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SpaceDiffusion: Over-the-Orbit Diffusion for Space Generate-and-Forward Communications
Jianhao Huang, Zhanwei Wang, Khaled B. Letaief, Kaibin Huang
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 95%
Last extracted: 9/21/2026, 3:46:27 AM
Summary
This paper proposes SpaceDiffusion, a novel over-the-orbit diffusion framework for satellite-assisted image transmission within 6G networks. It introduces a 'generate-and-forward' (GF) relaying paradigm where satellites use on-orbit generative AI to reconstruct corrupted or lost image tokens before forwarding them, overcoming the uplink bottleneck caused by limited ground device power. The core innovation is a channel-distortion-aware diffusion theory that integrates a correction term into the Denoising Diffusion Implicit Model (DDIM) to adapt to packet loss and compression without retraining. The study also derives a diffusion-step activation threshold and an energy-aware early-exit policy to optimize performance under orbital energy constraints. Experiments show SpaceDiffusion reduces end-to-end latency by up to 40% and saves approximately 15 dB of uplink transmit power compared to conventional decode-and-forward schemes with retransmission.
Entities (9)
Relation Signals (8)
Satellite Communications → iscomponentof → 6G
confidence 99% · Satellite communications are an essential component of sixth-generation (6G) mobile networks
SpaceDiffusion → implements → Generate-and-Forward
confidence 98% · Specifically, we propose SpaceDiffusion, an over-the-orbit diffusion framework for satellite-assisted image transmission... advocates a novel relaying paradigm termed generate-and-forward (GF) communications
SpaceDiffusion → reduces → End-to-end latency
confidence 95% · SpaceDiffusion achieves lower end-to-end latency compared to DF scheme with retransmission protocol
SpaceDiffusion → saves → uplink transmit power
confidence 95% · saves approximately 15 dB of uplink transmit power at a target perceptual quality
SpaceDiffusion → uses → DDIM
confidence 95% · incorporates a channel-distortion correction term directly into the conventional denoising diffusion implicit model (DDIM) update
SpaceDiffusion → outperforms → Decode-and-Forward
confidence 92% · predicts when SpaceDiffusion is expected to outperform conventional decode-and-forward (DF) relaying
SpaceDiffusion → validatedon → AFHQ
confidence 90% · Extensive experiments on the real-world AFHQ and Kodak image datasets validate SpaceDiffusion
SpaceDiffusion → →
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Abstract
Abstract:Satellite communications are an essential component of sixth-generation (6G) mobile networks, which provide ubiquitous connectivity for global services. However, the satellite uplink remains a critical bottleneck for ground devices: their limited transmit power and antenna apertures result in low data rates and high packet errors. To overcome this bottleneck, this paper advocates a novel relaying paradigm termed generate-and-forward (GF) communications, where satellites exploit on-orbit generative artificial intelligence (AI) to robustly reconstruct corrupted data prior to forwarding. Specifically, we propose SpaceDiffusion, an over-the-orbit diffusion framework for satellite-assisted image transmission. The core of this framework is a channel-distortion-aware diffusion theory developed using the following approach. By formulating the recovery of compressed and lost image tokens as an inverse problem, this theory incorporates a channel-distortion correction term directly into the conventional denoising diffusion implicit model (DDIM) update. As a result, this design enables a single pretrained diffusion model to adapt dynamically to varying packet-loss patterns and compression distortions without retraining. Furthermore, we analytically characterize the progressive token-reconstruction error and derive a diffusion-step activation threshold that predicts when SpaceDiffusion is expected to outperform conventional decode-and-forward (DF) relaying. Building on these theoretical insights, we further develop an energy-aware early-exit policy to efficiently deploy SpaceDiffusion in orbit. Experimental results demonstrate that SpaceDiffusion achieves lower end-to-end latency compared to DF scheme with retransmission protocol and saves approximately 15 dB of uplink transmit power at a target perceptual quality.
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- Source: https://arxiv.org/abs/2609.20899v1
- Canonical: https://arxiv.org/abs/2609.20899v1
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SpaceDiffusion: Over-the-Orbit Diffusion for Space Generate-and-Forward Communications Jianhao Huang Zhanwei Wang Khaled B. Letaief and Kaibin Huang †thanks: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.†thanks: J. Huang, Z. Wang, and K. Huang are with the Department of Electrical and Computer Engineering, The University of Hong Kong (HKU), Hong Kong SAR, China (Email: Jianhaoh@hku.hk, zhanweiw, huangkb@e.hku.hk). Corresponding author: K. Huang.†thanks: Khaled B. Letaief is with the Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology (HKUST), Hong Kong SAR, China (Email: eekhaled@ust.hk). Abstract Satellite communications are an essential component of sixth-generation (6G) mobile networks, which provide ubiquitous connectivity for global services. However, the satellite uplink remains a critical bottleneck for ground devices: their limited transmit power and antenna apertures result in low data rates and high packet errors. To overcome this bottleneck, this paper advocates a novel relaying paradigm termed generate-and-forward (GF) communications, where satellites exploit on-orbit generative artificial intelligence (AI) to robustly reconstruct corrupted data prior to forwarding. Specifically, we propose SpaceDiffusion, an over-the-orbit diffusion framework for satellite-assisted image transmission. The core of this framework is a channel-distortion-aware diffusion theory developed using the following approach. By formulating the recovery of compressed and lost image tokens as an inverse problem, this theory incorporates a channel-distortion correction term directly into the conventional denoising diffusion implicit model (DDIM) update. As a result, this design enables a single pretrained diffusion model to adapt dynamically to varying packet-loss patterns and compression distortions without retraining. Furthermore, we analytically characterize the progressive token-reconstruction error and derive a diffusion-step activation threshold that predicts when SpaceDiffusion is expected to outperform conventional decode-and-forward (DF) relaying. Building on these theoretical insights, we further develop an energy-aware early-exit policy to efficiently deploy SpaceDiffusion in orbit. Experimental results demonstrate that SpaceDiffusion achieves lower end-to-end latency compared to DF scheme with retransmission protocol and saves approximately 1515 dB of uplink transmit power at a target perceptual quality. Index Terms: Satellite communications, generative artificial intelligence, generate-and-forward, diffusion models. I Introduction Satellite communications are envisioned as an essential component of sixth-generation (6G) mobile networks, which enable ubiquitous coverage for global services such as artificial intelligence (AI), immersive Internet of Things (IoT), and multimedia access [1, 2, 3, 4, 5]. In conventional architectures, satellites are often regarded as spaceborne extensions of terrestrial relaying nodes, and their