## 2 Related Worked
[9] proposed a new recognition model, which first preprocesses the furnace flame video sequence, then uses a Convolutional Recurrent Neural Network (CRNN) to further learn the spatiotemporal features of the flame to obtain the recognition results. [PERSON] et al. [10] used the bidirectional recurrent multi-scale convolutional deep neural network algorithm to take into account the characteristics of the frequency-domain structure and the time-domain dynamic sequence. It was applied to the deep learning of BOF flame spectral information. Deep learning requires a large amount of balanced data with different sample numbers to support model training. However, abnormal burning conditions are rare in the field, and it is very difficult to collect a large amount of data with uniform distribution. Therefore, scholars have proposed the use of image generation models to expand training data to address this issue. [PERSON] et al. [11] established a VAE model to reconstruct a large amount of generated data by using flame images collected from coal-fired boilers as input and processed through an encoder and decoder. Recently, the image generation method based on Denoising Diffusion Probabilistic Models (DDPMs) has made great progress [12], and its potential in expanding image datasets has been increasingly recognized by scholars. Many scholars have begun to use this method to address the problem of uneven distribution of image sample data. [PERSON] and [PERSON] [13] proposed a DDPM to generate images similar to datasets including several different types of microstructures (such as polycrystalline alloys, carbonates, ceramics, copolymers, fiber composites, etc.). [PERSON] et al. [14] proposed the generation magnetic resonance images (MRIs) and computed tomography (CT) images using a DDPM and demonstrated that the generated images can be used to train image segmentation models. [PERSON] et al. [15] proposed a method for generating microscope image data that can effectively generate fully annotated microscope image datasets by establishing a DDPM and training the model. This helps reduce the reliance on manual annotation when training deep learning-based segmentation methods, enabling the segmentation of different datasets without the need for manual annotation. [PERSON] et al. [16] improved an original network based on a DDPM to address the spatiotemporal characteristics of remote sensing data and proposed the DiffusionSat model for the generation satellite remote sensing images. [PERSON] et al. [17] proposed the GradPaint method to generate a coordinated image by calculating a custom loss to measure its consistency with the masked input image. Existing diffusion-based inpainting methods are limited to single-modal guidance and require task-specific training, hindering their cross-modal scalability. To solve this problem, [PERSON] et al. [18] proposed the Uni-paint generation model. Uni-paint is based on pre-trained stable diffusion and does not require task-specific training on a specific dataset, achieving a few-shot generalization capability on custom images. This article proposes a flame combustion image generation method based on RE-DDPM to address the problems of insufficient data and severely uneven sample distribution. In this paper, the RE-DDPM method is used to generate a large number of images that are extremely similar to real data based on a small number of live burning strip images, solving the problem of insufficient training samples for deep learning. Experiments show that following the use of the method proposed in this paper to expand the data, the generated data are more similar to the real data, and the recognition accuracy of the model can be improved. Secondly, to address the problem of low accuracy in combustion state recognition, a combustion state recognition method based on DAF-FasterNet is proposed. This article improves upon the original FasterNet network [19] to significantly improve recognition accuracy while ensuring recognition speed.