ICDM: Interference Cancellation Diffusion Models for Wireless Semantic Communications

Dazhi He; Feng Yang; Meixia Tao; Ping Zhang; Tong Wu; Wenjun Zhang; Xiaodong Xu; Zhiyong Chen

REVIEW 4 major objections 5 minor 1 cited by

ICDM: Interference Cancellation Diffusion Models for Wireless Semantic Communications

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Interference cancellation can be cast as a MAP problem solved by two diffusion models, cutting MSE by 4.54 dB.

desk verdict Promising empirical recipe for interference cancellation in semantic communications, but the core Bayes-derived guidance gradient is algebraically wrong and the theory is weaker than advertised. read the letter →

arxiv 2505.19983 v1 pith:NCA3ALCK submitted 2025-05-26 cs.IT cs.AIcs.CVmath.IT

Tong Wu , Zhiyong Chen , Dazhi He , Feng Yang , Meixia Tao , Xiaodong Xu , Wenjun Zhang , Ping Zhang This is my paper · ORCID

classification cs.ITcs.AIcs.CVmath.IT

keywords semanticcommunicationsinterferencecancellationdiffusionmodelsMAPestimationjointposteriorscore-basedgenerativedeepJSCCRayleighfading

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

This paper proposes a way to remove unknown interference from received wireless signals in semantic communication systems by treating the task not as denoising but as joint estimation. It formulates interference cancellation as a maximum a posteriori (MAP) problem over the posterior of the transmitted signal and the interference together, and proves that the solution's error is bounded by a term that shrinks with the signal-to-noise condition. To solve the MAP problem, the paper builds ICDM, two diffusion models that learn the score functions of the signal and interference priors, plus a derived analytical gradient for the channel transition. On image transmission tasks, ICDM lowers mean squared error by several decibels and improves perceptual metrics across three datasets and two JSCC backbones.

What carries the argument

The load-bearing object is the joint-posterior MAP objective with the decomposition $\nabla_v \log p(v|y,h_x) = [\nabla_x \log p_{y|x,z,h_x}; \nabla_z \log p_{y|x,z,h_x}] + [\nabla_x \log p_x(x_t); \nabla_z \log p_z(z_t)]$. The first two gradients are estimated by two independently trained Diffusion Transformer (DiT) models acting as score functions of the signal and interference priors; the transition gradient is derived in closed form from a Gaussian surrogate prior and then simplified by replacing the covariance $\Theta_t$ and scaling $\zeta_t$ with the surrogates $\Theta_t\approx \frac{\sigma^2}{2}W_n^2$ and $\zeta_t \approx 1/(2-\alpha_t)$. These estimated gradients are fed into a predict-correct sampler (UniPC-style, with accuracy order $p+1$) that integrates the probability-flow ODE for both $x_t$ and $z_t$ in parallel, yielding the final estimates $\hat{x}$ and $\hat{z}$ in about 40 steps.

What would settle it

Compute the true transition posterior numerically by sampling many $(v_t, y)$ pairs from the trained diffusion models and measuring the actual $\Theta_t$ and $\zeta_t$; if the surrogate gradients in Eq. (38) deviate from the empirical gradients by more than the improvement margin the paper reports, the 'accurate estimation' claim would fail. A cheaper check is to run the same ICDM pipeline on features with a deliberately bimodal prior and test whether the MAP-error bound still holds.

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Extended reading notes

Core claim

The central claim is that interference cancellation in a wireless semantic link can be solved as a MAP estimation over the joint posterior $p(x,z|y,h_x)$ of the desired semantic feature vector $x$ and the unknown interference $z$, and that this MAP solution is provably close to the ground truth: the joint estimation error satisfies $(\xi+\lambda_{\min})\sqrt{\|\hat{x}-x^*\|^2+\|\hat{z}-z^*\|^2} \le \|\Sigma n\|$, where $\xi$ measures local strong convexity of the log-priors, $\lambda_{\min}$ is the smallest eigenvalue of the weighted channel Gram matrix, and $\Sigma n$ is a noise term. The paper then converts the MAP problem into an ODE whose score is the sum of two learned prior gradients and a closed-form transition gradient, and shows numerically that this ICDM pipeline reduces MSE by 4.54 dB and improves LPIPS by 2.47 dB on CelebA under Rayleigh fading at SINR 0 dB, with similar gains on bird and real-world images.

