{"id":"0bb2c3e7-ba76-4b56-a036-df33de73b898","arxiv_id":"2505.04930","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A diffusion-model-based posterior sampler, trained on simulated fluid antenna channels, achieves lower normalized mean squared error than compressed sensing baselines for 2D FAS channel estimation and is accelerated by skipping sampling steps.","lead":"This paper applies a diffusion model as a learned prior to reconstruct channel state information for two-dimensional fluid antenna systems from partial port observations. The method reports higher estimation accuracy than compressed sensing baselines and a large speedup via a skipped-sampling acceleration.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Algorithm 2/Eq. (21) divides the predicted clean channel by sqrt(αbar), an undefined scaling in DDRM that would make the sampler diverge; the paper's algorithm description does not reproduce its own results.","rationale":"This stress-test focused on the internal consistency of the proposed algorithm, since the central claim (higher accuracy and 20× speedup) depends on Algorithm 2 being a working DDRM posterior sampler. The reader's weakest assumption concerned train/test distribution shift, a valid limitation but not the most fundamental issue. The most load-bearing concern is a scaling inconsistency in Eq. (21) and Algorithm 2 line 5. The VE/VP transformation is correctly stated: hVE = hVP / sqrt(αbar), and Algorithm 2 line 3 correctly converts the VE spectral latent back to the VP original-domain latent. The DDPM clean estimate from Eq. (20) is an estimate of h0. Yet Eq. (21) divides this estimate by sqrt(αbar) before using it as the predicted ground truth in the DDRM update (19). In DDRM, the predicted x0 is used directly; no such division appears in the original formulation [11]. With the given noise schedule, αbar decays to about 0.007 at T=500, so the first update would multiply the inpainted estimate by about 12, and the recursion would grow without bound over 25 steps. Thus the pseudocode cannot yield the reported NMSE. This is not a matter of tuning or distribution shift: it is a mismatch between the described method and the claimed performance. The paper provides no code or formal verification, so we cannot check whether the implementation matches Eq. (21) or an uncorrected version. Consequently, the correctness of the reported results is unverified. The skipped-sampling idea itself is plausible and the comparison methodology (aside from unquantified speedups) is conventional, but the algorithm description must be corrected before the claims can be assessed. This is why the verdict should move from CONDITIONAL to UNVERDICTED.","tokens_in":9974,"tokens_out":15361,"duration_ms":145616,"concrete_test":"Reimplement Algorithm 2 exactly as written, including the division by sqrt(αbar) in Eq. (21), using the stated schedule (β from 1e-4 to 0.02, T=500, T'=25, N=51×51, M=4, L=125, ηa=0, ηb=1, ηc=1) and measure NMSE at SNR=10 dB. If the output diverges (NMSE > 0 dB), the described algorithm contradicts Fig. 3; then rerun with Eq. (21) replaced by hbar_θ = P h_hat and confirm that Fig. 3 is recovered, which would prove Eq. (21) is an error in the paper.","verdict_should_be":"UNVERDICTED","load_bearing_attack":"In the proposed DDRM posterior sampler, Algorithm 2 line 3 defines hbar as the variance-exploding (VE) latent: h = sqrt(αbar) P^T hbar. Line 4 computes h_hat via Eq. (20), which is the standard DDPM clean-data estimate. Because hbar is the VE latent, the VE clean signal is h0 itself; after the permutation, the predicted clean channel in the spectral domain is P h_hat. Line 5 and Eq. (21), however, set hbar_θ = P h_hat / sqrt(αbar). This division has no counterpart in DDRM: in the VE formulation the latent is v_t = h0 + σ_t ε, and the generative update in Eq. (19) uses the denoiser's output as the clean estimate x0_hat directly. With the paper's schedule (β1 = 1e-4 to βT = 0.02, T = 500), αbar_500 ≈ 0.007, so the first step in the unobserved branch of Eq. (19) would amplify the inpainted estimate by about 12, and the recursion would diverge over the T' = 25 steps. The NMSE values in Figs. 3–4 could not be produced by the pseudocode as written. Either the implementation omits the /sqrt(αbar) term, in which case Eq. (21) misdescribes the method, or it includes it, in which case the reported accuracy is unexplained. The central accuracy claim is therefore not reproducible from the manuscript.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes a diffusion-model-based channel estimator for two-dimensional fluid antenna systems (FAS) with limited RF chains. The authors train a simplified U-Net as a diffusion prior on synthetic FAS channel samples, then perform posterior sampling through the denoising diffusion restoration model (DDRM) framework, which exploits the fact that the selection matrix reduces to a permutation so that estimation becomes denoising on observed ports and inpainting on unobserved ports. A DDIM-style skipped sampling strategy is introduced to reduce the number of reverse diffusion steps. Numerical simulations compare NMSE and latency against OMP and SBL baselines, reporting accuracy gains and a large speedup for the accelerated version.","tokens_in":10369,"tokens_out":10890,"duration_ms":112776,"significance":"If corrected and validated, the paper would provide a practically relevant application of diffusion priors to a challenging high-dimensional inverse problem in wireless communications. The idea of replacing hand-crafted sparsity priors with a learned channel prior is timely for FAS, and the skipped-sampling acceleration addresses an important latency concern. The paper is honest in scope: it evaluates only a synthetic channel model, and the results are strong in that in-distribution setting. However, the central algorithm is not reproducible as written because of an apparent scaling error in Eq. (21), and the baseline comparison is biased in favor of the proposed method because the classical baselines do not have access to the training distribution. These issues must be resolved before the main claims can be considered established.","major_comments":[{"comment":"The division by sqrt(alpha_bar_tau_i) in Eq. (21) is inconsistent with the variance-exploding (VE) representation used in Eqs. (16)-(19). In the VE formulation the latent is bar_h_t = P h0 + sigma_t epsilon, so the predicted clean latent should be bar_h_theta,t = P hat_h_theta(h_tau_i, tau_i) with no additional scaling. With the chosen schedule (beta_1=10^-4, beta_T=0.02, T=500), sqrt(alpha_bar_500) is approximately 0.084, so the division in Eq. (21) would amplify the predicted channel by a factor of about 12 at the first reverse step. Since Eq. (19) substitutes bar_h_theta,t into the update for the unobserved ports and, for eta_a=0, into the small-noise observed branch, this amplification propagates through the recursion and cannot yield the NMSE values reported in Figs. 3-4. Please either remove the division in Eq. (21) and in Algorithm 2 or provide a different definition of bar_h that makes the scaling correct.","section":"Section III-B, Algorithm 2 line 5, Eq. (21)"},{"comment":"The comparison with OMP and SBL is biased as stated. The proposed estimator is trained on Ntrain=40,000 samples generated from the same channel model (1) and the same parameter values (Np=90, p(theta,phi)=cos(phi)/(2pi), W=4lambda by 4lambda) as the test data, whereas OMP and SBL receive no training data and rely only on sparsity or angular-grid priors. The accuracy gains in Figs. 3 and 4 therefore reflect the advantage of an in-distribution learned prior rather than a general advantage over CS-based estimation. I ask the authors to add a baseline that also uses the training data, such as a learned denoiser or a trained CS/ISTA network, to evaluate robustness under distribution shift (different Np, AoA distributions, or array sizes), and to revise the conclusion accordingly.","section":"Section IV, training and baseline setup"},{"comment":"The caption of Fig. 5 says 'NMSE performance versus sampling ratio' but the axis labels and the surrounding text indicate that the figure actually plots latency. In addition, the Abstract claims 'over 20x speedup compared to state-of-the-art compressed sensing-based methods,' but the body text states that the accelerated method has latency 'comparable to that of OMP,' so the 20x speedup is supported only against SBL. Please correct the caption and restate the speedup claim relative to the specific baseline (SBL, not OMP).","section":"Section IV, Fig. 5 and Abstract"}],"minor_comments":[{"comment":"The decomposition S = I Sigma P should be written as the SVD S = U Sigma V^T, here with U = I and V = P^T (or P), and the dimensions of Sigma should be given explicitly.","section":"Section III-B, around Eq. (5)"},{"comment":"The variance parameter sigma_t of the VE diffusion process is never defined; please state explicitly that sigma_t^2 = (1 - alpha_bar_t) / alpha_bar_t so that the equivalence with the VP process and the scaling in Algorithm 2 can be checked.","section":"Section III-B, Eqs. (16)-(19)"},{"comment":"The simplified U-Net architecture is described only qualitatively; please provide the number of channels at each level, the embedding dimension, the number of trainable parameters, or release the code, so that the numerical results are reproducible.","section":"Section IV, training details"},{"comment":"The relationship between the sampling ratio delta = LM/N and the number of pilot slots L used for each plotted point is not stated; please include the L values or explain how the sampling ratio is varied.","section":"Section IV, Fig. 4"},{"comment":"With all weights gamma_t set to 1, the objective in Eq. (11) is the simplified denoising objective of [9], not the ELBO itself; please rephrase 'the ELBO objective is reduced to' accordingly.","section":"Section II-B, Eq. (11)"}],"recommendation":"major_revision","confidential_remarks":"The decisive issue is whether Eq. (21) is a typographical error or faithfully describes the implementation. If the implementation actually includes the division by sqrt(alpha_bar), the reported NMSE values are not credible; if it does not, the manuscript misdescribes the method. I recommend major revision rather than rejection because the underlying approach is sound and fixable, and because the skipped-sampling contribution has practical potential. The baseline-fairness concern should also be addressed, ideally by adding a data-driven baseline and out-of-distribution experiments."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe short version: this is a competent domain application of DDRM to 2D fluid-antenna channel estimation, but the core algorithm as written has a scaling error that would make the sampler diverge. The reported MSE and latency numbers cannot be reproduced from the pseudocode. I think it is likely a typo rather than a fundamental flaw, but it needs to be fixed before the results are believable.\n\nWhat is actually new: the authors port DDRM and DDIM-style skipped sampling to 2D FAS channel estimation, with a simplified U-Net as the denoiser. That fills a real gap in the FAS literature, and the latency results, if they hold, are the strongest point—a 20x speedup over SBL with comparable accuracy is practically relevant.\n\nSoft spots, in order of weight. First, Algorithm 2 line 5 and Eq. (21) divide the predicted clean channel by sqrt(alpha_bar). Eq. (20) already returns an estimate of h0 in the VP space used to train the network. The VE clean signal is the same h0, not h0/sqrt(alpha_bar). With their noise schedule, alpha_bar at t=500 is about 0.007, so this step amplifies the estimate by ~12, and the recursion would diverge over the 25 sampled steps. Either the implementation omits the division (and the paper misdescribes the method) or the described algorithm simply cannot produce the figures. Second, the baselines (OMP, SBL) lack access to the training distribution, while the proposed method exploits a learned prior from the very same synthetic model—an unfair comparison that should at least be discussed. Third, train and test channels are drawn from the identical distribution (Eq. (1), Np=90, the same AoA model), so no distribution-shift robustness is shown. Fourth, there are no error bars, and the speedup claim is only backed by a latency bar chart without precise numbers.\n\nOn net: the application idea is sound, and the evaluation is adequate apart from these issues, but the algorithm error is load-bearing. The paper deserves serious refereeing, but only conditionally. I would send it to review and require a corrected Eq. (21) or (20), a rerun of the experiments, and a clearer baseline comparison. If the same results survive the fix, it becomes a solid application paper for the FAS community.\n\nBest,\n[Your name]","headline":"A reasonable DDRM-for-FAS application that is currently undermined by a scaling error in its core pseudocode; the reported results are not reproducible as written.","tokens_in":10853,"tokens_out":7330,"would_cite":false,"duration_ms":71876,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that an offline-trained diffusion model can serve as a learned implicit prior for reconstructing full two-dimensional fluid-antenna channels from partial port observations, beating compressed-sensing baselines in…","keywords":["fluid antenna systems","channel estimation","diffusion models","posterior sampling","denoising diffusion restoration models","compressed sensing","sparse Bayesian learning","unsupervised learning"],"falsifier":"Generate a test set from a different scatterer distribution—say uniform AoA instead of $\\cos(\\varphi)/(2\\pi)$, or $N_p=20$ instead of 90—and compare the trained diffusion estimator against SBL and OMP at 10 dB SNR with the same 500 observations; if the diffusion method loses its margin or falls below SBL, the claim that the learned prior captures general 2D FAS channel structure is falsified.","tokens_in":9785,"feed_emoji":"📡","tokens_out":6000,"duration_ms":57069,"temperature":0.7,"pith_summary":"This