Generative CKM Construction using Partially Observed Data with Diffusion Model

Di Wu; Shen Fu; Yong Zeng; Zijian Wu

REVIEW 5 major objections 4 minor 17 references

Generative CKM Construction using Partially Observed Data with Diffusion Model

T0 review · 5 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A conditional diffusion model reconstructs complete channel knowledge maps from partial observations, outperforming interpolation baselines.

desk verdict A competent empirical application of decoupled diffusion models to CKM inpainting, with real gains over interpolation baselines but one headline result (BS localization) that is underspecified to the point of being unverifiable. read the letter →

arxiv 2412.14812 v1 pith:UT2MOIZ4 submitted 2024-12-19 eess.SP

Shen Fu , Zijian Wu , Di Wu , Yong Zeng This is my paper · ORCID

classification eess.SP

keywords channelknowledgemapCKMconstructiondiffusionmodeldecoupledinverseproblemimageinpaintingbasestationlocalizationradioenvironment

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Channel knowledge maps (CKMs) are site-specific databases of channel properties at every location, and building a complete map from sparse measurements is an ill-posed inverse problem. The paper proposes to solve this problem with a conditional decoupled diffusion model that learns the prior distribution of CKMs from partially observed channel gain images alone, without auxiliary environment maps or transmitter positions. On the CKMImageNet dataset, the model reconstructs missing regions with lower MSE, NMSE, RMSE, and MAE than KNN, Kriging, bilinear, and RBF interpolation, in both building-masked and non-building-masked scenarios. It also predicts channel knowledge around a base station accurately enough to locate the base station to 3.30 m in a complex urban environment. If the result holds, generative inpainting is a viable route to environment-aware wireless communication when dense channel measurements are unavailable.

What carries the argument

The mechanism is the conditional decoupled diffusion model (DDM). Instead of DDPM's discrete noise schedule, DDM uses a continuous forward process $x_t = x_0 + \int_0^t f_s\,ds + \int_0^t dw_s$ with the image-to-zero drift chosen as $f_t = -x_0$, so $x_t = (1-t)x_0 + \sqrt{t}\,\epsilon$ and $x_1$ is pure Gaussian noise. The reverse process predicts both the drift $c_\theta$ and the noise $\epsilon_\theta$ with a UNet that has two decoder branches, conditioned on multi-level features $e(y)$ extracted by a Swin-B encoder from the masked CKM image; training minimizes the sum of squared errors on $c$ and $\epsilon$. A VAE maps pixel space to latent space to reduce computation. This decoupling lets sampling use arbitrary step sizes with few steps, while the condition encoder injects the observed locations at every reverse step.

What would settle it

Take the trained model and run it on a held-out set of ray-traced 128 by 128 CKMs from an environment not represented in the training cities, or generated at a different carrier frequency such as 3.5 GHz or with a different receiver height. If the resulting RMSE and MAE on unobserved locations no longer beat Kriging or RBF interpolation, the claimed advantage is an artifact of the training distribution rather than a general CKM prior.

Watch

Extended reading notes

Core claim

The central claim is that a conditional decoupled diffusion model, trained only on masked and unmasked CKM images, can serve as a generative prior that turns partial observations $y = Hx$ into a complete CKM $\hat{x}$ by sampling from the posterior, circumventing the rank-deficiency of the mask $H$. The authors report that on 500 test images without building masking the proposed method reaches RMSE 10.7758 dB and MAE 5.1412 dB, the best among the four interpolation baselines; with building masking, RMSE is 20.6712 dB versus 43.2206 dB for Kriging, the best baseline. In a base-station vicinity masking test over 1000 images, the method's BS localization error is 3.30 m, compared with 8.81 m for KNN. The same architecture also produces visually plausible inpainted maps, supporting the claim that learned diffusion priors capture global propagation structure that local interpolation misses.

Load-bearing premise

The load-bearing assumption is that the diffusion prior learned from CKMImageNet's 20,000 ray-traced 128 by 128 channel gain images (28 GHz, fixed 10 m transmitter and 1 m receiver heights, specific cities) is the true prior for every test CKM; if a target area differs in layout, frequency, building materials, or antenna heights, the learned prior will not match and the reported gains may disappear.