Load-bearing premise

The method derives its transition gradient by pretending the true joint prior of signal and interference is a unit-variance Gaussian, then replaces the resulting covariance and scaling by simplified surrogates with no error bound quantifying how close those surrogates are to the real transition.

Editorial extensions

If this is right

The same ICDM module can be inserted after any equalizer and before any JSCC decoder, since it is agnostic to the source codec; the paper demonstrates this with both MambaJSCC and SwinJSCC backbones.
The gains transfer across data domains, not only faces: the paper reports LPIPS improvements on the BIRDS 525 and Kodak/Open Images datasets under the same Rayleigh fading channel.
The method is most effective when signal and interference powers are comparable (around SINR=0 dB), and its advantage shrinks outside roughly $[-4,7]$ dB, where either the interference is too strong to extract a signal or the no-ICDM baseline is already clean.
Because the interference score is learned independently, ICDM can adapt to a new interferer with only a few hundred training iterations of the interference diffusion model.
The 40-step sampler reduces inference time to about 1.6 seconds on a single GPU, compared with 7.8 and 39.2 seconds for standard DiT and DDPM sampling at 200 and 1000 steps.

Reading between the lines

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

If the Gaussian-surrogate derivation were replaced by a non-parametric estimate of the true transition posterior, the same ODE formulation could in principle handle interference that is strongly non-Gaussian, such as impulsive or structured interference from other users.
The reported error bound depends on the local strong convexity parameter $\xi$; for multimodal feature distributions from modern neural codecs, that parameter may be very small, so the practical guarantee may be much weaker than the theorem suggests.
A direct testable extension is to report the actual values of the guidance intensities $\beta$ and $\gamma$; sweeping them would reveal whether the method's success is sensitive to the unstated constants rather than to the derived gradient.

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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

Bottom line: the paper has a useful empirical idea and a genuinely new problem formulation, but the theoretical derivation at its core does not hold up. I checked the stress-test note and it is correct. Eq. (32) is algebraically wrong. For the forward process v_t = √α_t v_T + √(1−α_t)ε with a Gaussian prior N(0, σ̂²I), Bayes' rule gives posterior mean √α_t σ̂²/(α_t σ̂² + 1 − α_t) v_t, not σ̂²/((1−α_t)+σ̂²) v_t as written. With σ̂²=1 the correct coefficient is √α_t, while the paper uses ζ_t ≈ 1/(2−α_t). At α_t=0.01 that is 0.1 versus 0.503, a factor of five. So the claimed 'Bayes-derived' guidance gradient in Eq. (38) is not the Bayes estimate. That is load-bearing, because the paper advertises the method as solving the MAP problem through these accurate gradients.

There is also a sign inconsistency. Eq. (29) says ∇x log p_x(x_t) = −ε_x/√(1−α_t), so the score is the negative noise prediction. But Eq. (40) sets r_θ = s_θ − β r̄_x, which has s_θ with the opposite sign. The ODE update may compensate with its own minus sign, but as written r_θ is not the posterior gradient in Eq. (23). The authors need to fix the sign convention and show the algebra.

The theoretical bound in Theorem 1 is also weaker than advertised. Assumption 2 requires the ground truth to be a local optimum of both priors and the log-priors to be locally strongly convex. For natural images or JSCC features that is a big ask, and there is no evidence it holds. The bound is more a plausibility argument than a proof of 'excellent estimates'.