paper aims to solve a practical bottleneck of fluid antenna systems (FAS): reconstructing the full channel over thousands of densely packed ports while only a few radio-frequency chains can observe a handful of ports at a time. The proposed answer is to stop relying on hand-crafted sparsity or Gaussian-process priors and instead learn the spatial correlation structure of 2D FAS channels offline with a diffusion model, then use that model online as an implicit prior and reconstruct the channel by sampling from the posterior. The paper reports that this posterior-sampling estimator beats sparse Bayesian learning and orthogonal matching pursuit in normalized mean-squared error across SNR and sampling-ratio ranges, and that a skipped-sampling acceleration cuts computation by more than 20 times, bringing latency down to roughly that of OMP. If right, this makes high-dimensional FAS channel estimation feasible without a sparsity assumption and opens a data-driven route to real-time CSI acquisition for fluid antennas.","feed_headline":"Diffusion models cut FAS channel estimation error and latency","feed_subtitle":"A learned prior plus posterior sampling reconstructs full 2D fluid-antenna channels from few ports, beating sparse Bayesian learning.","key_machinery":"The load-bearing object is the denoising network $\\epsilon_\\theta$—a simplified U-Net with four encoder/decoder levels, sinusoidal time embedding, and skip connections—trained offline in an unsupervised way to predict the noise added at each step of a variance-preserving diffusion process. In deployment it acts as an implicit prior inside the DDRM posterior sampler: after transforming each latent sample to the variance-exploding representation and spectral domain $P$, each element is updated according to whether the corresponding port was observed; observed elements are denoised toward the noisy measurement, unobserved elements are inpainted from the prior. Skipped sampling over a sub-sequence $\\{\\tau_i\\}$ of the 500 diffusion steps, the mechanism borrowed from DDIM, is what converts the method from accurate-but-iterative into a low-latency estimator. The whole argument turns on the measurement matrix being a pure port-selection operator, so the spectral domain is simply a permutation of the spatial ports.","core_discovery":"On the paper's own terms, the central discovery is that the ill-posed FAS channel estimation problem—recover $\\tilde{h}\\in\\mathbb{C}^{N_1\\times N_2}$ from $y = Sh + n$ with $M\\ll N$ observed ports—can be solved by a learned diffusion prior together with the denoising diffusion restoration model (DDRM). Because the measurement matrix $S$ for port selection is a permuted identity (after real-valued stacking its SVD has the form $S = I\\Sigma P$), the spectral domain is just the reordered spatial domain: observed port positions receive a denoising update, unobserved positions receive an inpainting update, and the trained denoising network supplies the prior for both. The paper's numerical claim is that this scheme achieves lower normalized mean-squared error than sparse Bayesian learning over the whole tested SNR range and sampling-ratio range, and that skipping most diffusion steps—using only 25 of 500 latent steps—loses negligible accuracy while cutting online latency by a factor above 20, to a level comparable with OMP.","pith_inferences":["A natural test is distribution shift: train on the paper's channel model (1) with $N_p=90$ and $p(\\theta,\\varphi)=\\cos(\\varphi)/(2\\pi)$, then evaluate on a test set with a different path count or AoA distribution; if the diffusion estimator loses its margin over SBL, the learned prior is specific to the training geometry rather than general FAS structure.","The skipped-sampling trajectory is constructed by uniformly quantizing the diffusion steps; choosing the trajectory adaptively or learning it is a testable extension that could reduce $T'$ further without accuracy loss.","Because the 2D FAS channel is treated as an image-like tensor, the same pipeline could transfer to other linear port-selection problems—1D fluid antennas, irregular or curved surfaces, or movable-antenna position optimization—though the paper only demonstrates the rectangular 2D case."],"forward_implications":["Full CSI for a 51-by-51 port FAS can be recovered from as few as 500 total observations (4 RF chains over 125 slots) with lower NMSE than compressed-sensing baselines, even in a rich-scattering environment with 90 paths where sparsity is weak.","The accelerated version's latency is comparable to OMP, so the method is a candidate for real-time channel estimation rather than offline