Distance-Aware Fidelity Enhancement

• Distance-aware fidelity enhancement is a paradigm that integrates distance-sensitive metrics and architectures to improve the quality of signals and images across multiple domains.
• It employs statistical measures like FAD, MMD, and Wasserstein distances alongside adaptive regularization to overcome the limitations of traditional fidelity assessments.
• Its practical applications span audio enhancement, image restoration, quantum error correction, and robotic policy generalization, highlighting its multidisciplinary impact.

Distance-aware fidelity enhancement is a comprehensive paradigm that elevates the assessment and optimization of signal, data, or system quality by leveraging metrics, representations, and architectures that explicitly account for spatial, temporal, latent, or geometric distances. This concept extends across audio, image, video, robotics, and quantum domains, employing formal mathematical and computational frameworks that disentangle fidelity from naive similarity measures, enable robust distributional matching, and achieve superior perceptual or operational performance under realistic, distance-dependent conditions.

1. Metric Foundations and Statistical Distance Measures

Distance-aware fidelity enhancement critically depends on statistically meaningful metrics that are sensitive to the underlying structure of data. The Fréchet Audio Distance (FAD) (Kilgour et al., 2018) exemplifies this approach for audio enhancement by comparing the mean and covariance of neural embeddings from distorted and clean audio distributions:

$$FAD(\mathcal{N}_b, \mathcal{N}_e) = \|\mu_b - \mu_e\|^2 + \operatorname{tr}(\Sigma_b + \Sigma_e - 2\sqrt{\Sigma_b\Sigma_e})$$

FAD, adapted from Fréchet Inception Distance (FID) in the image domain, robustly aligns with human perception of quality and outperforms signal-level metrics (SDR, cosine, L2) in correlating with subjective ratings across a wide distortion spectrum. Distributional comparison metrics such as Maximum Mean Discrepancy (MMD) (Delbracio et al., 2020, Han et al., 2021, Biswas et al., 23 Sep 2025) and Wasserstein distances offer non-parametric flexibility for quantifying differences between deep feature distributions, further enhancing perceptual alignment and providing robust proxies for information fidelity.

2. Distance-Aware Network Architectures and Adaptive Regularization

Neural architectures for fidelity enhancement now commonly incorporate explicit distance cues—such as depth, geometric structure, or scale—into both model parameters and regularization terms. The dual-branch PFIQA network (Lin et al., 15 May 2024) for super-resolution IQA integrates both perception-aware (global ViT/local ResNet features) and fidelity-aware (SR–LR difference) branches, fusing features adaptively with scale-factor conditionality. Similarly, the depth-aware super-resolution framework (Guo et al., 6 Sep 2025) formulates image restoration as an inverse problem governed by a pseudodifferential degradation operator with symbol $\sigma(x, \xi, \mathcal{D}(x))$ encoding depth-dependent spectral attenuation:

$$[\mathcal{K}_\mathcal{D}u](x) = \iint e^{i\langle x - y, \xi \rangle}\, \sigma(x, \xi, \mathcal{D}(x))\, u(y)\, dy\, d\xi$$

Distance-adaptive regularization $\mathcal{R}_\mathcal{D}[u]$ and spectral constraints calibrated via atmospheric scattering theory ensure local geometric fidelity is maintained while mitigating noise in far-field regions.

3. Distributional Learning and Information Fidelity in Latent Spaces

Restricting solution spaces to high-quality priors and maintaining fidelity through distributional losses is pivotal in generative modeling. The StyleGAN-based restoration method (Han et al., 2021) anchors optimization to a GAN manifold, regulating the empirical latent distribution $q_\mathcal{W}$ by minimizing MMD relative to the prior $p_\mathcal{W}$:

$$d^2[k, p_\mathcal{W}, q_\mathcal{W}] = \mathbb{E}_{x,x' \sim p_\mathcal{W}} [k(x,x')] - 2\mathbb{E}_{x \sim p_\mathcal{W},y \sim q_\mathcal{W}} [k(x,y)] + \mathbb{E}_{y,y' \sim q_\mathcal{W}} [k(y,y')]$$

Simultaneously, the degradation likelihood $P(I_L|I_H)$ serves as a fidelity-aware likelihood, ensuring that restored images are both perceptually plausible and correctly reflect the degradation process.

