1
(5)
A, (6)
with scalar variance vpost ≜
1 tr(Vpost ). M
(7)
OAMP reduces the correlation issue between the Linear Estimator (LE) and the Non-Linear Estimator (NLE) module through an orthogonalization step, which converts orth (xpost , vpost ) into (xorth post , vpost ): −1 orth mmse −1 vpost = vpost − (vpri )
−1
,
−1 orth mmse −1 mmse xorth xpri . post = vpost vpost xpost − (vpri )
(8) (9)
orth The pair (xorth post , vpost ) serves as an extrinsic pseudoobservation that connects channel-aware estimation in the x domain with generative reconstruction in the s domain.
C. Random Multiplexing In image compressed sensing, a classical design is the partial DFT sensing matrix ΦpDFT = SFDFT used in Turbo compressed sensing [7], where S randomly selects and reorders rows of a unitary DFT matrix. Random Multiplexing (RM) [16], developed for wireless communication, instead applies a channel-independent random transform before transmission. This transform makes the equivalent channel more suitable for the AMP-type receivers. Inspired by this idea, we use one operator to perform both compression and multiplexing: F = SΞ,
Ξ = PTDCT D,
(10)
where D is a diagonal random sign matrix, TDCT is an orthogonal DCT matrix, P is a random permutation matrix, and S ∈ RM ×N selects M rows, with compression ratio β = M/N . Thus, Ξ provides the RM-style multiplexing, while S provides compression, yielding the transmitted vector x = Fs. Since F is rectangular, F−1 in the receiver denotes the corresponding zero-filled inverse ΞT ST . D. Diffusion Models Diffusion [8] and Flow Matching [11] models have emerged as a powerful class of generative AI, achieving state-of-theart performance in high-quality image synthesis. Unlike traditional hand-crafted priors, diffusion models implicitly capture the underlying data distribution through an iterative denoising process. This intrinsic ability to learn complex data structures makes them an ideal mechanism for providing high-fidelity empirical priors in solving inverse problems. Beyond pure image generation, diffusion models have also been directly applied to solve linear inverse problems. Representative examples include DDRM [12], DDNM [13], and PnP-Flow [14]. However, these methods, as well as the closely related STMP [15], focus mainly on conventional image restoration or compressive image recovery. They are not specifically designed for joint image compression and wireless transmission. Motivated by this gap, we embed diffusion priors into the OAMP receiver for joint image compression and wireless transmission. The resulting framework uses the diffusion model as a plug-in nonlinear estimator and supports different priors, including DDIM and Flow Matching.
Fig. 1: Overall system diagram of the proposed framework. Left: the source image s is mapped by the joint random compression and multiplexing operator to produce x, then transmitted through a wireless channel corrupted by AWGN. Right: the DiffusionOAMP receiver alternates among an LMMSE estimator, inverse/forward RM transforms between x and s, and a diffusion-model prior to reconstruct the image. Algorithm 1 RM Transmission and Diffusion-OAMP Reception Input: Source image signal s, joint RM-compression operator F, channel A, noise variance σ 2 , DM denoiser ϕ(·, t), maximum iteration number K, tolerance τ . 1: Joint RM and compression: Fs → x 2: Transmission: Ax + n →y 1 mmse 3: Initialization: 0, M ∥y∥22 → (xmmse pri , vpri ) 4: for k = 1, . . . , K do mmse 5: Linear Estimator: (xmmse pri , vpri ) → (xpost , vpost ) orth 6: Orthogonalization: (xpost , vpost ) → (xorth post , vpost ) −1 orth 7: Inverse RM: F xpost → sin orth 8: SNR Matching: vpost → t∗ ∗ 9: NLE: (sin , t ) → ϕ⊥ (sin ) 10: Forward RM: Fϕ⊥ (sin ) → x̃ mmse mmse 11: MMSE Correction: (x̃, xorth post ) → (xpri , vpri ) mmse 12: if relative change of xpri < τ then 13: break 14: end if 15: end for 16: Inverse RM: F−1 xmmse pri → ŝ Output: Reconstructed source signal ŝ
III. D IFFUSION -OAMP A LGORITHM A. Algorithm Overview The overall system consists of an RM transmitter, a wireless channel, and a Diffusion-OAMP receiver. The RM transmitter produces x = Fs, and the wireless channel generates y = Ax + n. The receiver iterates the OAMP linear estimator, inverse RM, SNR matching, diffusion-based nonlinear estimation, forward RM, and MMSE correction until convergence. The complete procedure is summarized in Algorithm 1. B. Diffusion NLE We instantiate the generative prior using two distinct diffusion-based methods, namely DDIM [9] and Flow Matching [11].