primary role is to receive and forward information between ground terminals [4]. However, this relay-centric design faces inherent limitations in satellite uplinks due to long propagation distances, Doppler shifts, and limited transmit power of ground devices. To address the issue, fixed ground terminals have been provisioned with high-gain antennas, advanced beamformers, and higher-frequency spectrum resources, such as Ku- and Ka-band [6, 4]. However, these solutions are impractical for IoT and handheld devices as they are constrained by battery capacity, hardware complexity, and antenna size [7]. As a result, the low uplink transmission rates (typically ranging from a few to tens of Kbps for low-power devices) remain a critical bottleneck for bandwidth-demanding multimedia services [7, 8]. Recent advances in space AI and on-orbit computing have been transforming satellites from passive forwarding nodes into intelligent information-processing centers [9, 10, 11]. For example, several on-orbit AI computing platforms, such as Starcloud-1 [10] and the Three-Body Computing Constellation [11], have already been launched. This paradigm shift opens new opportunities to reduce the need of high-throughput uplink transmission by enabling on-orbit generative data recovery. Fig. 1: Comparison of the satellite generate-and-forward scheme with the conventional decode-and-forward scheme. For satellite communications with limited-power devices, the downlink capacity (on the order of Mbps) is much larger than the uplink capacity (on the order of Kbps) [12]. Under this uplink bottleneck, conventional satellite systems typically rely on either transparent or regenerative architectures to support reliable transmission [6, 13]. On one hand, the transparent architecture adopts the low-complexity amplify-and-forward (AF) scheme, where the satellite directly forwards the received signals after power amplification and frequency conversion [6, 4]. On the other hand, the regenerative architecture is based on the decode-and-forward (DF) scheme, where the satellite performs onboard channel decoding and re-encoding, thereby mitigating error propagation [6, 13]. Nevertheless, both architectures still depend on accurate bit-level delivery over the uplink. When packets are corrupted or fail to decode, acknowledgement (ACK)/negative acknowledgement (NACK) feedback and retransmission are required to recover the lost information [14, 13]. Due to the long round-trip time (RTT) of satellite links, such feedback-based retransmission mechanisms can significantly increase end-to-end (E2E) latency. Existing studies attempt to mitigate RTT-induced stalling through enhanced retransmission scheduling, advanced forward error correction, and increasing the number of parallel hybrid automatic repeat request (HARQ) processes [13]. However, these methods still operate within the feedback-based retransmission paradigm and thus cannot fundamentally overcome the mentioned limitations. This necessitates a paradigm shift from accurate bit delivery to more efficient AI-empowered data recovery. Recently, generative AI (GenAI) has achieved remarkable success in data recovery from low-dimensional prompts [15, 16, 17]. Motivated by this capability, existing studies have introduced GenAI into terrestrial communication networks to improve transmission efficiency and robustness against channel impairments [18, 19, 20, 21]. The communication efficiency can be improved by converting source data into low-dimensional feature or token domain for transmission, followed by generative recovery at the receiver. For example, transformer-based foundation models have been used to reconstruct latent tokens lost to packet erasures [18, 19], while diffusion models have been used to iteratively impute missing features for error-resilient transmission [20]. These generative techniques can be easily extended to satellite communications by treating the satellite as a conventional relay node. A representative example involves deploying a foundation model at the ground gateway to recover corrupted features forwarded by the satellite [21, 22]. However, such generative strategy falls short on exploiting satellite computation resources to overcome the uplink bottleneck. Moreover, when key features are lost, gateway-side recovery requires an additional uplink and downlink retransmission cycle, which substantially increases the latency. With the advancement in space AI computing, satellites can perform generative data processing on-orbit before forwarding [12, 23]. This alleviates the burden on resource-constrained uplink transmission. We refer to this new relaying paradigm as the generate-and-forward (GF) scheme, as illustrated in Fig. 1. The GF scheme leverages GenAI to recover missing features/tokens or lost information caused by packet error, rate control, or source compression under low-rate uplink transmissions. Consequently, the generated data allows the flexibility of having more detailed representations than the transmitted one. The resultant increased forwarding payload can be supported by leveraging the asymmetric uplink-downlink capacities and relaxing the conventional uplink-downlink rate-matching constraint. However, the realization of GF scheme in the satellite system faces two new challenges. The first is the design of efficient generative algorithms tailored to satellite communications. Existing generative models are predominantly data-driven and may not generalize well to dynamic satellite channel environments [16, 15]. The second is the deployment of potentially power-hungry GenAI algorithms on energy-constrained satellites, where the available energy harvested from solar power varies with orbital dynamics and illumination conditions. In this paper, we address these challenges by proposing SpaceDiffusion, a novel over-the-orbit diffusion framework for space-based GF image transmission. The techniques in the framework alleviate the uplink bottleneck by enabling the satellite to recover highly compressed and partially erased image tokens on board. The main contributions and findings of this study are summarized as follows. • Channel-distortion-aware diffusion theory: We formulate the problem of satellite token recovery under packet loss and lossy source compression as an inverse problem. Based on this model, we derive a posterior-based reverse-time stochastic differential equation (SDE) that progressively recovers clean tokens from Gaussian noise. The core of the derived SDE is the posterior score function that decomposes into a data-distribution term and a channel-distortion term determined by the packet-loss mask and source-compression noise covariance. By exploiting this additive decomposition, we develop a channel-distortion-aware denoising diffusion implicit model (DDIM) algorithm that inserts the channel-distortion term as a plug-in correction to the conventional DDIM update. This enables a single pre-trained diffusion model to adapt to varying satellite channel conditions without retraining. • Diffusion performance analysis: We analyze the progressive performance of the proposed channel-distortion-aware DDIM as the reverse-step index t decreases from T to 00, where T is the maximum reverse-step index. Leveraging the pseudo-inverse Gaussian approximation and the forward diffusion relation, we derive an approximate upper bound on the token-domain mean-squared error (MSE) at each step. Based on this bound and the progressive denoising property of reverse diffusion [15, 24], we further derive a diffusion-step threshold that predicts the minimum number of