RadioDiff-$k^2$: Helmholtz Equation Informed Generative Diffusion Model for Multi-Path Aware Radio Map Construction

In this paper, we propose a novel physics-informed generative learning approach, termed RadioDiff-$\bm{k^2}$, for accurate and efficient multipath-aware radio map (RM) construction. As wireless communication evolves towards environment-aware paradigms, driven by the increasing demand for intelligent and proactive optimization in sixth-generation (6G) networks, accurate construction of RMs becomes crucial yet highly challenging. Conventional electromagnetic (EM)-based methods, such as full-wave solvers and ray-tracing approaches, exhibit substantial computational overhead and limited adaptability to dynamic scenarios. Although, existing neural network (NN) approaches have efficient inferencing speed, they lack sufficient consideration of the underlying physics of EM wave propagation, limiting their effectiveness in accurately modeling critical EM singularities induced by complex multipath environments. To address these fundamental limitations, we propose a novel physics-inspired RM construction method guided explicitly by the Helmholtz equation, which inherently governs EM wave propagation. Specifically, we theoretically establish a direct correspondence between EM singularities, which correspond to the critical spatial features influencing wireless propagation, and regions defined by negative wave numbers in the Helmholtz equation. Based on this insight, we design an innovative dual generative diffusion model (DM) framework comprising one DM dedicated to accurately inferring EM singularities and another DM responsible for reconstructing the complete RM using these singularities along with environmental contextual information. Our physics-informed approach uniquely combines the efficiency advantages of data-driven methods with rigorous physics-based EM modeling, significantly enhancing RM accuracy, particularly in complex propagation environments dominated by multipath effects.

RadioDiff-Inverse: Diffusion Enhanced Bayesian Inverse Estimation for ISAC Radio Map Construction

Radio maps (RMs) are essential for environment-aware communication and sensing, providing location-specific wireless channel information. Existing RM construction methods often rely on precise environmental data and base station (BS) locations, which are not always available in dynamic or privacy-sensitive environments. While sparse measurement techniques reduce data collection, the impact of noise in sparse data on RM accuracy is not well understood. This paper addresses these challenges by formulating RM construction as a Bayesian inverse problem under coarse environmental knowledge and noisy sparse measurements. Although maximum a posteriori (MAP) filtering offers an optimal solution, it requires a precise prior distribution of the RM, which is typically unavailable. To solve this, we propose RadioDiff-Inverse, a diffusion-enhanced Bayesian inverse estimation framework that uses an unconditional generative diffusion model to learn the RM prior. This approach not only reconstructs the spatial distribution of wireless channel features but also enables environmental structure perception, such as building outlines, and location of BS just relay on pathloss, through integrated sensing and communication (ISAC). Remarkably, RadioDiff-Inverse is training-free, leveraging a pre-trained model from Imagenet without task-specific fine-tuning, which significantly reduces the training cost of using generative large model in wireless networks. Experimental results demonstrate that RadioDiff-Inverse achieves state-of-the-art performance in accuracy of RM construction and environmental reconstruction, and robustness against noisy sparse sampling.

Erasing Noise in Signal Detection with Diffusion Model: From Theory to Application

In this paper, a signal detection method based on the denoise diffusion model (DM) is proposed, which outperforms the maximum likelihood (ML) estimation method that has long been regarded as the optimal signal detection technique. Theoretically, a novel mathematical theory for intelligent signal detection based on stochastic differential equations (SDEs) is established in this paper, demonstrating the effectiveness of DM in reducing the additive white Gaussian noise in received signals. Moreover, a mathematical relationship between the signal-to-noise ratio (SNR) and the timestep in DM is established, revealing that for any given SNR, a corresponding optimal timestep can be identified. Furthermore, to address potential issues with out-of-distribution inputs in the DM, we employ a mathematical scaling technique that allows the trained DM to handle signal detection across a wide range of SNRs without any fine-tuning. Building on the above theoretical foundation, we propose a DM-based signal detection method, with the diffusion transformer (DiT) serving as the backbone neural network, whose computational complexity of this method is $\mathcal{O}(n^2)$. Simulation results demonstrate that, for BPSK and QAM modulation schemes, the DM-based method achieves a significantly lower symbol error rate (SER) compared to ML estimation, while maintaining a much lower computational complexity.

