PALM: Single-Station Super-Resolved Small-Scale Radio-Map Localization by Path-Atom Matching

Localizing from a single base station is a longstanding goal, since it removes the synchronized anchors that geometric methods require. A radio map (RM) answers a position query from this one-station survey, yet classical RMs store coarse received power and match it by correlation, ignoring the small-scale path structure a ray tracer provides. We instead build a small-scale RM and show that cell identification, rather than candidate generation, is its information-limited bottleneck. We propose path-atom localization by matching (PALM), which super-resolves a coarse angle-delay observation into scored atoms and matches them to a ray-traced RM by an exact marginal likelihood. The score marginalizes atom reality inside the logarithm, and we prove that the common posterior-scaled surrogate is a Jensen lower bound whose deficit grows with the number of strong paths. We match on the absolute delay axis under a clock nuisance, since relative delays jump across shadowing boundaries, and we prove a unit-gradient law, a capped miss cost, a minimum-mean-square local centroid, and finite-sample conformal coverage. On the real DeepMIMO campus scenario, PALM localizes to a 1.7 meter median from a single base station, cuts the ninetieth-percentile error of received-power RM matching by 34 to 62 percent, and halves the single-snapshot median to 7 meters.

RMPrior: Bridging Propagation Priors and Diffusion Refinement for Efficient Radio Map Construction

Diffusion models achieve high-fidelity radio map construction through iterative denoising, yet their sampling cost limits practicality in dynamic wireless systems where radio maps must be refreshed repeatedly. Meanwhile, classical propagation models encode valuable scene-level knowledge that standard diffusion inference discards entirely by initializing from pure Gaussian noise. This paper bridges propagation priors and diffusion refinement through a mid-start sampling strategy. A matched propagation prior is perturbed to an intermediate diffusion timestep, and the pretrained diffusion backbone executes only the remaining reverse steps, focusing computation on multipath-aware refinement rather than full reconstruction from noise. We provide theoretical analysis establishing an upper bound on the initialization gap, a sufficient condition under which truncation improves reconstruction fidelity, and a formal characterization of prior-quality sensitivity under aggressive truncation. Experiments on IRT4HighRes show that, at $P_{\text{start}}=0.5$, the proposed method achieves a $2.01\times$ speedup while simultaneously improving NMSE, RMSE, SSIM, and PSNR over the full-step baseline. A prior-quality ablation across three propagation models of different fidelity confirms that reconstruction quality tracks prior quality, with the sensitivity amplified under shorter reverse trajectories, consistent with the theoretical predictions. These results also suggest that mid-start reconstruction quality can serve as a proxy for ranking the scene-level fidelity of different propagation models.

Learning to Think in Physics: Breaking Shortcut Learning in Scientific Diffusion via Representation Alignment

Physics-informed diffusion models typically enforce PDE constraints only on final outputs, leaving intermediate representations unconstrained and prone to shortcut learning under shifted boundary conditions. We introduce **REPA-P**, a teacher-free, architecture-agnostic framework that aligns intermediate features with physical states using first-principles residuals. REPA-P attaches lightweight $1{\times}1$ projection heads to selected layers, decodes hidden activations into physical quantities, and applies PDE residual losses during training. These heads are discarded at inference, introducing **zero overhead**. Across four PDE tasks, including Darcy flow, topology optimization, electrostatic potential, and turbulent channel flow, REPA-P accelerates convergence by up to $2{\times}$, reduces physics residuals by up to $66.4\%$, and improves out-of-distribution robustness by up to $49.3\%$, with consistent gains on both U-Net and Diffusion Transformer backbones. Ablations show that supervising a small set of intermediate layers captures most benefits and complements output-level physics losses. Code is available at [https://github.com/Hxxxz0/REPA-P](https://github.com/Hxxxz0/REPA-P).