reverse steps required for SpaceDiffusion to outperform conventional DF relaying. • Energy-aware diffusion-step optimization: Based on the derived threshold, we formulate an optimization problem that maximizes the number of executable reverse diffusion steps under energy and latency constraints. By solving this problem, we derive a closed-form early-exit policy that activates on-board generation only when the available energy and time are sufficient to reach the diffusion step threshold; otherwise, the satellite falls back to DF relaying to avoid ineffective diffusion computation. • Experimental results: Extensive experiments on the real-world AFHQ and Kodak image datasets validate SpaceDiffusion under diverse channel and orbital conditions. Compared with a DF baseline employing retransmission, SpaceDiffusion reduces E2E latency by up to 40%40\% in LEO. In addition, SpaceDiffusion requires about 1515 dB less uplink transmit power than the non-generative compression baseline to achieve the same perceptual quality. This power efficiency makes it well suited to satellite applications, such as IoT connectivity over non-terrestrial networks (NTNs). Experiments across different orbital configurations further show that orbital illumination strongly affects the number of executable diffusion steps, while the proposed energy-aware policy adapts onboard generation to the available resources and consistently outperforms the no-generation baseline. The remainder of this paper is organized as follows. Section I gives an overview of the satellite GF communications. Section I presents the system blocks and problem formulations. Section IV develops the proposed posterior-based diffusion theory and the algorithm. Section V studies optimal diffusion steps under satellite energy limitations. Section VI provides experimental results, and Section VII concludes this paper. I Overview of Satellite Generate-and-Forward Communications Consider a satellite GF system, where a ground device uploads data to a satellite, and the satellite performs on-board generative recovery before forwarding the information to a ground device/station. The satellite is equipped with a GenAI-enabled module to reconstruct high-fidelity data from corrupted inputs due to poor satellite uplink transmissions. Specifically, the overall operation workflow consists of four sequential stages. 1. Tokenization: Let X denote the source data to be transmitted. At the transmitter, the semantic encoder Fϕ(⋅)F_ φ(·) transforms X into a token representation ∈ℝK×D,Y ^K× D, where K denotes the number of tokens and D is the token dimension. The token representation Y is then quantized and source-coded into bit streams. 2. Uplink transmission: The compressed token bitstream is interleaved and packetized into a sequence of fixed-length packets for transmission. Due to the poor satellite channel conditions and limited bandwidth, uplink transmission suffers from high compression and packet losses. 3. Over-the-orbit token generation: After uplink reception and decoding, the satellite obtains a distorted token representation ~∈ℝK×D, Y ^K× D, in which some tokens are correctly received while others are missing due to packet loss. We propose an over-the-orbit generation module G(⋅)G_ (·) to recover the corrupted tokens directly in the latent space to obtain ¯ Y. 4. Downlink forwarding: After the generation process, the satellite re-encodes and forwards the recovered information to the destination ground user through the downlink. The destination user reconstructs the image through a semantic decoder D(⋅)D_ ψ(·). In the following section, we elaborate on the above four stages in detail and then discuss the main challenges of the GF communication system. Fig. 2: The framework of the Satellite GF system I System Model and Problem Formulation In this section, we present the system model of the GF system and introduce its main problems. Here, we take image transmission as an example, but the proposed framework can be extended to other data types, such as video and audio, as shown in Fig. 2. I-A Tokenization I-A1 Token Representation For a given source image ∈ℝH×W×3X ^H× W× 3, the transmitter employs a neural network-based encoder Fϕ(⋅)F_ φ(·) to directly map the image into a token representation, i.e., =Fϕ()∈ℝK×D.Y=F_ φ(X) ^K× D. (1) The token representation can be written as =[1,2,…,K].Y= [y_1,y_2,…,y_K ] T. (2) Here, n∈ℝDy_n ^D denotes the n-th token, which represents a local latent patch of the source image. Tokenization converts the image into a sequence of local features, thereby reducing pixel-level redundancy and enabling efficient compression and packetization [18]. This local token representation is also well suited for the diffusion model in Section IV. I-A2 Digital Source Coding Due to the limited uplink bandwidth, the token representation Y needs to be compressed in a lossy manner before transmission. The design of an efficient lossy source coder generally requires knowledge of the token distribution. However, the exact distribution of Y is difficult to characterize due to the intractable image distribution and the nonlinear semantic encoder. To facilitate tractable source-coding design, we assume that the tokens are independent and identically distributed (i.i.d.) and that each token ny_n approximately follows a multivariate Gaussian distribution11 1 This Gaussian approximation is introduced only for the source coding design in this subsection. It is not assumed in the later diffusion-based recovery process, where the accuracy of token prior plays a critical role in the reconstruction quality., i.e., n∼(,),y_n ( μ, ), (3) where ∈ℝD μ ^D and ∈ℝD×D ^D× D denote the mean vector and covariance matrix estimated from training samples. The covariance matrix captures the statistical correlations among token components. Here, we adopt linear transform coding [25] to encode the correlated Gaussian sources, as it naturally exploits their second-order correlation structure while retaining low implementation complexity. Moreover, it allows the source coding rate to be conveniently adapted to the uplink channel conditions by adjusting the quantization resolution. Specifically, the eigendecomposition of the covariance matrix is =, =U U T, where U is orthogonal and =diag(λ1,λ2,…,λD) =diag( _1, _2,…, _D) contains the eigenvalues. Each token is decorrelated as n=(n−),z_n=U T(y_n- μ), where n=[zn,1,…,zn,D]z_n=[z_n,1,…,z_n,D] T. Each coefficient is uniformly quantized [26] as z^n,k=Δk⌊zn,kΔk+12⌋, z_n,k= _k z_n,k _k+ 12 , (4) where ⌊⋅⌋ · is the floor operator and Δk=λks, _k= _ks, with s>0s>0 controlling the quantization resolution. Huffman coding [27] then encodes each value using approximately Bn,k≈−log2Pk(z^n,k),B_n,k≈- _2P_k( z_n,k), bits, where PkP_k is the probability mass function. After entropy decoding, the inverse transform gives ^n=^n+. y_n=U z_n+ μ. According to (4), we have ^n=n+n, y_n=y_n+q_n, (5) where n=nq_n=Ue_n and n=^n−ne_n= z_n-z_n is the quantization error. For sufficiently large D, the Central Limit Theorem [28] gives n∼(,q)q_n (0, _q), where q=diag(Δ1212,…,ΔD212)=112s2. _q=Udiag\! ( _1^212,…, _D^212 )U T= 112s^2 . (6) I-B Uplink Transmissions After tokenization and source coding, the compressed bitstream is transmitted from the ground device to the relay satellite. I-B1 Interleaving & Packetization Denote the source-coded bitstream of an image as =1,2,…,Kb=\b_1,b_2,…,b_K\, where nb_n is the compressed bit sequence of the n-th token. To mitigate the impact of burst errors during transmission, an interleaving operation is applied to the sequence. Defined by