Generative Semantic Communication via Alternating Dual-Domain Posterior Sampling

1. Problem Statement

The paper addresses the limitations of existing Generative Semantic Communication (SemCom) systems, particularly under challenging conditions of severe bandwidth compression and low Signal-to-Noise Ratio (SNR).

• The Core Issue: Current generative SemCom receivers typically rely on Maximum A Posteriori (MAP) estimation. MAP is a point estimator that collapses the full posterior distribution into a single solution. The authors argue that this fundamentally fails to preserve the original data distribution, leading to blurry, over-smoothed reconstructions with poor perceptual quality.
• Limitations of Current Diffusion Approaches: While recent methods use diffusion models for posterior sampling, they face a dilemma in guidance strategies:
  • Latent-domain (Z-domain) guidance: Highly sensitive to channel noise at low SNRs, often amplifying artifacts.
  • Image-domain (X-domain) guidance: Robust to noise but may discard semantic evidence from the received signal and inherit biases from the decoder.
  • Simultaneous Guidance: Simply combining both domains at every step creates an "overconfident pseudo-posterior" because it treats correlated evidence (the received signal and the decoder output) as independent, leading to gradient conflicts and instability.

2. Methodology: Alternating Dual-Domain Posterior Sampling (ADDPS)

The authors propose ADDPS, a diffusion-based receiver that reformulates semantic decoding as a Bayesian inverse problem and solves it via posterior sampling rather than optimization.

A. Theoretical Foundation

• Bayesian Formulation: The reconstruction task is defined as sampling from the posterior $p(x|\hat{z})$, where $x$ is the source image and $\hat{z}$ is the noisy received signal.
• Proof of Optimality: The paper proves that while MAP estimation distorts the data distribution (reducing variance), posterior sampling theoretically preserves the original data distribution ($p_{\hat{x}} = p_{data}$), thereby achieving optimal perceptual quality.
• Score Approximation: Since the likelihood score $\nabla_{x_t} \log p(\hat{z}|x_t)$ is intractable, the authors approximate it using the posterior mean estimator (Tweedie's formula) and the semantic encoder/decoder.

B. The ADDPS Algorithm

The core innovation is an alternating guidance strategy that decomposes the joint posterior sampling into simpler subproblems:

1. Dual-Domain Consistency: The method utilizes two consistency constraints:
   • Z-domain: Ensures the reconstructed image, when encoded, matches the received signal $\hat{z}$.
   • X-domain: Ensures the reconstructed image, when passed through the decoder, matches the initial decoder output $\tilde{x}$.
2. Alternating Schedule: Instead of applying both gradients simultaneously, ADDPS alternates between them at each diffusion step ($t$):
   • If $t$ is even: Apply Z-domain guidance (enforcing semantic consistency with the channel signal).
   • If $t$ is odd: Apply X-domain guidance (enforcing image-domain consistency with the decoder output).
3. Benefits of Alternation:
   • Avoids gradient conflicts between the two domains.
   • Prevents the "overconfident" pseudo-posterior caused by treating correlated evidence as independent.
   • Allows each domain to fully correct the intermediate estimate before the other refines it, leveraging the robustness of the X-domain against noise and the fidelity of the Z-domain to the channel.

3. Key Contributions

1. Theoretical Insight: Formulated generative semantic decoding as a Bayesian inverse problem and proved that MAP estimation is distributionally suboptimal, whereas posterior sampling is necessary for high perceptual quality.
2. Novel Algorithm (ADDPS): Proposed an alternating dual-domain guidance scheme that exploits the complementary strengths of latent and image domains while avoiding the pitfalls of simultaneous guidance (gradient conflict and overconfidence).
3. State-of-the-Art Performance: Demonstrated that ADDPS significantly outperforms existing methods in perceptual quality under extreme low-SNR conditions without requiring retraining of the encoder-decoder backbone.

4. Experimental Results

The method was evaluated on the FFHQ dataset (256x256 resolution) with a bandwidth compression ratio of 1/192 and an extremely low SNR of 1 dB.

• Perceptual Quality (FID):
  • ADDPS (T=1000): Achieved an FID of 56.94.
  • HiFi-DiffCom (SOTA baseline, T=1000): FID of 59.54.
  • DeepJSCC: FID of 108.62 (indicating severe over-smoothing).
  • Note: ADDPS with only 300 steps (FID 58.68) still outperformed HiFi-DiffCom with 1000 steps.
• Other Metrics: ADDPS achieved the best scores in PIEAPP, DISTS, and LPIPS, and competitive scores in PSNR/MS-SSIM.
• Ablation Study:
  • Z-only: Performed worst (FID 87.03) due to noise amplification.
  • X-only: Robust (FID 58.99) but slightly worse than ADDPS.
  • Simultaneous (X+Z): Improved distortion (PSNR) but degraded perceptual quality (FID 61.64) compared to X-only, confirming the "overconfident" hypothesis.
  • ADDPS (Alternating): Achieved the best overall perceptual quality (FID 58.38 in ablation), validating the alternating strategy.

5. Significance

This paper provides a critical theoretical correction to the field of Generative SemCom, shifting the paradigm from optimization (MAP) to sampling (Posterior). By introducing the ADDPS framework, the authors solve the long-standing trade-off between noise robustness and semantic fidelity in diffusion-based receivers. The method is particularly significant because it acts as a plug-in receiver that can enhance existing SemCom systems using pretrained diffusion priors, achieving superior visual realism in extremely noisy and bandwidth-constrained wireless environments.