Map2APS: A Physically Grounded Benchmark for Direct Angle Power Spectrum Prediction from Urban Geometry

Angle power spectrum (APS) characterizes the directional distribution of received signal power and is directly relevant to beam management and MIMO processing. While environment-aware learning has been widely studied for radio maps and path loss, direct map-to-APS prediction still lacks a standardized large-scale benchmark. This paper presents Map2APS, a physically grounded benchmark constructed from intelligent ray-tracing (IRT) path-level propagation records. Map2APS covers 51 equal-height urban maps and approximately 2.55 million Tx--Rx samples, with a strict cross-map split for evaluating generalization to unseen urban layouts. We benchmark representative model families and introduce MS-AReg as a strong reference baseline. On the full held-out test set of 249{,}993 samples, MS-AReg achieves a cosine similarity of 0.948, a peak location error of 1.20$^\circ$, and an inference latency of 0.101 ms/sample. We further report dominant-direction metrics, including Top-1 dominant peak hit rate and dominant peak recall, to evaluate whether predicted spectra preserve decision-relevant arrival directions. The benchmark, code, and evaluation scripts are released at https://github.com/UNIC-Lab/aps-data.

RadioDiff-FS: Physics-Informed Manifold Alignment in Few-Shot Diffusion Models for High-Fidelity Radio Map Construction

Radio maps (RMs) provide spatially continuous propagation characterizations essential for 6G network planning, but high-fidelity RM construction remains challenging. Rigorous electromagnetic solvers incur prohibitive computational latency, while data-driven models demand massive labeled datasets and generalize poorly from simplified simulations to complex multipath environments. This paper proposes RadioDiff-FS, a few-shot diffusion framework that adapts a pre-trained main-path generator to multipath-rich target domains with only a small number of high-fidelity samples. The adaptation is grounded in a theoretical decomposition of the multipath RM into a dominant main-path component and a directionally sparse residual. This decomposition shows that the cross-domain shift corresponds to a bounded and geometrically structured feature translation rather than an arbitrary distribution change. A Direction-Consistency Loss (DCL) is then introduced to constrain diffusion score updates along physically plausible propagation directions, suppressing phase-inconsistent artifacts that arise in the low-data regime. Experiments show that RadioDiff-FS reduces NMSE by 59.5% on static RMs and by 74.0% on dynamic RMs relative to the vanilla diffusion baseline, achieving an SSIM of 0.9752 and a PSNR of 36.37 dB under severely limited supervision.

Learn for Variation: Variationally Guided AAV Trajectory Learning in Differentiable Environments

Autonomous aerial vehicles (AAVs) empower sixth-generation (6G) Internet-of-Things (IoT) networks through mobility-driven data collection. However, conventional reward-driven reinforcement learning for AAV trajectory planning suffers from severe credit assignment issues and training instability, because sparse scalar rewards fail to capture the long-term and nonlinear effects of sequential movements. To address these challenges, this paper proposes Learn for Variation (L4V), a gradient-informed trajectory learning framework that replaces high-variance scalar reward signals with dense and analytically grounded policy gradients. Particularly, the coupled evolution of AAV kinematics, distance-dependent channel gains, and per-user data-collection progress is first unrolled into an end-to-end differentiable computational graph. Backpropagation through time then serves as a discrete adjoint solver, which propagates exact sensitivities from the cumulative mission objective to every control action and policy parameter. These structured gradients are used to train a deterministic neural policy with temporal smoothness regularization and gradient clipping. Extensive simulations demonstrate that L4V consistently outperforms representative baselines, including a genetic algorithm, DQN, A2C, and DDPG, in mission completion time, average transmission rate, and training cost

BeamAgent: LLM-Aided MIMO Beamforming with Decoupled Intent Parsing and Alternating Optimization for Joint Site Selection and Precoding

Integrating large language models (LLMs) into wireless communication optimization is a promising yet challenging direction. Existing approaches either use LLMs as black-box solvers or code generators, tightly coupling them with numerical computation. However, LLMs lack the precision required for physical-layer optimization, and the scarcity of wireless training data makes domain-specific fine-tuning impractical. We propose BeamAgent, an LLM-aided MIMO beamforming framework that explicitly decouples semantic intent parsing from numerical optimization. The LLM serves solely as a semantic translator that converts natural language descriptions into structured spatial constraints. A dedicated gradient-based optimizer then jointly solves the discrete base station site selection and continuous precoding design through an alternating optimization algorithm. A scene-aware prompt enables grounded spatial reasoning without fine-tuning, and a multi-round interaction mechanism with dual-layer intent classification ensures robust constraint verification. A penalty-based loss function enforces dark-zone power constraints while releasing optimization degrees of freedom for bright-zone gain maximization. Experiments on a ray-tracing-based urban MIMO scenario show that BeamAgent achieves a bright-zone power of 84.0\,dB, outperforming exhaustive zero-forcing by 7.1 dB under the same dark-zone constraint. The end-to-end system reaches within 3.3 dB of the expert upper bound, with the full optimization completing in under 2 s on a laptop.