a permutation π(⋅)π(·), the interleaved bitstream is π=π(1),π(2),…,π(K)b^π=\b_π(1),b_π(2),…,b_π(K)\. After interleaving, the tokens are assembled into fixed-length packets of length LpL_ p. Each packet comprises a header of length LhL_h and a payload of length Lpay=Lp−LhL_pay=L_ p-L_h. To prevent error propagation [29], each token’s bitstream is treated as an indivisible unit, meaning a token cannot be fragmented across multiple packets. If the allocated token bits are less than the payload capacity, the packet is simply padded with zeros. Let ℐmI_m denote the ordered set of token indices allocated to the m-th packet. The m-th packet is constructed as m=[m,π(i1),…,π(ik), 0],p_m= [h_m,\,b_π(i_1),\,…,\,b_π(i_k),\,0 ], (7) where mh_m is the header, ik∈ℐmi_k _m, and 0 denotes zero-padding bits. The header carries the control information required for token reconstruction, including the ordered token indices, and the padding length. Accordingly, the final packet sequence is denoted by =1,2,…,MP=\p_1,p_2,…,p_M\, where M denotes the total number of packets. I-B2 Channel Coding Each packet is channel-coded as m=(m)∈ℂLc,c_m=C(p_m) ^L_c, (8) where (⋅)C(·) is the encoder and LcL_c is the block length. The code rate is ru=LpLc.r_ u= L_ pL_c. Thus, the uplink bit rate over bandwidth B is Ru=Bru.R_ u=Br_ u. I-B3 Uplink Model Consider a block fading channel model [8], where the received signal at the satellite for packet m is given by m=hmpum+m,r_m=h_m p_u\,c_m+w_m, (9) where pup_u is the transmit power, hmh_m is the channel coefficient, and m∼(,σ2)w_m (0,σ^2I) is additive noise. The channel is decomposed as hm=ℓmgm,h_m= _m\,g_m, where ℓm _m is the large-scale gain and gmg_m is the Rician fading coefficient. The former is ℓm=GtGrLfs(dm,fc)ξm, _m= G_tG_rL_fs(d_m,f_c) _m, (10) where GtG_t and GrG_r are the antenna gains, dmd_m is the propagation distance, fcf_c is the carrier frequency, LfsL_fs is the free-space path loss, and ξm _m captures additional attenuation. The received SNR is γm=pu|hm|2σ2. _m= p_u|h_m|^2σ^2. With block length LcL_c, the decoding error probability is approximated by [30] ρm≈Q(Lc(C(γm)−ru)V(γm)), _m≈ Q\! ( L_c (C( _m)-r_ u ) V( _m) ), (11) where C(γm)=log2(1+γm)C( _m)= _2(1+ _m), V(γm)=(1−(1+γm)−2)(log2e)2V( _m)= (1-(1+ _m)^-2 )( _2e)^2, and Q(⋅)Q(·) denote the channel capacity, channel dispersion, and Gaussian Q-function, respectively. I-C Over-the-Orbit Token Generation After receiving the uplink signals, the satellite performs demodulation and channel decoding to recover the transmitted packets. By collecting all decoded packets and performing depacketization, deinterleaving, and source decoding, the satellite obtains a distorted token representation, denoted by ~=[~1,~2,…,~K]∈ℝK×D. Y= [ y_1, y_2,…, y_K ] T ^K× D. (12) Due to the severe channel impairments in satellite communications, some packets may be decoded incorrectly or lost entirely. The lost tokens are replaced by an all-zero vector. Equivalently, the distorted token representation can be modeled as ~=⊙^, Y=A Y, (13) where ∈0,1K×DA∈\0,1\^K× D is the error mask matrix indicating the positions of lost tokens and ⊙ denotes the Hadamard product. Specifically, if the n-th token is lost, then the n-th row of A is an all-zero vector; otherwise, it is an all-one vector. Since the packet loss is determined by the channel decoding outcome, the error mask A can be obtained at the satellite through channel decoding and a cyclic redundancy check (CRC) [31]. Based on the received signal ~ Y, we design the generation module to recover the corrupted tokens, yielding ¯=G(~,), Y=G_ \! ( Y,A ), (14) I-D Downlink Forwarding Transmissions After the generation process, the satellite forwards the recovered token representation ¯ Y to the destination ground device. Let Rs,dlR_s,dl denote the average source bit length for encoding ¯ Y. The coding process is the same as the uplink process. Different from the uplink, where limited transmit power and antenna gain make token losses critical, the downlink is considered to operate at a sufficiently high transmission rate with a low packet-error rate [6]. Therefore, the downlink rate (bits/s) is modeled by the Shannon capacity Rd=Bdllog2(1+γdl),R_ d=B_dl _2(1+ _dl), (15) where BdlB_dl denotes the downlink bandwidth and γdl _dl is the received downlink signal-to-noise ratio. After receiving the downlink bitstream, the destination ground user performs entropy decoding and token reconstruction to recover the token representation. Let ˘∈ℝK×D Y ^K× D denote the finally received token representation at the user side. The reconstructed image is then obtained through the semantic decoder D(⋅)D_ ψ(·) as ^=D(˘). X=D_ ψ( Y). (16) I-E Problem Formulation Designing the satellite GF system gives rise to two major problems. I-E1 Token Generation as an Inverse Problem According to (5) and (13), the token representation received at the satellite can be modeled as ~=⏟packet loss⊙(+⏟compression loss). Y= A_ loss (Y+ Q_ loss ). (17) Accordingly, the received tokens are corrupted by channel-induced packet loss and source-compression loss. Given A and the covariance matrix of Q, recovering Y from ~ Y becomes an ill-posed inverse problem [32]. Conventional methods, such as Bayesian-based restoration [32], require an accurate prior model of the token distribution; otherwise, their performance can degrade substantially. This motivates the use of diffusion models, which learn the token distribution directly from training data. However, conventional diffusion-based methods, such as diffusion posterior sampling (DPS) [17], are primarily designed for image-domain inverse problems such as inpainting and do not account for the specific characteristics of token representations in satellite systems. I-E2 On-Board Deployment Under Energy Limitation The on-board deployment of generation models remains challenging for satellite systems. Satellites are subject to stringent constraints on computational resources due to limited solar energy harvesting. Therefore, the design of the generation models must balance performance, computational complexity, and energy resources. This issue will be discussed in detail in Section V. IV Channel-distortion-aware Diffusion Theory In this section, we derive a channel-distortion-aware diffusion theory by solving the inverse problem in (17). First, we introduce the corresponding SDE and then present the solution algorithm. Then, we present the performance analysis by benchmarking against the DF scheme. IV-A Channel Posterior-based SDE The core idea of diffusion theory is to define a forward process that gradually perturbs a clean data into isotropic Gaussian noise, and then learn a reverse process that progressively removes the noise. To solve the inverse problem in (17), the reverse process is further developed to generate the desired data not only from noise but also conditioned on the received measurement ~ Y. Specifically, the forward process can be defined by Itô SDE [24]: dt=−α(t)2tdt+α(t)dt,dY_t=- α(t)2Y_tdt+ α(t)dW_t, (18) where t∈ℝK×DW_t ^K× D is the standard Wiener process [24] and α(t)>0α(t)>0 is the noise schedule of the process. When t=0t=0, 0=∼p()Y_0=Y p(Y). When t=Tt=T and T is sufficiently large, the data is overwhelmed by Gaussian noise, i.e., T∼(,)Y_T (0,I). Then, the reverse process iteratively generates the clean data from both the Gaussian noise and ~ Y, which follows the Itô reverse SDE [24]: dt= dY_t= [−α(t)2t−α(t)∇tlogpt(t∣~;,q)]dt [- α(t)2Y_t-α(t) _Y_t p_t(Y_t Y;A, _q) ]dt +α(t)d¯t, + α(t)d W_t, (19) where ¯t∈ℝK×D W_t ^K× D is the standard Wiener process [24] and pt(t|~;,q)p_t(Y_t| Y;A, _q) is