Editorial extensions

If this is right

CKM construction no longer requires auxiliary environmental data or transmitter location information, only a set of partially observed channel knowledge images.
Diffusion-based inpainting can outperform classical interpolation (KNN, Kriging, bilinear, RBF) on both reconstruction error and downstream localization.
The same trained model can locate a base station to within 3.30 m from a masked 64 m by 64 m vicinity, even when most links are non-line-of-sight.
The decoupled formulation allows flexible sampling steps, so the method can trade computation against reconstruction quality for real-time deployment.
Because the model inpaints the full map, it can provide channel knowledge at unmeasured locations for environment-aware beamforming and resource allocation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper does not simulate angle-of-arrival or angle-of-departure maps even though the system model includes them; applying the same conditional DDM to those modalities is a direct test of whether the learned prior transfers beyond channel gain.
The model is a conditional generator rather than a measurement-consistent sampler; explicitly enforcing $y = Hx$ at the end of sampling could reduce residual error at the cost of extra steps.
The training distribution is narrow (28 GHz, fixed antenna heights, urban ray-tracing); one stress test is to train on multi-frequency or multi-city data and measure whether the RMSE advantage over Kriging persists out of distribution.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

You should know two things about this paper. First, it does something genuinely useful: it takes a published decoupled diffusion model, adapts it with a conditional encoder and dual-decoder UNet, and shows that it can inpaint a channel knowledge map (CKM) from sparse observations without any auxiliary environment or BS location data. On the CKMImageNet benchmark the gains over KNN, Kriging, Bilinear, and RBF are consistent and large, especially when buildings are masked (RMSE drops from about 66 dB to 20.7 dB). The training and sampling algorithms are clearly specified, and the dataset is public, so the non-BS inpainting results are at least reproducible in principle. That is real empirical work. Second, the BS localization result in Table III has a load-bearing gap: the paper reports a 3.30 m localization error but never says how the BS position is inferred from the reconstructed CKM. The masked region around the BS is 64m by 64m, so the high-gain area itself is unobserved; the method must be relying on context. Without knowing whether the localization uses argmax, centroid, template matching, or something else, the comparison against KNN et al. is not well-defined and the claimed improvement could come from the post-processing rule rather than the diffusion reconstruction. That is not a reason to dismiss the paper, but it is a reason to require the authors to specify the algorithm before taking the headline claim seriously.

The soft spots are otherwise proportionate. The paper omits comparisons with the generative baselines it cites—RadioUNet, RME-GAN, RadioDiff—which are the natural competitors. There are no error bars or significance tests, and the learned prior is trained only on CKMImageNet ray-traced data (28 GHz, fixed heights, specific cities); transferability to other environments is untested. No code or data are released, which makes the missing details harder to fill in. The mathematical framework is sound and the paper does not overclaim beyond its experiments, aside from the under-specified BS localization part.

Who is this for? Researchers working on CKM construction, radio map estimation, or inverse problems with diffusion models. It is a competent engineering contribution that advances a practical problem, but it is not a methodological breakthrough. It deserves a serious referee, and I would recommend acceptance only after the BS localization algorithm is specified, comparisons with generative baselines are added, and at least some variance estimates are reported.

Referee Report

5 major / 4 minor

Summary. The manuscript addresses CKM construction from partially observed channel gain images. It treats the problem as an inverse problem and applies a conditional decoupled diffusion model (DDM) from [14]: a VAE maps images into a latent space, a Swin-B encoder extracts features from the masked observation, and a dual-decoder UNet predicts both the signal-decay component and the noise component. Training and sampling are given in Algorithms 1 and 2. Experiments on CKMImageNet compare the method with KNN, Kriging, bilinear, and RBF interpolation under three masking settings (buildings masked, buildings not masked, and BS vicinity masked), reporting lower MSE/NMSE/RMSE/MAE in all settings and a BS localization error of 3.30 m.