What should be credited: the problem is real, unaware interference in wireless semantic communications is a practical deployment concern. Modeling interference cancellation as joint MAP over two separately learned diffusion priors is new relative to CDDM and DPS. The experimental comparison is broad: three datasets, two JSCC backbones, and ablations against DPS/GDM/projection. The gains are large and consistent within the reported SINR range, and Fig. 9 showing interference-prior training progress is a nice sanity check. The fast 40-step sampler is a useful engineering contribution.

Minor: abstract says 4.54 dB MSE and 2.47 dB LPIPS, conclusion says 5.67 and 2.65; they should reconcile. β and γ are never reported. There are typos in Eq. (42)/(49) using r_θ instead of r_ϕ.

Who this is for: researchers working on diffusion-based receivers or semantic communication robustness. The empirical recipe is worth trying, but the theory needs a significant rewrite, either correcting the Bayes step or explicitly reframing the gradient as a heuristic. I would send it to review because the empirical contribution deserves scrutiny, but I would not cite the theory as-is.

Referee Report

4 major / 5 minor

Summary. The paper proposes ICDM, a diffusion-model-based interference cancellation method for wireless semantic communications. The received/equalized signal is modeled as a linear combination of the desired signal and an unknown interference plus noise, and the recovery problem is formulated as joint MAP estimation over signal and interference. The authors prove (Theorem 1) a bound on the estimation error under local strong convexity assumptions, then propose to solve the MAP problem with two diffusion models that estimate the prior log-gradients and with a closed-form ``derived'' guidance gradient for the channel transition probability obtained via a Gaussian assumption and Bayes' rule. The resulting gradients are combined with a p-order predictor-corrector sampler. Experiments on CelebA, BIRDS 525, and Kodak, with MambaJSCC and SwinJSCC, report consistent gains in MSE, LPIPS, and CLIP over not using ICDM and over several alternative guidance-gradient estimators.

Significance. If the theoretical derivation and the theorem were correct, this would be a useful contribution to semantic communications: it extends diffusion-based channel recovery from pure Gaussian denoising to structured interference, proposes a principled joint MAP formulation, and provides a fast high-order sampler. The empirical study is broad: three datasets, two JSCC architectures, two channel models, and comparisons against DPS, GDM, Projection, and CDDM. The observation that the interference diffusion model needs only about 600 training iterations to be useful is also interesting. However, the central derivation of the guidance gradient contains a load-bearing Bayes-rule error and a sign inconsistency, and the theorem's strong-convexity assumption is self-contradictory for a local optimum of a density. These issues mean that the paper's advertised claim of ``accurately estimated'' gradients is not established, and the theoretical performance guarantee does not follow as stated.

major comments (4)