the probability density function (PDF) of tY_t conditioned on ~ Y with A and q _q. Note that ∇tlogpt(t∣~;,q) _Y_t p_t(Y_t Y;A, _q) is known as the posterior-based score function, which points toward the direction how a noisy sample can be closer to the data sample. By Bayesian rule [28], the score function can be written as ∇tlogpt(t|~;,q)= _Y_t p_t(Y_t| Y;A, _q)= ∇tlogpt(t) _Y_t p_t(Y_t) +∇tlogpt(~∣t;,q) + _Y_t p_t( Y _t;A, _q) (20) The first term is the prior score, which can be approximated by a pre-trained score network ∇tlogpt(t)≈(t,t) _Y_t p_t(Y_t) _ (Y_t,t) with parameter . The main challenge is to characterize the PDF pt(~∣t;,q)p_t( Y _t;A, _q). For notation simplicity, we omit ,q\A, _q\ in the PDFs. By Bayes’ rule, pt(~∣t)p_t( Y _t) can be factorized as pt(~∣t) p_t( Y _t) =∫pt(~,∣t) = p_t( Y,Y _t)\,dY =∫pt(∣t)p(~∣). = p_t(Y _t)\,p( Y )\,dY. (21) The conditional PDF pt(∣t)p_t(Y _t) is intractable. Hence, we adopt a pseudo-inverse Gaussian approximation [33]: pt(∣t)≈(ˇt,rt2K×D), p_t(Y _t) ( Y_t,r_t^2I_K× D), (22) where ˇt≜(∣t), Y_t (Y _t), and rt>0r_t>0 is a time-dependent parameter of the Gaussian approximation. Moreover, p(~∣)p( Y ) can be directly obtained from the inverse model in (17). Based on these models, we have the following proposition. Proposition 4.1 (Channel Posterior-based Score Function). For the inverse problem in (17) with given ,q\A, _q\, the posterior-based score function can be approximated as ∇tlogpt(t∣~)≈(t,t)+unvec(t⊤vec(t))⏟≜ℒt, _Y_t p_t(Y_t Y) _ (Y_t,t)+ unvec\! (J_t vec(G_t) )_ _t, (23) where vec(⋅)vec(·) and unvec(⋅)unvec(·) denote the vectorization and unvectorization operations, respectively, t≜∂vec(ˇt)∂vec(t),J_t ( Y_t) (Y_t), denotes the vectorized Jacobian matrix of ˇt Y_t w.r.t. tY_t, and t≜⊙((~−ˇt)(rt2D+q)−1). _t (( Y- Y_t)(r_t^2I_D+ _q)^-1 ). (24) Proof: Please see Appendix A. ∎ Based on the score function in Proposition 4.1, the reverse SDE in (19) can be solved by generic stochastic samplers, such as Euler–Maruyama algorithm [34]. However, these methods usually require many steps with repeated random perturbations, resulting in high computational cost and unstable reconstruction quality. IV-B Channel-distortion-aware DDIM Algorithm In this subsection, we resort to an efficient discretization algorithm, namely, the DDIM sampler [15], to solve the SDEs in (18) and (19). Compared with generic stochastic samplers, DDIM provides more stable reconstruction quality while requiring only a small number of sampling steps. We discretize time into a total of T steps, where t∈0,1,…,Tt∈\0,1,…,T\ denotes the discrete step index. We then present the forward and reverse processes in detail. IV-B1 Forward process After discretization, the forward process at step t is given by t=α¯t0+1−α¯tϵt,ϵt∼(,K×D),Y_t= α_t\,Y_0+ 1- α_t\, ε_t, ε_t (0,I_K× D), (25) where α¯t∈(0,1] α_t∈(0,1] is a predesigned cumulative noise schedule [15]. Fig. 3: Illustration of the proposed posterior-based Diffusion theory. (a) Comparison of the reverse process with and without the plug-in term ℒtL_t. (b) Computational flow of the reverse process of the plug-and-play DDIM algorithm. IV-B2 Reverse process with plug-in term In the reverse process, the goal is to predict the data sample t−1Y_t-1 from the noisy sample tY_t and the measurement ~ Y. Essentially, this is equivalent to learning the conditional probability p(t−1∣t,~)p_ (Y_t-1 _t, Y), where denotes the deep neural network (DNN) parameters. According to the conventional DDIM update [15], we propose to model p(t−1∣t,~)p_ (Y_t-1 _t, Y) as (t−1,α¯t−1^tpost+1−α¯t−1−σt2ϵ^,t,σt2K×D), \! (Y_t-1;\, α_t-1 Y^post_t+ 1- α_t-1- _t^2\, ε_ ,t,\, _t^2I_K× D ), (26) where ^tpost≜(∣t,~) Y^post_t (Y _t, Y) is the posterior mean, and σt2 _t^2 is a variance parameter that controls the randomness of the reverse process. It is usually set close to zero for stable sampling. Here, ϵ^,t(t,t) ε_ ,t(Y_t,t) is the noise predictor. It is implemented by a U-Net [16] and trained by minimizing the following MSE loss: min0,t,ϵ[‖ϵt−ϵ^(t,t)‖22], _ \;E_Y_0,t, ε [ \| ε_t- ε_ (Y_t,t) \|_2^2 ], (27) where tY_t is generated according to (25). The noise predictor is related to the score function by (t,t)≈−ϵ^,t1−α¯t.S_ (Y_t,t)≈- ε_ ,t 1- α_t. In (26), the posterior mean can be calculated as ^tpost Y^post_t =(a)1α¯t(t+(1−α¯t)∇tlogpt(t∣~)) (a)= 1 α_t (Y_t+(1- α_t) _Y_t p_t(Y_t Y) ) ≈(b)1α¯t(t+(1−α¯t)(t,t)+(1−α¯t)ℒt) (b)≈ 1 α_t (Y_t+(1- α_t)S_ (Y_t,t)+(1- α_t)L_t ) =1α¯t(t+(1−α¯t)(t,t))+1−α¯tα¯tℒt = 1 α_t (Y_t+(1- α_t)S_ (Y_t,t) )+ 1- α_t α_tL_t =(c)ˇt+1−α¯tα¯tℒt. (c)= Y_t+ 1- α_t α_tL_t. (28) where (a)(a) follows by applying Tweedie’s approach [15] into posterior mean calculations, (b)(b) follows from Proposition 4.1, and (c)(c) uses the ˇt≜(∣t)=1α¯t(t+(1−α¯t)(t,t)) Y_t (Y _t)= 1 α_t (Y_t+(1- α_t)S_ (Y_t,t) ) from Tweedie’s formula [15]. Further, according to the score-noise relation, we have ˇt≈1α¯t(t−1−α¯tϵ^,t). Y_t≈ 1 α_t (Y_t- 1- α_t\, ε_ ,t ). (29) According to the reverse conditional model in (26), for each reverse step t→t−1t→ t-1, t−1Y_t-1 can be written as t−1 _t-1 =α¯t−1^tpost+1−α¯t−1−σt2ϵ^,t+σtt, = α_t-1 Y^post_t+ 1- α_t-1- _t^2\, ε_ ,t+ _tz_t, (30) where t∼(,K×D)z_t (0,I_K× D). Substituting (28) into (30) yields t−1=t−1ddim⏟Direction to p()+ηtℒt⏟Direction based on channel distortion,Y_t-1= Y^ddim_t-1_ to p(Y)+ _tL_t_ based on channel distortion, (31) where ηt=ηα¯t−1(1−α¯t)/α¯t _t=η α_t-1(1- α_t)/ α_t and t−1ddim=α¯t−1ˇt+1−α¯t−1−σt2ϵ^,t+σtt.Y^ddim_t-1= α_t-1 Y_t+ 1- α_t-1- _t^2\, ε_ ,t+ _tz_t. Here, we introduce a parameter η>0η>0 to control the strength of the channel distortion correction. From (31), the first term is exactly the conventional DDIM step [15], which drives the sample toward the data distribution, whereas the second term is a channel-aware correction term determined by the received signal ~ Y and the channel condition. Note that in the proposed DDIM algorithm, the posterior correction ℒtL_t is directly inserted into the reverse update in (31) without additional training. IV-C Performance Analysis In this subsection, we analyze the performance of the proposed DDIM algorithm as the reverse step index t decreases from T to 00. Denote δt≜ηα¯t−1(1−α¯t)α¯t. _t η α_t-1(1- α_t) α_t. Then, we calculate the reconstruction error at each reverse step: ℰt−1≜[‖t−1−‖F2].E_t-1 \! [ \|Y_t-1-Y \|_F^2 ]. (32) The expectation is taken over the diffusion noise, image token Y, the error mask A and the compression noise Q. The error mask A is caused by channel impairments and is determined by packet decoding. Specifically, if the n-th packet is decoded successfully, the corresponding mask row is all-one; otherwise, it is all-zero. Thus, we model =D,an∼i.i.d.Bernoulli(1−ρ),A=a1_D T, a_n i.i.d. Bernoulli(1-ρ), (33) where ρ=ρmρ=E\ _m\ denotes the average packet error probability. Approximation 1 (Denoising error model). At reverse step t, the noise predictor is approximated as: ϵ^,t≈ϵt+t, ε_ ,t≈ ε_t+U_t, (34) where t∈ℝK×DU_t ^K× D denotes the training-induced denoising error independent of ϵt ε_t. The entries of tU_t are i.i.d. Gaussian random variables with zero mean and fixed variance σu2 _u^2, which can be estimated by offline training. Then, we have the following result. Proposition 4.2 (Approximate Error Characterization). Under Approximation 1 and pseudo-inverse approximation in (22), the deterministic DDIM setting σt=0 _t=0, and the Jacobian bound ‖t‖2≤κ\|J_t\|_2≤κ, the error at each reverse step t−1t-1 can be approximately upper bounded by ℰt−1 _t-1 ≲(atddim+δtκχt)2≜ℰt−1up. ( a_t^ddim+ _tκ _t )^2 _t-1^up. (35) where t≜(rt2D+q)−1,B_t (r_t^2I_D+ _q)^-1, (36) χt≜(1−ρ)Ktr(t(q+1−α¯tα¯tσu2D)t), _t (1-ρ)Ktr\! (B_t ( _q+ 1- α_t α_t _u^2I_D )B_t ), (37) and atddim a_t^ddim =(α¯t−1−1)2K(‖22+tr()) =( α_t-1-1)^2K\! (\| μ\|_2^2+tr( ) ) (38) +(1−α¯t−1)KD +(1- α_t-1)KD +KDσu2(1−α¯t−1−α¯t−1(1−α¯t)α¯t)2. +KD _u^2 ( 1- α_t-1- α_t-1(1- α_t) α_t )^2. Here, ℰT=[‖T−‖F2]=K(‖22+tr())+KDE_T=E [\|Y_T-Y\|_F^2 ]=K\! (\| μ\|_2^2+tr( ) )+KD with T∼(0,)Y_T (0, I). Proof: Please see Appendix B. ∎ Remark 4.1 (Progressive Denoising Trend). The reverse-time SDE in (19) progressively transports noisy samples toward the data distribution as the step index t decreases [24]. Accordingly, α¯t−1 α_t-1 approaches one and the prescribed diffusion variance decreases. When the diffusion model is well trained, such that σu2 _u^2 is sufficiently small, and the posterior correction remains bounded, these schedule-dependent contractions dominate the error bound. Consequently, ℰt−1upE_t-1^up exhibits an overall decreasing trend under the considered noise schedule, consistent with the progressive denoising behavior of the reverse SDE. Based on the tractable upper bound in Proposition 4.2, we can further analyze the performance of the plug-and-play DDIM by comparing it with the conventional DF scheme for transmitting the corrupted tokens ~ Y. Here, we assume that the compression loss for downlink transmission is negligible. Then, we have the following result. Corollary 4.1 (Diffusion Activation Threshold). For the DF scheme, the corrupted tokens ~ Y are transmitted to the receiver without generation process. Hence, the mean-squared error is calculated by MSE =[‖~−‖F2] =E\! [ \| Y-Y \|_F^2 ] (39) =K[ρ(‖22+tr())+(1−ρ)tr(q)]. =K\! [ρ (\| μ\|_2^2+tr( ) )+(1-ρ)tr( _q) ]. The reverse step predicted by (35) to outperform the DF scheme is tthreshold=maxt∈0,…,T−1:ℰtup<MSE.t^threshold= \\,t∈\0,…,T-1\:E_t^up<MSE\,\. (40) Proof: According to the inverse model in (17) , the MSE in (39) can be easily calculated. Then, the threshold step tthresholdt^threshold is derived by comparing the upper bound ℰtupE_t^up in (35) with the MSE. ∎ Fig. 4: LPIPS score versus the number of reverse diffusion steps. The total step T, the average packet error ρ, and the quantization step s are set as 4040, 0.10.1, and 11, respectively. Effect on E2E Image Quality. Note that the above analysis is conducted in the token domain. To examine how the recovered tokens affect E2E image quality, we feed the intermediate token representation at each reverse step into the image recovery module and obtain ^t=D(t). X_t=D_ ψ(Y_t). (41) Then, we compare ^t X_t with the original image X using the Learned Perceptual Image Patch Similarity (LPIPS) metric [35]. As shown in Fig. 4, the LPIPS score decreases as the number of diffusion steps increases. Although Corollary 4.1 is derived from the token-domain squared Frobenius norm, it still provides an effective estimate of the number of diffusion steps required to outperform the DF scheme in terms of image quality. The reason is that the learned tokens are trained to preserve perceptually relevant information of image, reducing the reconstruction error in the token domain can generally improve the preservation of visual quality. V Optimal Diffusion Steps on Satellite This section optimizes the number of reverse diffusion steps that can be executed by the satellite under orbital energy limitations. First, we model the harvested solar energy and the energy consumed by diffusion computation and downlink forwarding. Then, we derive the optimal number of diffusion steps. V-A Energy Harvesting Model V-A1 Solar Energy Harvesting Denote the physical orbital time by τ to avoid confusion with the reverse diffusion index t. When τ=0τ=0, the satellite is at the point that has the greatest distance to the Sun. The harvested solar power is modeled as [36] Ph(τ)=0,τ∈Ωecl,Pmaxcosθ(τ),otherwise.P_ h(τ)= cases0,&τ∈ _ ecl,\\[2.84526pt] P_max θ(τ),&otherwise. cases (42) where Ωecl _ ecl denotes the eclipse interval, PmaxP_max is the peak solar power determined by the solar-panel area and energy-conversion efficiency, and θ(τ)θ(τ) is the angle between the solar-panel normal and the Sun direction. With single-axis solar tracking [36], θ(τ)θ(τ) is given by θ(τ) θ(τ) =arccos(1−cos2βcos2(τω)), = \! ( 1- ^2β ^2(τω) ), (43) where β denotes the angle between the satellite orbital plane and the sunlight direction, and ω is the orbital angular velocity of the satellite. V-A2 Energy Consumption The energy consumption of the satellite comes from three parts: (i) reverse diffusion computation, (i) downlink forwarding, and (i) other satellite base systems, such as attitude control and heat management [37]. Let EstepE_ step denote the energy consumption of one reverse diffusion step. In general, it can be written as Estep=Pstepτstep,E_ step=P_ step _ step, (44) where PstepP_ step and τstep _ step denote the average execution power and execution time of one reverse diffusion step, respectively. From the downlink rate in (15), the downlink transmission time for forwarding the recovered tokens is Tdltx=Rs,dlRd,T_ dl tx= R_s,dlR_ d, where TdlT_dl denotes the maximum allowable downlink transmission duration. Let pdlp_ dl denote the satellite downlink transmit power. The downlink transmission energy is then Edl=pdlTdltx=pdlRs,dlRd.E_ dl=p_ dlT_ dl tx=p_ dl R_s,dlR_ d. (45) Let EbaseE_ base denote the energy consumption from other satellite systems. The total energy consumption relevant to diffusion scheduling is Econs(N)=NEstep+Ebase+Edl,E_ cons(N)=NE_ step+E_ base+E_ dl, (46) where N denotes the number of reverse diffusion steps to be executed. V-B Diffusion Step Optimization Let τ0 _0 denote the start time of on-board diffusion after uplink decoding. Let τend _ end denote the latest time by which the recovered tokens must be delivered to the destination. Since downlink forwarding requires TdltxT_ dl tx seconds, the maximum executable time for diffusion is Texe=[τend−τ0−Tdltx]+.T_ exe= [ _ end- _0-T_ dl tx ]^+. (47) During this interval, the harvested energy is Ehexe=∫τ0τ0+TexePh(τ)τ.E_ h exe= _ _0 _0+T_ exeP_ h(τ)dτ. (48) Let B0B_0 denote the battery energy at τ0 _0. The energy available for scheduling, after battery saturation and reserve protection, is Eav=[minBmax,B0+Ehexe−Bmin−Ebase−Edl]+,E_ av= [ \! \B_ ,B_0+E_ h exe \-B_ -E_ base-E_ dl ]^+, (49) where BmaxB_ is the battery capacity and BminB_ is the reserved battery energy. According to Corollary 4.1, the plug-and-play DDIM is predicted to outperform the decode-and-forward baseline when the reverse process reaches tthresholdt^threshold. Hence, the minimum number of required diffusion steps is Nth=T−tthresholdN_ th=T-t^threshold. Following the progressive denoising trend in Remark 4.1, our objective is to maximize the number of executable diffusion steps within the interval [τ0,τ0+Texe][ _0, _0+T_ exe], while ensuring that the executed steps reach NthN_ th: maxN _N N N (50a) s.t. s.t. N≥Nth, N≥ N_ th, (50b) Nτstep≤Texe, N _ step≤ T_ exe, (50c) NEstep≤Eav. NE_ step≤ E_ av. (50d) The first constraint enforces the minimum number of reverse diffusion steps. The second constraint is the executable-time constraint, and the third constraint is the energy-causality constraint after reserving the downlink transmission energy. The problem has a closed-form solution: N⋆=minT,⌊Texeτstep⌋,⌊EavEstep⌋,if Nmaxexe≥Nth,0,otherwise,N = cases \! \T, T_ exe _ step , E_ avE_ step \,&if N_ exe≥ N_ th,\\[8.53581pt] 0,&otherwise, cases (51) where Nmaxexe=minT,⌊Texeτstep⌋,⌊EavEstep⌋.N_ exe= \! \T, T_ exe _ step , E_ avE_ step \. (52) When Nmaxexe<NthN_ exe<N_ th, the predicted threshold cannot be reached under the