AI Diffusion Model Based on Stochastic Differential Equations: Noise Scheduling Variable Discrete Approximation
DOI:
https://doi.org/10.4108/eetsis.12089Keywords:
SDE-based Diffusion Model, Variable Noise Scheduling, Discretization Error Reduction, Generative Image Modeling, CIFAR-10 Image SynthesisAbstract
Recently, diffusion probabilistic models have shown great success in image synthesis, but their performance relies heavily on the pre-defined noise schedules, which have a direct impact on the convergence speed, stability, and quality of the generated images. Moreover, the traditional score-based SDE model is very sensitive to the choice of the step size in the numerical integration process. To overcome the above limitations, a variable discrete noise scheduling method combined with a Fully Connected Neural Network (FC-NN) denoiser is proposed in the SDE diffusion model. Experimental analysis on the CIFAR-10 dataset shows that the proposed Variable SDE model results in a final FID value of 8.7, which is better than DDPM (11.5), DDIM (10.9), and Score SDE (10.2), and an Inception Score of 9.4, which is better than 8.6 for the fixed scheduling approach. The proposed approach results in a reduction of convergence time by 20-25% and peak discretization error by 30-35%. The t-SNE analysis shows that the overlap between the real and generated distributions is good, and there is no mode collapse. The proposed approach provides faster convergence, better numerical stability, and improved generative quality compared to existing standard diffusion models.
References
[1] Li, J., Zhang, C., Zhu, W., & Ren, Y. (2025). A comprehensive survey of image generation models based on deep learning. Annals of Data Science, 12(1), 141–170. https://doi.org/10.1007/s40745-024-00544-1
[2] Zhang, J., Xu, S., Zhang, Z., Li, C., & Yang, L. (2025). A denoising diffusion probabilistic model-based digital twinning of ISAC MIMO channel. IEEE Internet of Things Journal, 12(15), 29121–29134. https://doi.org/10.1109/JIOT.2024.3495212
[3] Cheng, Z., et al. (2025). Med-Diffusion: Diffusion model-based imputation of multimodal sensor data for surgical patients. Sensors, 25(19), 6175. https://doi.org/10.3390/s25196175
[4] Chen, H., et al. (2025). Comprehensive exploration of diffusion models in image generation: A survey. Artificial Intelligence Review, 58(4), 99. https://doi.org/10.1007/s10462-025-11110-3
[5] Ambrogioni, L. (2024). In search of dispersed memories: Generative diffusion models are associative memory networks. Entropy, 26(5), 381. https://doi.org/10.3390/e26050381
[6] Yazdani, S., et al. (2025). