To realize the quantitative characterization of combustion stability based on boiler flame images and overcome the training problem of insufficient unstable combustion samples, a real-time and quantitative characterization method of combustion stability based on the convolutional variational autoencoding model is proposed. First, the model is trained by using the flame images under stable combustion conditions, and the high-dimensional latent probability distribution of the stable combustion image is obtained by using the convolutional variational autoencoder. The distribution characteristics of the latent variables corresponding to the model are recorded, the KL divergence value between the distribution and the standard normal distribution is calculated. The KL divergence is used to realize the quantitative characterization of combustion stability. In the simulation verification, the comparison experiments show that the introduction of variational inference theory can improve the reconstruction quality of the model for the combustion image, and the root mean square error before and after image reconstruction is 0. 005 48. The accuracy and effectiveness of the evaluation method are verified through the experiment of adjusting the coal feeding amount of the coal mill to artificially create the combustion conditions of the burner with different degrees of stability, and the evaluation accuracy rate is as high as 92. 1%. The comparison results with the coal fire inspection and evaluation show that the method has the quantitative judgment function of the coal fire inspection system for flame, and the sensing ability is more sensitive. It can give the warning of combustion instability in 167 s before the burner fires, which has certain engineering application value.