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@@ -51,7 +51,7 @@ Despite these advances, most existing work either focuses on packet-level genera
 \label{sec:related}
 Early generation of network data oriented towards "realism" mostly remained at the packet/flow header level, either through replay or statistical synthesis based on single-point observations. Swing, in a closed-loop, network-responsive manner, extracts user/application/network distributions from single-point observations to reproduce burstiness and correlation across multiple time scales \citep{10.1145/1151659.1159928}. Subsequently, a series of works advanced header synthesis to learning-based generation: the WGAN-based method added explicit verification of protocol field consistency to NetFlow/IPFIX \citep{Ring_2019}, NetShare reconstructed header modeling as flow-level time series and improved fidelity and scalability through domain encoding and parallel fine-tuning \citep{10.1145/3544216.3544251}, and DoppelGANger preserved the long-range structure and downstream sorting consistency of networked time series by decoupling attributes from sequences \citep{Lin_2020}. However, in industrial control system (ICS) scenarios, the original PCAP is usually not shareable, and public testbeds (such as SWaT, WADI) mostly provide process/monitoring telemetry and protocol interactions for security assessment, but public datasets emphasize operational variables rather than packet-level traces \citep{7469060,10.1145/3055366.3055375}. This makes "synthesis at the feature/telemetry level, aware of protocol and semantics" more feasible and necessary in practice: we are more concerned with reproducing high-level distributions and multi-scale temporal patterns according to operational semantics and physical constraints without relying on the original packets. From this perspective, the generation paradigm naturally shifts from "packet syntax reproduction" to "modeling of high-level spatio-temporal distributions and uncertainties", requiring stable training, strong distribution fitting, and interpretable uncertainty characterization.
 
-Diffusion models exhibit good fit along this path: DDPM achieves high-quality sampling and stable optimization through efficient $\epsilon$ parameterization and weighted variational objectives \citep{NEURIPS2020_4c5bcfec}, the SDE perspective unifies score-based and diffusion, providing likelihood evaluation and prediction-correction sampling strategies based on probability flow ODEs \citep{song2021score}. For time series, TimeGrad replaces the constrained output distribution with conditional denoising, capturing high-dimensional correlations at each step \citep{rasul2021autoregressivedenoisingdiffusionmodels}; CSDI explicitly performs conditional diffusion and uses two-dimensional attention to simultaneously leverage temporal and cross-feature dependencies, suitable for conditioning and filling in missing values \citep{tashiro2021csdiconditionalscorebaseddiffusion}; in a more general spatio-temporal structure, DiffSTG generalizes diffusion to spatio-temporal graphs, combining TCN/GCN with denoising U-Net to improve CRPS and inference efficiency in a non-autoregressive manner \citep{wen2024diffstgprobabilisticspatiotemporalgraph}, and PriSTI further enhances conditional features and geographical relationships, maintaining robustness under high missing rates and sensor failures \citep{liu2023pristiconditionaldiffusionframework}; in long sequences and continuous domains, DiffWave verifies that diffusion can also match the quality of strong vocoders under non-autoregressive fast synthesis \citep{kong2021diffwaveversatilediffusionmodel}; studies on cellular communication traffic show that diffusion can recover spatio-temporal patterns and provide uncertainty characterization at the urban scale \citep{11087622}. These results overall point to a conclusion: when the research focus is on "telemetry/high-level features" rather than raw messages, diffusion models provide stable and fine-grained distribution fitting and uncertainty quantification, which is exactly in line with the requirements of ICS telemetry synthesis. Meanwhile, directly entrusting all structures to a "monolithic diffusion" is not advisable: long-range temporal skeletons and fine-grained marginal distributions often have optimization tensions, requiring explicit decoupling in modeling.
+Diffusion models exhibit good fit along this path: DDPM achieves high-quality sampling and stable optimization through efficient $\epsilon$ parameterization and weighted variational objectives \citep{ho2020denoising}, the SDE perspective unifies score-based and diffusion, providing likelihood evaluation and prediction-correction sampling strategies based on probability flow ODEs \citep{song2021score}. For time series, TimeGrad replaces the constrained output distribution with conditional denoising, capturing high-dimensional correlations at each step \citep{rasul2021autoregressivedenoisingdiffusionmodels}; CSDI explicitly performs conditional diffusion and uses two-dimensional attention to simultaneously leverage temporal and cross-feature dependencies, suitable for conditioning and filling in missing values \citep{tashiro2021csdiconditionalscorebaseddiffusion}; in a more general spatio-temporal structure, DiffSTG generalizes diffusion to spatio-temporal graphs, combining TCN/GCN with denoising U-Net to improve CRPS and inference efficiency in a non-autoregressive manner \citep{wen2024diffstgprobabilisticspatiotemporalgraph}, and PriSTI further enhances conditional features and geographical relationships, maintaining robustness under high missing rates and sensor failures \citep{liu2023pristiconditionaldiffusionframework}; in long sequences and continuous domains, DiffWave verifies that diffusion can also match the quality of strong vocoders under non-autoregressive fast synthesis \citep{kong2021diffwaveversatilediffusionmodel}; studies on cellular communication traffic show that diffusion can recover spatio-temporal patterns and provide uncertainty characterization at the urban scale \citep{11087622}. These results overall point to a conclusion: when the research focus is on "telemetry/high-level features" rather than raw messages, diffusion models provide stable and fine-grained distribution fitting and uncertainty quantification, which is exactly in line with the requirements of ICS telemetry synthesis. Meanwhile, directly entrusting all structures to a "monolithic diffusion" is not advisable: long-range temporal skeletons and fine-grained marginal distributions often have optimization tensions, requiring explicit decoupling in modeling.
 
 Looking further into the mechanism complexity of ICS: its channel types are inherently mixed, containing both continuous process trajectories and discrete supervision/status variables, and discrete channels must be "legal" under operational constraints. The aforementioned progress in time series diffusion has mainly occurred in continuous spaces, but discrete diffusion has also developed systematic methods: D3PM improves sampling quality and likelihood through absorption/masking and structured transitions in discrete state spaces \citep{austin2021structured}, subsequent masked diffusion provides stable reconstruction on categorical data in a more simplified form \citep{Lin_2020}, multinomial diffusion directly defines diffusion on a finite vocabulary through mechanisms such as argmax flows \citep{hoogeboom2021argmaxflowsmultinomialdiffusion}, and Diffusion-LM demonstrates an effective path for controllable text generation by imposing gradient constraints in continuous latent spaces \citep{li2022diffusionlmimprovescontrollabletext}. From the perspectives of protocols and finite-state machines, coverage-guided fuzz testing emphasizes the criticality of "sequence legality and state coverage" \citep{meng2025aflnetyearslatercoverageguided,godefroid2017learnfuzzmachinelearninginput,she2019neuzzefficientfuzzingneural}, echoing the concept of "legality by construction" in discrete diffusion: preferentially adopting absorption/masking diffusion on discrete channels, supplemented by type-aware conditioning and sampling constraints, to avoid semantic invalidity and marginal distortion caused by post hoc thresholding.