Overcoming False Illusions in Real-World Face Restoration with Multi-Modal Guided Diffusion Model

We introduce a novel Multi-modal Guided Real-World Face Restoration (MGFR) technique designed to improve the quality of facial image restoration from low-quality inputs. Leveraging a blend of attribute text prompts, high-quality reference images, and identity information, MGFR can mitigate the generation of false facial attributes and identities often associated with generative face restoration methods. By incorporating a dual-control adapter and a two-stage training strategy, our method effectively utilizes multi-modal prior information for targeted restoration tasks. We also present the Reface-HQ dataset, comprising over 23,000 high-resolution facial images across 5,000 identities, to address the need for reference face training images. Our approach achieves superior visual quality in restoring facial details under severe degradation and allows for controlled restoration processes, enhancing the accuracy of identity preservation and attribute correction. Including negative quality samples and attribute prompts in the training further refines the model's ability to generate detailed and perceptually accurate images.

RadioDiff: An Effective Generative Diffusion Model for Sampling-Free Dynamic Radio Map Construction

Radio map (RM) is a promising technology that can obtain pathloss based on only location, which is significant for 6G network applications to reduce the communication costs for pathloss estimation. However, the construction of RM in traditional is either computationally intensive or depends on costly sampling-based pathloss measurements. Although the neural network (NN)-based method can efficiently construct the RM without sampling, its performance is still suboptimal. This is primarily due to the misalignment between the generative characteristics of the RM construction problem and the discrimination modeling exploited by existing NN-based methods. Thus, to enhance RM construction performance, in this paper, the sampling-free RM construction is modeled as a conditional generative problem, where a denoised diffusion-based method, named RadioDiff, is proposed to achieve high-quality RM construction. In addition, to enhance the diffusion model's capability of extracting features from dynamic environments, an attention U-Net with an adaptive fast Fourier transform module is employed as the backbone network to improve the dynamic environmental features extracting capability. Meanwhile, the decoupled diffusion model is utilized to further enhance the construction performance of RMs. Moreover, a comprehensive theoretical analysis of why the RM construction is a generative problem is provided for the first time, from both perspectives of data features and NN training methods. Experimental results show that the proposed RadioDiff achieves state-of-the-art performance in all three metrics of accuracy, structural similarity, and peak signal-to-noise ratio. The code is available at https://github.com/UNIC-Lab/RadioDiff.

Reliable Projection Based Unsupervised Learning for Semi-Definite QCQP with Application of Beamforming Optimization

In this paper, we investigate a special class of quadratic-constrained quadratic programming (QCQP) with semi-definite constraints. Traditionally, since such a problem is non-convex and N-hard, the neural network (NN) is regarded as a promising method to obtain a high-performing solution. However, due to the inherent prediction error, it is challenging to ensure all solution output by the NN is feasible. Although some existing methods propose some naive methods, they only focus on reducing the constraint violation probability, where not all solutions are feasibly guaranteed. To deal with the above challenge, in this paper a computing efficient and reliable projection is proposed, where all solution output by the NN are ensured to be feasible. Moreover, unsupervised learning is used, so the NN can be trained effectively and efficiently without labels. Theoretically, the solution of the NN after projection is proven to be feasible, and we also prove the projection method can enhance the convergence performance and speed of the NN. To evaluate our proposed method, the quality of service (QoS)-contained beamforming scenario is studied, where the simulation results show the proposed method can achieve high-performance which is competitive with the lower bound.