DDIM [9] defines a non-Markovian forward process that maps a clean image s0 to a noisy sample: √ √ ϵ ∼ N (0, I), (11) st = ᾱt s0 + 1 − ᾱt ϵ, where ᾱt is a decreasing noise schedule. A neural network ϵθ is trained to predict the added noise. Given st , a deterministic DDIM reverse update can be written as √ st − 1 − ᾱt ϵθ (st , t) √ ŝ0 = , (12) ᾱt p √ (13) st−1 = ᾱt−1 ŝ0 + 1 − ᾱt−1 ϵθ (st , t). Flow Matching (FM) [11] offers a simpler probability path from noise to data: zt = (1 − t) ϵ + t s0 ,
t ∈ [0, 1],
(14)
where a network vθ is trained to regress the transport velocity from the path state zt and time t. Signal recovery is then written as the ODE dzt = vθ (zt , t), z0 = ϵ, z1 = s0 . (15) dt C. Inverse RM and SNR Matching After the OAMP LE and orthogonalization steps, the orthogonalized estimate is mapped back to the source-image domain: sin = F−1 xorth post .
(16)
Since the multiplexing component of F is orthogonal, the AWGN structure is preserved under the inverse RM transform. Hence, q orth ϵ, ϵ ∼ N (0, I), (17) sin = s + vpost which matches the forward corruption model used by the diffusion prior. We select the diffusion time step by matching the effective OAMP error variance to the diffusion noise level: 1 q (Flow Matching), orth 1 + vpost ∗ t = (18) 1 (DDIM). orth 1 + vpost
IV. E XPERIMENTS
Fig. 2: Visualization of the simulated 3GPP TR 38.901 TDL-A channel characteristics. (a) The empirical amplitude distribution of the generated pure NLOS fading channel tightly matches the theoretical Rayleigh distribution. (b) Timeselective fading variations induced by the Doppler effect across 769 consecutive OFDM symbols. The underlying OFDM system is configured with a 3.5 GHz carrier frequency, 30 kHz subcarrier spacing, a 256-point FFT, a cyclic prefix length of 18, and a UE mobility of 30 km/h.
orth As vpost decreases across iterations, t∗ moves toward the clean end of the diffusion trajectory, so the NLE is called on progressively less corrupted observations.
D. MMSE Correction Given t∗ , the NLE evaluates the pre-trained denoiser ϕ(sin , t∗ ) and projects the estimation onto the learned image manifold. To produce an orthogonalized message for the next OAMP iteration, we use Stein’s Unbiased Risk Estimator (SURE) to construct
This section evaluates the proposed Diffusion-OAMP framework across four dimensions: 1) quantitative recovery in pure image compression under ideal AWGN conditions; 2) quantitative recovery in joint compression and transmission over 3GPP TR 38.901 [17] Tapped Delay Line (TDL) fading channels; 3) visual assessments of perceptual fidelity and structural preservation; and 4) convergence performance across successive OAMP iterations. By systematically comparing our approach with baseline methods under diverse compression ratios and noise levels, we validate the framework’s effectiveness in mitigating complex channel distortions. Fig. 3 provides detailed visual comparisons under various degradation cases, including mild, high-noise, and lowcompression settings. These visual results complement the quantitative evaluation, further highlighting the inherent robustness of our Diffusion-OAMP framework. Compared with conventional OAMP+BM3D and DDRM, our variants better preserve facial structures and fine-grained textures. By effectively suppressing over-smoothing, unwanted color shifts, and structural artifacts, the results clearly demonstrate the effectiveness of the proposed model-based diffusion reconstruction scheme. A. Experimental Setup We utilize the CelebA [18] dataset (256 × 256) with a compression ratio defined as β = M/N . The equivalent observation matrix is assumed to be right-unitarily invariant, and AWGN levels are set to σ ∈ {0.05, 0.5}. For the joint compression and transmission scenario, realistic TDLA fading channels are constructed via the Sionna [19] library, with specific OFDM configurations and visual channel characteristics detailed in Fig. 2. B. Quantitative Performance in Pure Image Compression
