## 1 Introduction
Simultaneously, each prediction for the short-term future requires a substantial volume of pre-existing data, imposing significant storage demands on coal mine databases, which is a challenge for many coal mines to meet. Some scholars have proposed a method for predicting the occurrence patterns of coal mine gas based on multi-source data fusion [26, 27]. Given these constraints, there is a pressing need for a rock burst early warning method capable of predicting an FEMR signal in the deep future with minimal reliance on known univariate signal data and recognizing precursor characteristics. Generative adversarial networks (GANs) consist of two parts: a generator that produces new data from random noise, and a discriminator that evaluates the generated samples against real data. These networks are trained simultaneously to achieve a Nash equilibrium, where neither network can improve its performance without the other adjust ing its approach. GANs are recognized as an unsupervised learning technique capable of generating new data that align with the distribution of the training dataset [28; 29; 30; 31; 32]. Some scholars have proposed guided learning methods to improve the training process of GANs. Guided generative adversarial networks (GGANs), an advanced variant of GANs, enable controlled data generation by incorporating auxiliary information like labels. These networks have shown enhanced performance over prediction-based models, particularly when applied to unseen data with limited training samples [33; 34; 35; 36]. These networks have been used to solve the spectrogram out-painting task, and predict the loss time-frequency data, which have the ability to predict the missing data [37; 38; 39]. While GAN-based architectures present numerous advantages compared to predictive models, including their proficiency in generalizing predictions across smaller and varied datasets and their aptitude for capturing complex conditional distributions, they are not devoid of limitations. A significant concern is the phenomenon of \"mode collapse\", wherein the generator yields outputs with restricted diversity, thereby inadequately reflecting the full spectrum of variability inherent in the training data. This issue can hinder the model's ability to generate realistic and diverse samples, ultimately impacting its effectiveness in applications requiring high variability and fidelity [33; 34; 40]. Moreover, these networks may encounter the challenge of \"non-convergence\", where the learning process fails to achieve a Nash equilibrium, leading to unstable performance. To address these shortcomings of GANs, diffusion-based models have been introduced as an alternative approach [41; 42]. To overcome the constraints inherent in GANs, diffusion models have been introduced. These models systematically incorporate Gaussian noise into the training samples until they are fully transformed into pure noise. This process enables the neural network to gradually eliminate noise and extract valuable insights from the data [43; 44; 45]. Recently, guided diffusion models have demonstrated remarkable prowess in tasks involving pixel matrix data predictions [46; 47; 48]. Notably, they have been successfully applied in generating pixel matrix data from textual descriptions, achieving pixel matrix data resolution and inpainting, and facilitating pixel-to-pixel convert, and pixel matrix data out-painting [49; 50; 51]. This underscores the extraordinary potential of diffusion-based models to enhance the accuracy of FEMR signal prediction in the deep future. The guided diffusion model provides new ideas for signal prediction tasks [52; 53; 54; 55]. This study converts the FEMR signal time-series data into corresponding time-frequency data through Fourier transform, and uses the guided diffusion model to predict the FEMR signal time-frequency data in the deep future based on known data. In order to achieve FEMR signal prediction in the deep future, we added the recurrent structure in the guided diffusion model in the super prediction process.