A Tutorial on Learning-Based Radio Map Construction: Data, Paradigms, and Physics-Awarenes

The integration of artificial intelligence into next-generation wireless networks necessitates the accurate construction of radio maps (RMs) as a foundational prerequisite for electromagnetic digital twins. A RM provides the digital representation of the wireless propagation environment, mapping complex geographical and topological boundary conditions to critical spatial-spectral metrics that range from received signal strength to full channel state information matrices. This tutorial presents a comprehensive survey of learning-based RM construction, systematically addressing three intertwined dimensions: data, paradigms, and physics-awareness. From the data perspective, we review physical measurement campaigns, ray tracing simulation engines, and publicly available benchmark datasets, identifying their respective strengths and fundamental limitations. From the paradigm perspective, we establish a core taxonomy that categorizes RM construction into source-aware forward prediction and source-agnostic inverse reconstruction, and examine five principal neural architecture families spanning convolutional neural networks, vision transformers, graph neural networks, generative adversarial networks, and diffusion models. We further survey optics-inspired methods adapted from neural radiance fields and 3D Gaussian splatting for continuous wireless radiation field modeling. From the physics-awareness perspective, we introduce a three-level integration framework encompassing data-level feature engineering, loss-level partial differential equation regularization, and architecture-level structural isomorphism. Open challenges including foundation model development, physical hallucination detection, and amortized inference for real-time deployment are discussed to outline future research directions.

Neural Electromagnetic Fields for High-Resolution Material Parameter Reconstruction

Creating functional Digital Twins, simulatable 3D replicas of the real world, is a central challenge in computer vision. Current methods like NeRF produce visually rich but functionally incomplete twins. The key barrier is the lack of underlying material properties (e.g., permittivity, conductivity). Acquiring this information for every point in a scene via non-contact, non-invasive sensing is a primary goal, but it demands solving a notoriously ill-posed physical inversion problem. Standard remote signals, like images and radio frequencies (RF), deeply entangle the unknown geometry, ambient field, and target materials. We introduce NEMF, a novel framework for dense, non-invasive physical inversion designed to build functional digital twins. Our key insight is a systematic disentanglement strategy. NEMF leverages high-fidelity geometry from images as a powerful anchor, which first enables the resolution of the ambient field. By constraining both geometry and field using only non-invasive data, the original ill-posed problem transforms into a well-posed, physics-supervised learning task. This transformation unlocks our core inversion module: a decoder. Guided by ambient RF signals and a differentiable layer incorporating physical reflection models, it learns to explicitly output a continuous, spatially-varying field of the scene's underlying material parameters. We validate our framework on high-fidelity synthetic datasets. Experiments show our non-invasive inversion reconstructs these material maps with high accuracy, and the resulting functional twin enables high-fidelity physical simulation. This advance moves beyond passive visual replicas, enabling the creation of truly functional and simulatable models of the physical world.

RadioDiff-Flux: Efficient Radio Map Construction via Generative Denoise Diffusion Model Trajectory Midpoint Reuse

Accurate radio map (RM) construction is essential to enabling environment-aware and adaptive wireless communication. However, in future 6G scenarios characterized by high-speed network entities and fast-changing environments, it is very challenging to meet real-time requirements. Although generative diffusion models (DMs) can achieve state-of-the-art accuracy with second-level delay, their iterative nature leads to prohibitive inference latency in delay-sensitive scenarios. In this paper, by uncovering a key structural property of diffusion processes: the latent midpoints remain highly consistent across semantically similar scenes, we propose RadioDiff-Flux, a novel two-stage latent diffusion framework that decouples static environmental modeling from dynamic refinement, enabling the reuse of precomputed midpoints to bypass redundant denoising. In particular, the first stage generates a coarse latent representation using only static scene features, which can be cached and shared across similar scenarios. The second stage adapts this representation to dynamic conditions and transmitter locations using a pre-trained model, thereby avoiding repeated early-stage computation. The proposed RadioDiff-Flux significantly reduces inference time while preserving fidelity. Experiment results show that RadioDiff-Flux can achieve up to 50 acceleration with less than 0.15% accuracy loss, demonstrating its practical utility for fast, scalable RM generation in future 6G networks.