ϕ⊥ (sin ) = ϕ(sin , t∗ ) − ϕ′ (sin ) sin ,
(19)
′
where the scalar divergence estimate ϕ (sin ) is computed by a single Monte Carlo perturbation with w ∼ N (0, I): ⟨w, ϕ(sin + ϵw, t∗ ) − ϕ(sin , t∗ )⟩ . ϵ→0 ϵ
ϕ′ (sin ) = lim
(20)
The denoised image estimate is then remodulated, x̃ = Fϕ⊥ (sin ),
(21)
and a posterior MMSE correction maps x̃ back to the next mmse prior pair (xmmse pri , vpri ): ∗ xmmse pri = β x̃,
Where β ∗ =
⟨x̃,xorth post ⟩ . ∥x̃∥22
mmse vpri =
1 2 ∥Axmmse pri − y∥2 . M
(22)
Table I summarizes the recovery metrics under ideal AWGN conditions. The proposed Diffusion-OAMP framework, instantiated with DDIM and Flow Matching priors, consistently outperforms traditional baselines such as DDRM [12] and OAMP+BM3D [7] across all evaluated compression ratios (β) and noise levels (σ). Specifically, Diffusion-OAMP (DDIM) achieves the highest PSNR, particularly in high-noise regimes (σ = 0.5). To evaluate sampling efficiency, we further analyze the trade-off between reconstruction quality and the Number of Function Evaluations (NFEs). As illustrated in Fig. 4, Diffusion-OAMP (FM) exhibits rapid convergence, reaching near-optimal PSNR and SSIM within only 6 NFEs. While Diffusion-OAMP (DDIM) requires a higher NFE count to reach its performance plateau, it ultimately yields a higher peak PSNR. Both variants demonstrate enhanced sampling efficiency compared to DDRM, necessitating fewer neural network evaluations to achieve competitive metrics.
Fig. 3: Visual comparison on CelebA over physical TDL-A fading channels under three representative conditions. Case 1 (mild): β = 0.7, σ = 0.05; Case 2 (high-noise): β = 0.4, σ = 0.5; and Case 3 (low-compression): β = 0.1, σ = 0.05. Notably, our proposed Diffusion-OAMP(DDIM) framework consistently preserves high-frequency facial details and identity characteristics, avoiding the severe artifacts or structural distortions evident in baseline methods under harsh regimes. TABLE I: Quantitative results for pure image compression under different compression ratios and AWGN levels. β
Method
σ = 0.05
σ = 0.5
PSNR ↑
SSIM ↑
PSNR ↑
SSIM ↑
0.7
Diffusion-OAMP (DDIM) (ours) Diffusion-OAMP (FM) (ours) OAMP+BM3D [7] DDRM (20) [12] DDRM (50) [12]
33.34 33.18 33.77 31.97 32.88
0.8930 0.9326 0.9160 0.8978 0.9107
25.99 23.92 23.05 24.50 24.85
0.7645 0.7066 0.5996 0.7025 0.7131
0.4
Diffusion-OAMP (DDIM) (ours) Diffusion-OAMP (FM) (ours) OAMP+BM3D [7] DDRM (20) [12] DDRM (50) [12]
32.62 31.69 32.05 28.16 30.17
0.8952 0.9125 0.8854 0.8259 0.8629
24.66 22.83 21.66 22.32 23.24
0.7235 0.6501 0.5438 0.6321 0.6575
0.1
Diffusion-OAMP (DDIM) (ours) Diffusion-OAMP (FM) (ours) OAMP+BM3D [7] DDRM (20) [12] DDRM (50) [12]
30.30 28.38 28.08 17.35 21.02
0.8640 0.8445 0.7856 0.5045 0.6259
21.69 17.70 17.58 15.48 18.00
0.6258 0.4663 0.3783 0.4367 0.5105
C. Quantitative Performance in Joint Image Compression and Wireless Transmission Table II presents the performance averaged over 10 TDLA fading channel realizations. In this scenario, time-selective fading renders the equivalent observation matrix severely illconditioned, leading to noticeable performance degradation for
Fig. 4: Performance trade-off regarding the Number of Function Evaluations (NFEs). (a) PSNR vs. NFEs and (b) SSIM vs. NFEs. Both Diffusion-OAMP (FM) and Diffusion-OAMP (DDIM) exhibit distinct convergence behaviors and enhanced sampling efficiency compared to DDRM.
conventional solvers. In contrast, the Diffusion-OAMP framework maintains stable reconstruction under these complex channel distortions. Specifically, Diffusion-OAMP (DDIM) yields the highest PSNR across most configurations, showing particular effectiveness in the challenging low-compression (β = 0.1) and high-noise (σ = 0.5) case. Diffusion-OAMP (FM) retains competitive structural preservation (SSIM) under milder conditions. These results indicate that embedding generative priors as non-linear estimators within OAMP effectively regularizes
TABLE II: Quantitative results for joint image compression and wireless transmission (averaged over 10 selected TDL-A channels). β
σ = 0.05
Method
σ = 0.5
PSNR ↑
SSIM ↑
PSNR ↑
SSIM ↑
Diffusion-OAMP (DDIM) (ours) Diffusion-OAMP (FM) (ours) OAMP+BM3D [7] DDRM (20) [12] DDRM (50) [12]
33.15 32.85 31.32 31.19 32.41
0.8855 0.9206 0.9106 0.8845 0.9038
25.86 22.04 20.88 24.10 24.48
0.7715 0.4861 0.5468 0.6886 0.7006
0.4
Diffusion-OAMP (DDIM) (ours) Diffusion-OAMP (FM) (ours) OAMP+BM3D [7] DDRM (20) [12] DDRM (50) [12]
32.25 30.86 29.56 27.60 29.74
0.8725 0.8691 0.8795 0.8105 0.8532
24.74 19.98 19.60 21.95 22.75
0.7439 0.3412 0.4850 0.6233 0.6415
0.1
Diffusion-OAMP (DDIM) (ours) Diffusion-OAMP (FM) (ours) OAMP+BM3D [7] DDRM (20) [12] DDRM (50) [12]
29.63 26.66 24.83 16.51 21.05
0.8115 0.7483 0.7295 0.5254 0.6605
21.95 17.39 16.20 14.73 17.40
0.6484 0.2133 0.3392 0.4349 0.5263
0.7
Fig. 5: PSNR convergence across OAMP iterations under (a) pure AWGN and (b) TDL-A channels. Both Diffusion-OAMP variants stabilize within 3 iterations. Final converged PSNRs (DDIM / FM) are 33.15 dB / 28.52 dB in (a), and 29.56 dB / 24.36 dB in (b).
the ill-posed inversion problem induced by fading channels. D. Convergence Performance Figure 5 evaluates the PSNR convergence behavior against the number of outer OAMP iterations under both pure image compression and joint transmission scenarios. The results show that both Diffusion-OAMP (DDIM) and DiffusionOAMP (Flow Matching) demonstrate a rapid initial increase in PSNR, achieving stable convergence within 3 iterations across all evaluated scenarios. This fast convergence behavior verifies the operational efficiency of the proposed framework for iterative image reconstruction. V. C ONCLUSION In this paper, we proposed Diffusion-OAMP, a training-free receiver framework for joint image compression and wireless transmission over practical fading channels. By integrating
pre-trained diffusion models as non-linear estimators to regularize the severely ill-posed inverse problem, the proposed framework significantly outperforms the evaluated baselines. Specifically, it achieves higher image recovery accuracy and maintains stable structural fidelity even under highly illconditioned scenarios, such as low compression ratios and high noise over time-selective fading channels, while exhibiting rapid algorithmic convergence. R EFERENCES [1] Z. Li, Z. Gao, X. Liu, Z. Wang, X. Zhou, L. Liu, Y. Wu, W. Feng, and Y. Huang, “Large model enabled embodied intelligence for 6g integrated perception, communication, and computation network,” arXiv preprint arXiv:2512.15109, 2025. [2] D. L. Donoho, A. Maleki, and A. Montanari, “Message-passing algorithms for compressed sensing,” Proceedings of the National Academy of Sciences, vol. 106, no. 45, p. 18914–18919, Nov. 2009. [Online]. Available: http://dx.doi.org/10.1073/pnas.0909892106 [3] M. Bayati and A. Montanari, “The dynamics of message passing on dense graphs, with applications to compressed sensing,” IEEE Transactions on Information Theory, vol. 57, no. 2, p. 764–785, Feb. 2011. [Online]. Available: http://dx.doi.org/10.1109/TIT.2010.2094817 [4] J. Ma and L. Ping, “Orthogonal amp,” IEEE Access, vol. 5, pp. 2020– 2033, 2017. [5] L. Liu, S. Huang, and B. M. Kurkoski, “Memory amp,” IEEE Transactions on Information Theory, vol. 68, no. 12, pp. 8015–8039, 2022. [6] K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising with block-matching and 3d filtering,” in Image processing: algorithms and systems, neural networks, and machine learning, vol. 6064. SPIE, 2006, pp. 354–365. [7] J. Ma, X. Yuan, and L. Ping, “Turbo compressed sensing with partial dft sensing matrix,” IEEE Signal Processing Letters, vol. 22, no. 2, pp. 158–161, 2015. [8] J. Ho, A. Jain, and P. Abbeel, “Denoising diffusion probabilistic models,” Advances in neural information processing systems, vol. 33, pp. 6840– 6851, 2020. [9] J. Song, C. Meng, and S. Ermon, “Denoising diffusion implicit models,” 2022. [Online]. Available: https://arxiv.org/abs/2010.02502 [10] Y. Song, J. Sohl-Dickstein, D. P. Kingma, A. Kumar, S. Ermon, and B. Poole, “Score-based generative modeling through stochastic differential equations,” arXiv preprint arXiv:2011.13456, 2020. [11] Y. Lipman, R. T. Q. Chen, H. Ben-Hamu, M. Nickel, and M. Le, “Flow matching for generative modeling,” 2023. [Online]. Available: https://arxiv.org/abs/2210.02747 [12] B. Kawar, M. Elad, S. Ermon, and J. Song, “Denoising diffusion restoration models,” Advances in neural information processing systems, vol. 35, pp. 23 593–23 606, 2022. [13] Y. Wang, J. Yu, and J. Zhang, “Zero-shot image restoration using denoising diffusion null-space model,” in The Eleventh International Conference on Learning Representations, 2023. [Online]. Available: https://openreview.net/forum?id=mRieQgMtNTQ [14] S. Martin, A. Gagneux, P. Hagemann, and G. Steidl, “Pnp-flow: Plug-and-play image restoration with flow matching,” 2025. [Online]. Available: https://arxiv.org/abs/2410.02423 [15] C. Cai, X. Yuan, and Y.-J. A. Zhang, “Score-based turbo message passing for plug-and-play compressive image recovery,” in 2025 IEEE 26th International Workshop on Signal Processing and Artificial Intelligence for Wireless Communications (SPAWC), 2025, pp. 1–5. [16] L. Liu, Y. Chi, S. Huang, and Z. Zhang, “Random multiplexing,” IEEE Transactions on Information Theory, vol. 72, no. 4, pp. 2277–2306, 2026. [17] 3GPP, “Study on channel model for frequencies from 0.5 to 100 GHz,” 3rd Generation Partnership Project (3GPP), Technical Report (TR) 38.901, Apr. 2022, version 17.0.0, Release 17. [18] Z. Liu, P. Luo, X. Wang, and X. Tang, “Deep learning face attributes in the wild,” in Proceedings of International Conference on Computer Vision (ICCV), December 2015. [19] J. Hoydis, S. Cammerer, F. A. Aoudia, A. Vem, N. Binder, G. Marcus, and A. Keller, “Sionna: An open-source library for next-generation physical layer research,” arXiv preprint arXiv:2203.11854, 2022.