4. Quantum and Physical Systems: Trace Distance Optimization

In quantum networks, fidelity enhancement must combat distance-dependent decoherence. The trace-distance-based TDPP algorithm (Kumar et al., 21 Oct 2024) leverages closeness centrality for optimal path selection, evaluates

$$D_{u,v}(\rho, \sigma) = \frac{1}{2} \operatorname{tr}|\rho - \sigma|$$

across candidate links, and selectively applies purification operations governed by fidelity constraints

$$F_{u,v}(\rho, \sigma) = \operatorname{tr}(\sqrt{\rho}\sqrt{\sigma})$$

to boost E2E entanglement fidelity. Quantum error correction protocols (Shubha et al., 2023, Zhang et al., 24 Jun 2025) for shuttling and communication explicitly differentiate short- and long-distance settings, exploit spatiotemporal correlations in noise, and encode logical qubits into entangled states or decoherence-free subspaces, yielding arbitrarily high fidelity under appropriate delay and noise correlation conditions.

5. Latent Representation Geometry and Robot Policy Generalization

Robust generalization in policy learning hinges on fidelity-aware data composition. The CIFT framework (Tong et al., 29 Sep 2025) employs proxies for information fidelity based on feature-space geometry, tunes data mixture ratios to avoid decoherence points, and uses Multi-View Video Augmentation to synthesize causally disentangled spectra with quantifiable cross-view and temporal consistency. Metrics such as FID, CVFC, MVDC, Ewarp, T-LPIPS, TCJ, and CLIP Score collectively profile spatial and temporal fidelity for video data, ensuring generalist robot policies remain robust to OOD scenarios.

6. Embedding Distances and Zero-Shot Quality Assessment

Distance-aware fidelity metrics in generative audio (Biswas et al., 23 Sep 2025) demonstrate that latent distances in neural audio codec embeddings are strongly correlated with subjective ratings. NACs such as DACe encode input waveforms into compact, perceptually salient embeddings, enabling FAD and MMD to serve as zero-shot, reference-free quality predictors. Popular embedding models like CLAP-M and OpenL3-128M enhance correlation due to scale and semantic diversity in training, but the practical utility of codec embeddings lies in dual-purpose deployment for both compression and perceptual evaluation.

7. Applications, Generalization, and Future Directions

Distance-aware fidelity enhancement enables significant advancements across diverse domains:

• Music and speech enhancement: robust, reference-free perceptual evaluation and optimization (Kilgour et al., 2018, Biswas et al., 23 Sep 2025).
• Image and video restoration: adaptive regularization and spectral filtering under geometric and degradation-aware priors (Delbracio et al., 2020, Han et al., 2021, Lin et al., 15 May 2024, Guo et al., 6 Sep 2025, Tong et al., 29 Sep 2025).
• Quantum and multi-fidelity optimization: selective routing, error correction, and purification in complex physical systems (Chen et al., 2020, Foumani et al., 2022, Shubha et al., 2023, Kumar et al., 21 Oct 2024, Zhang et al., 24 Jun 2025).
• Unsupervised RL and robotics: temporal and latent distance-encoded representations for intrinsically guided exploration and generalization (Bae et al., 11 Jul 2024, Tong et al., 29 Sep 2025).

Ongoing research will further refine the theoretical foundations, incorporate more nuanced distance metrics, and develop architectures with dynamic, context-sensitive fidelity adaptation.

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In sum, distance-aware fidelity enhancement leverages mathematically principled, task-aligned distance metrics—often via statistical, latent, geometric, or temporal representations—to drive high-quality, generalizable solutions in audio, image, video, robotics, and quantum information processing. This paradigm is grounded in deep metric learning, adaptive regularization, fidelity-aware composition, and rigorous variational and statistical analysis, establishing a robust foundation for state-of-the-art fidelity optimization and evaluation.