Significance. If the results are taken at face value, the paper demonstrates that a conditional diffusion model trained only on partially observed CKM images can reconstruct radio maps more accurately than classical interpolation and can support BS localization. The use of a public benchmark dataset and the explicit training and sampling algorithms are strengths. However, the current validation has several load-bearing gaps: the building-masking evaluation appears to exclude the missing pixels, the BS localization rule is not specified, and no generative baselines or statistical uncertainties are reported. These issues must be resolved before the central claims can be accepted.

major comments (5)

[IV-B, Table I] The evaluation for the building-masking scenario appears circular. Section IV-B states that error metrics are computed for all locations without building occupancy after masking buildings. Since the mask removes exactly the building pixels, the non-building pixels are the observed part of the input, and the missing building regions are excluded from the reported errors. Table I therefore does not demonstrate accurate reconstruction of the missing data. Please report metrics computed only on the masked (unobserved) pixels, or clarify the evaluation protocol if I have misread it.
[IV-B, Table III] The BS localization result is not reproducible as reported. The paper states that a 64 m by 64 m region around the BS is masked and then reports a BS localization error of 3.30 m for the proposed method, but it never specifies how the BS position is estimated from the reconstructed CKM (e.g., global argmax, centroid, template matching, or a learned regressor). Without this rule, and without confirmation that the same rule is applied to all baselines, the comparison in Table III is not well defined. Please specify the localization algorithm and the test protocol.
[III-B, Algorithms 1-2 and Fig. 2] There is an inconsistency between the latent-space description and the algorithms. The text and Fig. 2 state that a VAE maps the pixel-space image x to a latent z and that diffusion is performed in latent space, but Algorithms 1 and 2 use x0, xt, and c = -x0 throughout and return xt as the reconstructed image. It is unclear whether the diffusion operates in pixel space or latent space, where the VAE encoder and decoder enter, and how the conditioning encoder e(y) is combined with the latent code. Please rewrite the algorithms to match the actual pipeline; this is essential for reproducibility.
[IV-B, Tables I-III] The reported gains are point estimates without error bars, standard deviations, or significance tests. Tables I-III aggregate over 500-1000 images, but no variability is reported, so the reader cannot judge whether the improvements over the best baseline (e.g., RBF in Table II) are stable. Please report per-image statistics or confidence intervals, and avoid the word 'significantly' unless a statistical test is performed.
[I and IV-B] The paper is positioned against generative CKM methods, citing RadioUNet [10], RME-GAN [11], and RadioDiff [12], but none of these is used as a baseline. The experimental comparison is limited to interpolation methods, so the abstract's claim of significantly improving CKM construction compared with benchmarking schemes is only supported relative to interpolation. Please add at least one generative baseline (e.g., RadioDiff or RME-GAN) on the same dataset, or explicitly narrow the claim.

minor comments (4)

[IV-B] The sentence 'our proposed diffusion based model significantly outperforms significantly the benchmark approaches' contains a duplicated adverb; please revise.
[IV-B, Table I] The phrase 'Table I plots the average error metrics' should be 'lists'; consider also adding units to the table headers.
[IV-A] The phrase 'the smallest time step is 1×104' should be '1×10^-4' if that is the intended value.
[Algorithm 1] Algorithm 1 samples a random mask matrix H but does not specify its distribution; please state how the masks are generated during training.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the diffusion-based CKM construction is a standard conditional generative inverse problem solved with an externally published model and evaluated on held-out CKMImageNet test images.