current energy and time constraints. In this case, the diffusion process is infeasible, N⋆=0N =0, and the system degenerates into the DF scheme. VI Experimental Results (a) Latency versus satellite altitude. (b) Latency breakdown (2000 km height). Fig. 5: E2E latency comparisons. The LPIPS for all the schemes are around 0.20.2. VI-A Experimental Settings VI-A1 Model architecture We implement the tokenization coders by using the first-stage convolutional autoencoder of a stable latent diffusion model [16]. For the proposed plug-and-play DDIM algorithm, we employ the pretrained noise predictor from the stable latent diffusion model [16]. All neural-network modules are implemented in PyTorch [38]. The NVIDIA A100 GPU is used as a terrestrial profiling platform for measuring the execution cost of the diffusion workload. This setting is reasonable because the recent orbital AI-computing platforms, such as Starcloud [10], have adopted H100-class GPUs with higher AI throughput. VI-A2 Dataset The experiments are conducted on the AFHQ dataset [39], a well-known large-scale image dataset for high-quality image synthesis. AFHQ contains 15,00015,000 images with an original resolution of 512×512512× 512. We use the training dataset to estimate the token statistics ,\ μ, \, while all reported results are evaluated on the validation set. We further validate the visual performance on the Kodak dataset [40]. VI-A3 Onboard deployment discussion The denoising UNet contains 859.52859.52 million parameters and occupies approximately 1.601.60 GiB using FP16 weights. For a 512×512512× 512 image, each reverse step with automatic mixed precision (AMP) takes approximately 167167 ms on the A100. These requirements are compatible with emerging high-performance orbital platforms such as Starcloud-1, while resource-constrained CubeSats would require model compression. VI-A4 Parameter settings The orbital parameters and computation-energy settings are chosen with reference to recent AI-computing satellite efforts, such as Starcloud and NASA microsatellite settings [10, 37], which are summarized in Table I. The source rate is controlled by the quantization step scale s and the packet error rate is calculated according to the finite block length theory in (11). The small scale fading follows the Rician distribution with factor being 11, i.e., gm∼(12,12)g_m ( 12, 12). Downlink transmissions are assumed to be error-free. The overhead of the packet header is around 20%20\% of the total source bits. The uplink transmission rate is around 1818 kb/s, while the downlink transmission rate can be hundred kHz according channel conditions. The downlink compression bit per pixel (bpp) is set as 0.40.4. TABLE I: Default simulation parameters. Parameter Default setting DDIM parameters σt=0,η=0.8 _t=0,η=0.8 Packet length 20482048 Uplink channel coding rate 0.10.1 Carrier frequency 22 GHz Bandwidth 180180 kHz Uplink transmit power 2323 dBm Downlink transmit power 3030 dBm Device transmit/receive antenna gain 00 dBi Satellite receive antenna gain 1515 dBi Satellite transmit antenna gain 2525 dBi The elevation angle 30∘30 Solar energy harvesting peak power 800800 W Computational power 200200 W Satellite base energy consumption 200200 W VI-A5 Benchmarking schemes Instead of using pixel-level MSE as the performance metric, we adopt the LPIPS metric to evaluate the perceptual quality of the received images. The proposed SpaceDiffusion scheme is compared with the following schemes. • JPEG2000+DF: The source image is compressed by JPEG2000 [41], protected by the same channel code, decoded at the satellite, and forwarded to the destination without generative recovery. • Tokenization+DF: This scheme uses exactly the same first-stage autoencoder, transform coding, quantization, entropy coding, packetization, and channel coding as SpaceDiffusion. After channel decoding, the corrupted latent tokens are directly forwarded without on-board generative recovery. • DPS+GF: As a generative baseline, we employ the conventional DPS algorithm [17] for token generation at the satellite. Since DPS is originally used for image-domain inverse problem, we redesign it for token-domain generation without changing its main structure. VI-B E2E Latency Comparisons First, we investigate the E2E latency of the proposed SpaceDiffusion scheme over different satellite heights. The elevation angle is set to 5∘5 to investigate the poor channel conditions of satellite communications. The packet error rate is set as 0.10.1. The considered DF relay adopts single-process stop-and-wait retransmission protocol in NB-IoT NTN setting. When an uplink packet is decoded, the satellite feeds back an ACK/NACK to the source, and the source retransmits the lost packet until successful decoding. Therefore, the latency of the DF scheme explicitly includes both the extra transmission time caused by retransmissions and the ACK/NACK-induced RTT penalty. Fig. 5 compares the schemes at the same target quality of approximately 0.20.2 LPIPS. SpaceDiffusion maintains a nearly constant latency of 66–77 s/image across the considered satellite heights because it avoids uplink retransmissions and ACK/NACK feedback. In contrast, the DF baselines become increasingly slow as altitude increases, with JPEG2000+DF exceeding 300300 s/image at high altitude. SpaceDiffusion consequently achieves a 44–50×50× latency reduction over the DF baselines and is also faster than DPS+GF, which requires 100100 rather than 2020 reverse steps. The breakdown in Fig. 5(b) explains these gains. Generative recovery enables SpaceDiffusion to use about 6×6× lower bpp than JPEG2000 at the same perceptual quality. It also replaces the 7.87.8 s/image RTT component of Tokenization+DF with 3.93.9 s/image of local diffusion computation, reducing latency by about 40%40\%. Moreover, using 2020 rather than 100100 reverse steps reduces the DPS computation latency from 23.523.5 to 3.93.9 s/image. It is worth noticing that the computation latency of the proposed scheme can be further reduced by using more lightweight models and parallel image processing. VI-C Reconstruction Performance Comparisons In this subsection, we investigate the performance of the proposed SpaceDiffusion scheme compared with the benchmarking schemes. The quantization step is set as 0.80.8, the bpp is around 0.10.1, and the bandwidth ratio is 0.490.49 for all schemes. The satellite height is set as 600600 km. The solar power is enough to support the diffusion computation. Fig. 6: Reconstruction quality versus packet error rate. Fig. 7: Reconstruction quality versus uplink transmit power. Fig. 8: Visual reconstruction examples on the AFHQ dataset. Fig. 9: Visual reconstruction examples on the Kodak dataset [40]. Fig. 6 shows the LPIPS performance as a function of the packet error rate. The retransmission protocol is disabled to evaluate the robust performance of all the schemes. Here, we omit the JPEG2000 scheme because its robust performance is much poorer than the other schemes. It is observed that all the benchmarking schemes degrade under severe packet losses, but SpaceDiffusion consistently achieves the lowest LPIPS. For example, at a packet error rate of 0.10.1, SpaceDiffusion obtains an LPIPS of about 0.220.22, while GF with DPS and tokenization without generation achieve about 0.300.30 and 0.390.39, respectively. The performance gap becomes more pronounced in the medium-to-high error regime, where the non-generative tokenization baseline suffers from unrecovered token erasures. This demonstrates that the proposed SpaceDiffusion scheme can effectively recover the missing content and improve the E2E image quality under lossy uplink channels. Fig. 7 further evaluates the performance as a function of the uplink transmit power. As the transmit power increases, the channel becomes more reliable and the LPIPS of all token-based schemes decreases. The proposed SpaceDiffusion scheme requires much lower transmit power to achieve high-quality image transmission. For example, when the target LPIPS is around 0.250.25, SpaceDiffusion saves about 1515 dB of uplink transmit power compared with the non-generative tokenization baseline. This power saving makes the proposed scheme particularly suitable for power-constrained NTN IoT terminals and handheld devices. To examine generative fidelity and potential hallucinations, Figs. 8 and 9 show reconstruction examples on the AFHQ and Kodak datasets at an uplink rate of approximately 0.110.11 bpp and a packet error rate of 0.10.1. JPEG2000 with retransmission produces visible blurring, while tokenization without generation leaves structured gaps caused by packet erasures. DPS partially fills the missing regions but exhibits texture inconsistency and residual artifacts. In comparison, SpaceDiffusion produces more coherent structures and textures and achieves the lowest LPIPS on both datasets. Although the generated local details may not match the source exactly, SpaceDiffusion helps preserve enough semantic information for human interpretation. VI-D Discussions on Energy-Limited Scenarios (a) Solar power and optimized diffusion steps over orbital time. (b) Average LPIPS versus solar beta angle. Fig. 10: Energy-limited diffusion scheduling. We finally examine whether SpaceDiffusion remains practical when the satellite energy supply is constrained by orbital illumination. Fig. 10(a) compares a dawn-dusk Sun-synchronous orbit (DDSSO) and a non-Sun-synchronous orbit (Non-SSO). The DDSSO case has nearly continuous solar illumination, and the harvested power stays close to the peak value. Here, we set the maximum diffusion step size to be N=40N=40. The satellite height is around 600600 km. The maximum executable time and initial battery capacity are set as 88 s and 00 mAh, respectively. Fig. 10(a) shows that the nearly continuous illumination in DDSSO supports the full N⋆=40N =40 reverse steps, whereas the Non-SSO case executes diffusion only when the available energy supports at least NthN_ th steps; otherwise, it sets N⋆=0N =0 and falls back to DF. This threshold policy prevents ineffective partial generation. As shown in Fig. 10(b), a larger solar beta angle shortens the eclipse and increases the energy available for generation. The optimized policy consequently reduces the average LPIPS from about 0.360.36 to 0.320.32 in energy-scarce cases and to 0.240.24 at sufficiently large beta angles, while avoiding the poor intermediate reconstructions produced by ungated generation. VII Concluding Remarks This paper proposed the SpaceDiffusion framework that exploits on-board computing resources for efficient image transmission over limited satellite links. An interesting insight is that the channel-distortion model can act as an inserted “prompt” that guides diffusion reconstruction. Thus, the GF framework can reuse well-trained latent diffusion models developed for image-generation tasks without channel-specific retraining. Simulation results further show that on-board generation significantly reduces E2E latency because it replaces feedback-driven uplink retransmissions with generative reconstruction. This latency reduction particularly benefits delay-sensitive IoT and handheld applications. Several directions merit further study. SpaceDiffusion can be extended to multi-user and multi-satellite networks through joint communication, computation, and energy allocation. To mitigate generative hallucinations, future work may investigate unequal error protection for semantically important data tokens. Other promising topics include multimodal GF for video, audio, and sensing data and hardware-aware acceleration for practical on-board deployment. Appendix -A Proof of Proposition 4.1 Let an∈0,1a_n∈\0,1\ denote the common entry of the n-th row of A, i.e., []n,d=an,∀d∈1,…,D.[A]_n,d=a_n, ∀ d∈\1,…,D\. (53) Also, let ~n y_n and ˇt,n y_t,n denote the n-th rows of ~ Y and ˇt Y_t, respectively. Under the pseudo-inverse Gaussian approximation in (22), each row satisfies n|t≈(ˇt,n,rt2D).y_n _t ( y_t,n,r_t^2I_D). (54) According to the inverse model in (17), the row-wise observation model is ~n=n+n,an=1,,an=0, y_n= casesy_n+q_n,&a_n=1,\\ 0,&a_n=0, cases (55) where n∼(,q)q_n (0, _q). Therefore, when an=1a_n=1, pt(~n∣t) p_t( y_n _t) =∫pt(n∣t)p(~n∣n)dn = p_t(y_n _t)\,p( y_n _n)\,dy_n ≈∫(n,ˇt,n,rt2D)(~n,n,q)dn ≈ (y_n; y_t,n,r_t^2I_D)N( y_n;y_n, _q)\,dy_n =(~n,ˇt,n,rt2D+q). =N( y_n; y_t,n,r_t^2I_D+ _q). (56) When an=0a_n=0, ~n= y_n=0 is deterministic and thus contributes only a constant independent of tY_t. Hence, up to an additive constant c independent of tY_t, logpt(~∣t) p_t( Y _t) =c−12∑n=1Kan(~n−ˇt,n)(rt2D+q)−1(~n−ˇt,n)⊤. =c- 12 _n=1^Ka_n( y_n- y_t,n)(r_t^2I_D+ _q)^-1( y_n- y_t,n) . (57) Differentiating the above expression with respect to ˇt Y_t yields ∇ˇtlogpt(~∣t)=⊙((~−ˇt)(rt2D+q)−1). _ Y_t p_t( Y _t)=A (( Y- Y_t)(r_t^2I_D+ _q)^-1 ). (58) Then, by the chain rule in vectorized form, we have vec(∇tlogpt(~∣t)) \! ( _Y_t p_t( Y _t) ) =(∂vec(ˇt)∂vec(t))⊤vec(∇ˇtlogpt(~∣t)) = ( ( Y_t) (Y_t) ) vec\! ( _ Y_t p_t( Y _t) ) =t⊤vec(t). =J_t vec(G_t). (59) Equivalently, we have ∇tlogpt(~∣t)=unvec(t⊤vec(t)). _Y_t p_t( Y _t)=unvec\! (J_t vec(G_t) ). Finally, by substituting the above result into (20), we obtain ∇tlogpt(t∣~)≈(t,t)+unvec(t⊤vec(t)). _Y_t p_t(Y_t Y) _ (Y_t,t)+unvec\! (J_t vec(G_t) ). (60) This completes the proof. -B Proof of Proposition 4.2 Under the deterministic DDIM setting σt=0 _t=0, we have t−1=α¯t−1ˇt+1−α¯t−1ϵ^,t+δtℒt. _t-1= α_t-1 Y_t+ 1- α_t-1 ε_ ,t+ _tL_t. (61) Let t=t−1ddim−.e_t=Y_t-1^ddim-Y. Then, the reconstruction error can be calculated as ℰt−1 _t-1 =[‖t−1−‖F2] =E\! [\|Y_t-1-Y\|_F^2 ] =[‖t+δtℒt‖F2] =E\! [\|e_t+ _tL_t\|_F^2 ] =[‖t‖F2]+2δt[⟨t,ℒt⟩]+δt2[‖ℒt‖F2] =E\! [\|e_t\|_F^2 ]+2 _tE\! [ _t,L_t ]+ _t^2E\! [\|L_t\|_F^2 ] ≤(a)([‖t‖F2]+δt[‖ℒt‖F2])2 (a)≤ ( E\! [\|e_t\|_F^2 ]+ _t E\! [\|L_t\|_F^2 ] )^2 ≈(b)(atddim+δt[‖ℒt‖F2])2 (b)≈ ( a_t^ddim+ _t E\! [\|L_t\|_F^2 ] )^2 ≲(c)(atddim+δtκχt)2, (c) ( a_t^ddim+ _tκ _t )^2, (62) where ⟨⋅,⋅⟩ ·,· denotes the Frobenius inner product. The justifications of the steps are as follows. • Step (a)(a): By the Cauchy–Schwarz inequality [28], we have |[⟨t,ℒt⟩]|≤[‖t‖F2][‖ℒt‖F2]. |E\! [ _t,L_t ] |≤ E[\|e_t\|_F^2]E[\|L_t\|_F^2]. (63) • Step (b)(b): From (29) and Assumption 1, the conventional DDIM error can be written as t _t =α¯t−1α¯tt− = α_t-1 α_tY_t-Y +(1−α¯t−1−α¯t−1(1−α¯t)α¯t)(ϵt+t). + ( 1- α_t-1- α_t-1(1- α_t) α_t )( ε_t+U_t). (64) Using the forward-trajectory approximation in (25), t≈α¯t+1−α¯tϵt.Y_t≈ α_tY+ 1- α_t ε_t. (65) substitution into (64) gives t _t ≈(α¯t−1−1)+1−α¯t−1ϵt ≈( α_t-1-1)Y+ 1- α_t-1 ε_t +(1−α¯t−1−α¯t−1(1−α¯t)α¯t)t. + ( 1- α_t-1- α_t-1(1- α_t) α_t )U_t. (66) Since ϵt ε_t and tU_t are zero-mean and independent of Y, taking expectations gives [‖t‖F2]≈atddimE[\|e_t\|_F^2]≈ a_t^ddim as defined in (38). • Step (c)(c): For the n-th row t,ng_t,n of tG_t, Proposition 4.1 gives t,n=an(~n−ˇt,n)t=an(n+1−α¯tα¯tt,n)t, _t,n=a_n( y_n- y_t,n)B_t=a_n (q_n+ 1- α_t α_tu_t,n )B_t, (67) where ~n=n+n y_n=y_n+q_n for an=1a_n=1 and ˇt,n≈n−(1−α¯t)/α¯tt,n y_t,n _n- (1- α_t)/ α_t\,u_t,n. Since ana_n, nq_n, and t,nu_t,n are independent, [‖t‖F2]=χt.E\! [\|G_t\|_F^2 ]= _t. 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