[Section III-B, Eq. (32)] The posterior p(v_T | v_t) is computed incorrectly. From the forward process (24) with p(v_T) = N(0, σ̂² I), Bayes' rule gives p(v_T | v_t) = N(v_T; [√α_t σ̂² / (α_t σ̂² + 1 − α_t)] v_t, [(1 − α_t) σ̂² / (α_t σ̂² + 1 − α_t)] I). Equation (32) instead gives the mean coefficient as σ̂² / ((1 − α_t) + σ̂²) and the covariance as (1 − α_t) σ̂² / ((1 − α_t) + σ̂²) I, dropping both the √α_t factor in the numerator and the α_t σ̂² term in the denominator. With σ̂² = 1, the correct coefficient is √α_t, but Eq. (37) sets ζ_t ≈ 1/(2 − α_t). At α_t = 0.01 these differ by a factor of about 5 (0.503 versus 0.1). Since ζ_t and Θ_t enter the closed-form gradient (35) and hence the final guidance gradient (38), Eq. (38) is not the Bayes estimate even under the paper's own Gaussian-prior assumption. The replacements (36)–(37) are therefore not a minor approximation; they replace the derived quantities with substantially different ones, and no error bound is supplied.
[Section III-C, Eq. (40), with Eqs. (23), (27), (29)] The definition of r_θ is inconsistent with the score relations earlier in the paper. Since the training objective (27) minimizes ‖s_θ(x_t,t) − ε_x‖², the learned model satisfies s_θ ≈ ε_x, and Eq. (29) gives ∇_x log p_x(x_t) = −s_θ / √(1 − α_t). The posterior-gradient decomposition (23) requires adding the likelihood gradient to the prior gradient. Equation (40), however, forms r_θ = s_θ − β r̄_x. Thus, if s_θ is a noise prediction and r̄_x approximates the likelihood gradient, the prior term has the wrong sign and the likelihood term is subtracted rather than added. Consequently r_θ is not an estimate of ∇_{x_t} log p(x_t, z_t | y, h_x) as claimed immediately below (40). The update (41) uses −r_θ, so the overall iteration may accidentally move in a correct direction, but the identification of r_θ with the posterior gradient is algebraically inconsistent. The authors need to define signs coherently among Eqs. (23), (29), (40), and (41).
[Section II-B, Assumption 2 and Theorem 1] Assumption 2 is self-contradictory and the proof of Theorem 1 therefore does not hold. The assumption states that log p_x and log p_z are locally strongly convex (parameters µ, ν > 0) and that the ground-truth x*, z* are local optima of these log-densities. A local maximum of a smooth density has a negative semidefinite Hessian (or a zero Hessian), so it cannot be locally strongly convex with a positive curvature parameter. The inequalities (11)–(12) have the wrong sign under the stated assumption, so the lower bound ξ‖v̂ − v*‖² in (13) is not justified. This is load-bearing because the positive denominator ξ + λ_min in (5) and (18) is essential for the claimed error bound. The authors must either replace the assumption with a mathematically consistent one and re-derive the bound, or remove the theorem.
[Section III-C, Eq. (40), and Section IV experiments] The values of the guidance intensities β and γ are never reported for any experiment, and no ablation or sensitivity study is provided. The paper describes them in Remark 1 as balancing consistency with the received signal versus generation realism, but they multiply the supposedly derived gradient r̄_x. Without reporting their values or showing that the results are robust to their choice, it is impossible to tell whether the gains of ICDM come from the derived guidance gradient or from tuning these two free parameters. At a minimum, provide the chosen values, the search range, and a sensitivity table.

minor comments (5)

[Section III-C, Eqs. (42) and (49)] The updates for z_t use r_θ (...) instead of r_φ (...) in the first line of both equations; the interference update should use the interference diffusion model r_φ, not the signal model r_θ.
[Section V and Section IV-B] The conclusion reports that ICDM reduces MSE by 5.67 dB and improves LPIPS by 2.65 dB on CelebA, while the abstract and Section IV-B report 4.54 dB and 2.47 dB. These numbers should be reconciled.
[Figure 8] The caption and legend labels in Figure 8 appear to be inconsistent: the caption says SwinJSCC-based schemes but the legends still read ``MambaJSCC With ICDM'' / ``MambaJSCC Without ICDM''. Please correct the labels.
[Notation, Eq. (24) and Algorithm 3] The time indexing is nonstandard and confusing: Eq. (24) uses x_T as the clean sample, while Algorithm 3 initializes x_0 as pure noise and outputs x_T as the estimate. Since the meaning of increasing t is opposite to the usual diffusion-model convention, please define the direction of the noise schedule explicitly and use consistent notation throughout.
[Throughout] There are many typos and grammatical slips, e.g., ``beacuse'' (Section III-A), ``polts'' and ``continuous'' (Section IV-B), ``Exapmles'' (Figure 7), ``vextor'' (Section II-A), and ``unware'' (Section IV-A). A careful proofreading pass is needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the MAP bound and guidance gradients rest on stated assumptions and explicit approximations, and the empirical claims are benchmarked against external baselines.