full rationale

The paper's derivation chain is y=Hx in (1), followed by the posterior q(x|y) ∝ q(y|x)q(x), with q(x) learned by training a conditional decoupled diffusion model on the CKMImageNet training set. The training objective in (10), min E[||c-cθ||² + ||ϵ-ϵθ||²] with c=-x0, is the standard DDM loss from the external reference [14]; it learns to reverse the forward process (6)-(7), and Algorithm 2 samples without any fitted constant chosen to force the reported errors. Evaluation is on held-out test images (1000 for Table I, 500 for Table II, 1000 for Table III), so the reported RMSE/MAE and BS localization errors are not statistically forced by a parameter fit to the same test points. The main self-citation is the dataset paper [15], but CKMImageNet is a ray-tracing benchmark generated with Wireless Insite from OpenStreetMap city data, independent of the proposed reconstruction method and externally falsifiable; hence it does not make the empirical claim circular. The BS localization procedure is not fully specified, which is a reproducibility weakness, but the 3.30 m error is computed after training and is not part of the training loss; unexplained methodology is not circularity. No step reduces by definition to its own input, and no load-bearing claim depends on an unverified self-citation.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a learned prior from a specific ray-tracing dataset, on the correctness of the existing DDM formalism, and on a noiseless independent-mask model. The paper introduces no new physical entities. The main free parameters are the trained network weights and the unspecified sampling step count, along with unstated implementation details that affect reproducibility.

free parameters (2)

Learned model parameters theta (VAE, Swin-B encoder, dual-decoder UNet) = Trained on 20,000 CKMImageNet images with AdamW, 300,000 iterations, batch size 48
The central reconstruction quality is a product of these fitted weights; no analytic or physical prior is provided, so the method's success is a function of the trained network rather than a derivation.
Sampling steps S in Algorithm 2 = Not specified
The reconstruction accuracy depends on the reverse-process discretization S, but no value is given in the paper, preventing exact reproduction of the results.

assumptions (4)

standard math The forward and reverse process definitions and training objective of the decoupled diffusion model, Eqs. (6)-(10), are taken from [14] and assumed correct.
The paper does not re-derive the decoupled diffusion model; it relies on the published derivation of Huang et al.
domain assumption A diffusion model trained on CKMImageNet channel gain images learns the true prior q(x) of complete CKMs, and this prior transfers to all test areas.
This is the core premise that makes inpainting possible; it is stated implicitly in Section II and used throughout Section IV.
domain assumption The mask H is a diagonal 0/1 matrix applied independently to locations, and observed channel values are noiseless.
The problem formulation in Eq. (1) assumes no observation noise and independent masking; real measurements would include noise and non-independent sampling.
ad hoc to paper Base station position can be inferred from reconstructed channel gain images, and evaluation excludes building-occupied pixels.
The method for BS localization is never given, and the error metrics are computed only over non-building locations, making the evaluation protocol paper-specific.

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Cite this review

Pith. "Pith review of Generative CKM Construction using Partially Observed Data with Diffusion Model." pith.science (2026). https://pith.science/paper/UT2MOIZ4

@misc{pith2026241214812,
  author       = {Pith},
  title        = {Pith review of: Generative CKM Construction using Partially Observed Data with Diffusion Model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UT2MOIZ4}},
  note         = {Machine review of arXiv:2412.14812}
}

read the original abstract

Channel knowledge map (CKM) is a promising technique that enables environment-aware wireless networks by utilizing location-specific channel prior information to improve communication and sensing performance. A fundamental problem for CKM construction is how to utilize partially observed channel knowledge data to reconstruct a complete CKM for all possible locations of interest. This problem resembles the long-standing ill-posed inverse problem, which tries to infer from a set of limited observations the cause factors that produced them. By utilizing the recent advances of solving inverse problems with generative artificial intelligence (AI), in this paper, we propose generative CKM construction method using partially observed data by solving inverse problems with diffusion models. Simulation results show that the proposed method significantly improves the performance of CKM construction compared with benchmarking schemes.

Figures

Figures reproduced from arXiv: 2412.14812 by the authors.

**Figure 1.** CKM image inpainting task framework. of interest. We discretize the area into l × w locations, each involving several types of channel knowledge like channel gain map, angle of arrival (AoA) map, and angle of departure (AoD) map. For each channel knowledge type, the incomplete CKM can be represented as y = Hx, (1) where y ∈ C lw×1 and x ∈ C lw×1 denote the partially observed CKM and complete CKM, respectively. H ∈ C… view at source ↗

**Figure 2.** Conditional decoupled diffusion model for generative CKM construction. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Visualization results of different methods when buildings are masked. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Visualization results of different methods without masking buildings. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: Visualization results of different methods to localize the BS. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

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