processing.","Because the diffusion prior is learned from data rather than hand-crafted, the approach bypasses the sparsity assumption that limits compressed sensing in dense-scattering FAS settings.","The gap over sparse Bayesian learning widens at high SNR and at low sampling ratios, suggesting the learned prior buys the most accuracy exactly where the compressed-sensing baselines degrade.","The method inherits DDRM's applicability to any linear inverse problem; the same trained prior could in principle be reused for different port selection patterns and numbers of observations without retraining."],"supporting_citations":[{"why":"Defines the forward/reverse diffusion process and the simplified denoising objective used for the unsupervised offline training of the prior.","marker":"[9]"},{"why":"Supplies the DDRM conditional generation framework that converts the trained prior into a posterior sampler for partial observations.","marker":"[11]"},{"why":"Supplies the deterministic skipped-sampling / DDIM trajectory idea used to reduce the number of online diffusion steps.","marker":"[14]"},{"why":"The sparse Bayesian learning baseline, generalized from 1D, that the proposed method must beat.","marker":"[7]"},{"why":"Provides the OMP-style compressed-sensing baseline and its 1D FAS channel estimation context.","marker":"[8]"},{"why":"Supports the claim that posterior sampling with a deep generative prior can achieve near-optimal estimation error in inverse problems.","marker":"[10]"}],"fun_headline_variants":["20x faster FAS channel estimation via diffusion priors","Diffusion prior turns sparse FAS ports into full channel map","FAS channel estimation: diffusion beats sparse Bayesian, 20x faster","Diffusion model speeds fluid-antenna channel estimation 20x"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that channels synthesized from the simulation model with 90 paths and the cosine-weighted angle-of-arrival distribution match real fluid-antenna propagation well enough that the prior learned offline still holds when the estimator is deployed.","fun_headline_variants_meta":{"raw":{"variants":["20x faster FAS channel estimation via diffusion priors","Diffusion prior turns sparse FAS ports into full channel map","FAS channel estimation: diffusion beats sparse Bayesian, 20x faster","Diffusion model speeds fluid-antenna channel estimation 20x"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000721,"raw_usage":{"total_tokens":3242,"prompt_tokens":960,"completion_tokens":2282,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":576,"completion_tokens_details":{"reasoning_tokens":2211}},"tokens_in":576,"tokens_out":2282,"duration_ms":14619,"temperature":1.0,"reasoning_tokens":2211,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T23:17:50.812280+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Generate a test set from a different scatterer distribution—say uniform AoA instead of $\\cos(\\varphi)/(2\\pi)$, or $N_p=20$ instead of 90—and compare the trained diffusion estimator against SBL and OMP at 10 dB SNR with the same 500 observations; if the diffusion method loses its margin or falls below SBL, the claim that the learned prior captures general 2D FAS channel structure is falsified.","supporting_citations":[{"cited_title":"Denoising diffusion proba bilistic models,","cited_arxiv_id":null,"evidence_quote":"Defines the forward/reverse diffusion process and the simplified denoising objective used for the unsupervised offline training of the prior."},{"cited_title":"Denoising diff usion restoration models,","cited_arxiv_id":null,"evidence_quote":"Supplies the DDRM conditional generation framework that converts the trained prior into a posterior sampler for partial observations."},{"cited_title":"Denoising diffusion imp licit models,","cited_arxiv_id":null,"evidence_quote":"Supplies the deterministic skipped-sampling / DDIM trajectory idea used to reduce the number of online diffusion steps."},{"cited_title":"Sparse baye sian learning-based channel estimation for fluid antenna system s,","cited_arxiv_id":null,"evidence_quote":"The sparse Bayesian learning baseline, generalized from 1D, that the proposed method must beat."},{"cited_title":"Successive baye sian reconstructor for channel estimation in fluid antenna syste ms,","cited_arxiv_id":null,"evidence_quote":"Provides the OMP-style compressed-sensing baseline and its 1D FAS channel estimation context."},{"cited_title":"Robust compressed sensing MRI with deep generative priors ,","cited_arxiv_id":null,"evidence_quote":"Supports the claim that posterior sampling with a deep generative prior can achieve near-optimal estimation error in inverse problems."}],"review_version":1}