Trapezoidal Gradient Descent for Effective Reinforcement Learning in Spiking Networks

With the rapid development of artificial intelligence technology, the field of reinforcement learning has continuously achieved breakthroughs in both theory and practice. However, traditional reinforcement learning algorithms often entail high energy consumption during interactions with the environment. Spiking Neural Network (SNN), with their low energy consumption characteristics and performance comparable to deep neural networks, have garnered widespread attention. To reduce the energy consumption of practical applications of reinforcement learning, researchers have successively proposed the Pop-SAN and MDC-SAN algorithms. Nonetheless, these algorithms use rectangular functions to approximate the spike network during the training process, resulting in low sensitivity, thus indicating room for improvement in the training effectiveness of SNN. Based on this, we propose a trapezoidal approximation gradient method to replace the spike network, which not only preserves the original stable learning state but also enhances the model's adaptability and response sensitivity under various signal dynamics. Simulation results show that the improved algorithm, using the trapezoidal approximation gradient to replace the spike network, achieves better convergence speed and performance compared to the original algorithm and demonstrates good training stability.

Constructing and Evaluating Digital Twins: An Intelligent Framework for DT Development

The development of Digital Twins (DTs) represents a transformative advance for simulating and optimizing complex systems in a controlled digital space. Despite their potential, the challenge of constructing DTs that accurately replicate and predict the dynamics of real-world systems remains substantial. This paper introduces an intelligent framework for the construction and evaluation of DTs, specifically designed to enhance the accuracy and utility of DTs in testing algorithmic performance. We propose a novel construction methodology that integrates deep learning-based policy gradient techniques to dynamically tune the DT parameters, ensuring high fidelity in the digital replication of physical systems. Moreover, the Mean STate Error (MSTE) is proposed as a robust metric for evaluating the performance of algorithms within these digital space. The efficacy of our framework is demonstrated through extensive simulations that show our DT not only accurately mirrors the physical reality but also provides a reliable platform for algorithm evaluation. This work lays a foundation for future research into DT technologies, highlighting pathways for both theoretical enhancements and practical implementations in various industries.

Toward Enhanced Reinforcement Learning-Based Resource Management via Digital Twin: Opportunities, Applications, and Challenges

This article presents a digital twin (DT)-enhanced reinforcement learning (RL) framework aimed at optimizing performance and reliability in network resource management, since the traditional RL methods face several unified challenges when applied to physical networks, including limited exploration efficiency, slow convergence, poor long-term performance, and safety concerns during the exploration phase. To deal with the above challenges, a comprehensive DT-based framework is proposed to enhance the convergence speed and performance for unified RL-based resource management. The proposed framework provides safe action exploration, more accurate estimates of long-term returns, faster training convergence, higher convergence performance, and real-time adaptation to varying network conditions. Then, two case studies on ultra-reliable and low-latency communication (URLLC) services and multiple unmanned aerial vehicles (UAV) network are presented, demonstrating improvements of the proposed framework in performance, convergence speed, and training cost reduction both on traditional RL and neural network based Deep RL (DRL). Finally, the article identifies and explores some of the research challenges and open issues in this rapidly evolving field.

Imperfect Digital Twin Assisted Low Cost Reinforcement Training for Multi-UAV Networks

Deep Reinforcement Learning (DRL) is widely used to optimize the performance of multi-UAV networks. However, the training of DRL relies on the frequent interactions between the UAVs and the environment, which consumes lots of energy due to the flying and communication of UAVs in practical experiments. Inspired by the growing digital twin (DT) technology, which can simulate the performance of algorithms in the digital space constructed by coping features of the physical space, the DT is introduced to reduce the costs of practical training, e.g., energy and hardware purchases. Different from previous DT-assisted works with an assumption of perfect reflecting real physics by virtual digital, we consider an imperfect DT model with deviations for assisting the training of multi-UAV networks. Remarkably, to trade off the training cost, DT construction cost, and the impact of deviations of DT on training, the natural and virtually generated UAV mixing deployment method is proposed. Two cascade neural networks (NN) are used to optimize the joint number of virtually generated UAVs, the DT construction cost, and the performance of multi-UAV networks. These two NNs are trained by unsupervised and reinforcement learning, both low-cost label-free training methods. Simulation results show the training cost can significantly decrease while guaranteeing the training performance. This implies that an efficient decision can be made with imperfect DTs in multi-UAV networks.