full rationale

I find no circular step that reduces a prediction to its inputs by construction. The MAP formulation (2) is defined independently of the proposed solver, and Theorem 1 is proven from explicit Assumptions 1 and 2. Those assumptions—independence, local strong convexity, and ground-truth stationarity—are strong and unverified premises, but they are premises, not imported conclusions, so the bound is a conditional theorem rather than a circular definition. In the guidance-gradient derivation of Section III-B, the paper explicitly assumes a Gaussian prior p(vT) = N(0, σ̂²) and then explicitly replaces the derived ζt and Θt with surrogates in Eqs. (36) and (37). This makes the final gradient (38) an acknowledged approximation, not a quantity that is claimed to equal the derived expression by construction. Whether Eq. (32) is algebraically correct, or whether the surrogate ζt ≈ 1/(2 − αt) is accurate, is a correctness and validity concern, not a circularity concern: the paper does not define the prediction as the fit. The tunable intensities β and γ in Eq. (40) are free hyperparameters, but they are not fitted to the reported performance numbers and then renamed as predictions. The empirical gains are measured against external baselines (MambaJSCC without ICDM, SwinJSCC without ICDM, DPS, GDM, Projection, CDDM) on real datasets, so the main experimental claim is self-contained. Self-citations such as CDDM [14] and MambaJSCC [26] provide motivation, baselines, and system components, but the load-bearing MAP-to-ODE-to-sampler argument does not reduce to those citations. No uniqueness theorem is imported from the authors' prior work, and no known result is merely renamed. Overall, the paper's derivation chain may contain mathematical approximations or errors, but it is not circular.

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

The central claim rests on two unverifiable assumptions (local strong convexity and ground-truth optimality, Gaussian prior surrogates) and on unreported tuning parameters β and γ. No new physical entities are introduced.

free parameters (4)

β (signal guidance intensity) = not reported
Introduced in Eq (40) to balance data consistency and realism for the signal prior. The paper never gives its value or a sensitivity study.
γ (interference guidance intensity) = not reported
Same role as β for the interference prior. Value not reported.
ζ_t (transition scaling surrogate) = 1/(2 - α_t) with σhat^2=1
In Eq (37), the derived scaling factor is replaced by this expression after arbitrarily setting σhat^2=1.
σhat^2 (assumed prior variance) = 1
Set to 1 to obtain a closed-form gradient; no justification from the actual JSCC feature distribution.

assumptions (4)

domain assumption The transmitted signal x and interference z are independent.
Assumption 1 in Section II-B. Standard for modeling, needed for the factorization of the joint prior.
ad hoc to paper log px(x) and log pz(z) are locally strongly convex with parameters µ, ν > 0, and the ground truth x*, z* are local optima of both priors.
Assumption 2 in Section II-B. This is not verified and is necessary for the error bound in Theorem 1. If the ground truth is not a local mode, the bound does not follow.
ad hoc to paper The prior p(vT) is Gaussian N(0, σhat^2 I) for the purpose of deriving the guidance gradient.
Eq (31)-(32) in Section III-B. This is known to be false for image features but is needed to marginalize the transition probability.
domain assumption The learned diffusion models sθ and sφ accurately approximate the true score functions at every time step.
Assumed in Section III-A as the basis for using sθ and sφ as prior gradients. Score estimation error is not incorporated into the error bounds.

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Cite this review

Pith. "Pith review of ICDM: Interference Cancellation Diffusion Models for Wireless Semantic Communications." pith.science (2026). https://pith.science/paper/NCA3ALCK

@misc{pith2026250519983,
  author       = {Pith},
  title        = {Pith review of: ICDM: Interference Cancellation Diffusion Models for Wireless Semantic Communications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NCA3ALCK}},
  note         = {Machine review of arXiv:2505.19983}
}

abstract

Diffusion models (DMs) have recently achieved significant success in wireless communications systems due to their denoising capabilities. The broadcast nature of wireless signals makes them susceptible not only to Gaussian noise, but also to unaware interference. This raises the question of whether DMs can effectively mitigate interference in wireless semantic communication systems. In this paper, we model the interference cancellation problem as a maximum a posteriori (MAP) problem over the joint posterior probability of the signal and interference, and theoretically prove that the solution provides excellent estimates for the signal and interference. To solve this problem, we develop an interference cancellation diffusion model (ICDM), which decomposes the joint posterior into independent prior probabilities of the signal and interference, along with the channel transition probablity. The log-gradients of these distributions at each time step are learned separately by DMs and accurately estimated through deriving. ICDM further integrates these gradients with advanced numerical iteration method, achieving accurate and rapid interference cancellation. Extensive experiments demonstrate that ICDM significantly reduces the mean square error (MSE) and enhances perceptual quality compared to schemes without ICDM. For example, on the CelebA dataset under the Rayleigh fading channel with a signal-to-noise ratio (SNR) of $20$ dB and signal to interference plus noise ratio (SINR) of 0 dB, ICDM reduces the MSE by 4.54 dB and improves the learned perceptual image patch similarity (LPIPS) by 2.47 dB.

Figures

Figures reproduced from arXiv: 2505.19983 by the authors.

**Figure 2.** The overall structure of the proposed ICDM. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** The overall sampling process of ICDM. xt and zt are invisible signals and we decode them into images here for illustration. 𝒔𝒔𝜃𝜃(𝒙𝒙𝑡𝑡,𝑡𝑡) 𝑥𝑥𝑡𝑡 𝑧𝑧𝑡𝑡 𝑦𝑦 Signal Prior Gradient Joint Conditional Gradient 𝒔𝒔𝜃𝜃(𝒙𝒙𝑡𝑡,𝑡𝑡) Guide Gradients 𝒔𝒔𝜙𝜙(𝒛𝒛𝑡𝑡,𝑡𝑡) 𝒔𝒔𝜃𝜃(𝒙𝒙𝑡𝑡,𝑡𝑡) 𝒓𝒓𝜃𝜃(𝒙𝒙𝑡𝑡, 𝒛𝒛𝑡𝑡, 𝒚𝒚, 𝒉𝒉𝒙𝒙,𝑡𝑡) 𝑟𝑟𝑥𝑥̅(𝒙𝒙𝑡𝑡, 𝒛𝒛𝑡𝑡, 𝒚𝒚, 𝒉𝒉𝒙𝒙,𝑡𝑡) 𝑟𝑟̅ 𝑧𝑧(𝒙𝒙𝑡𝑡, 𝒛𝒛𝑡𝑡, 𝒚𝒚, 𝒉𝒉𝒙𝒙,𝑡𝑡) −𝑟𝑟𝑥𝑥̅(𝒙𝒙𝑡𝑡, 𝒛𝒛𝑡𝑡, 𝒚𝒚, 𝒉𝒉𝒙𝒙,𝑡𝑡) −𝑟𝑟̅ 𝑧𝑧(𝒙𝒙𝑡𝑡, 𝒛𝒛𝑡𝑡, 𝒚𝒚, 𝒉𝒉𝒙𝒙,𝑡𝑡) Joi… view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: The illustration of the JCG module. interference PC sampling module. Given the previous p samples {xt−m} p m=1 and {zt−m} p m=1, the p JCG modules compute 2p joint conditional gradients {rθ(xt−m, zt−m, y, hx, t− m)} p m=1 and {rϕ(xt−m, zt−m, y, hx, t − m)} p m=1, whi…

**Figure 5.** Figure 5: MSE, LPIPS and CLIP performance of the MambaJSCC-based schemes on the CelebA dataset under both the AWGN and Rayleigh [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 6.** Figure 6: MSE, LPIPS and CLIP performance of the MambaJSCC-based schemes on the BIRDS 525 and Kodak datasets under the Rayleigh [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: (a) Exapmles of the visual comparison between the source images and the images reconstructed with or without the ICDM under [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

**Figure 8.** Figure 8: MSE, LPIPS and CLIP performance of the SwinJSCC-based schemes on the CelebA datasets under the Rayleigh fading channel. [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

**Figure 9.** Figure 9: LPIPS performance of MambaJSCC with ICDM on the [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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Pith tools

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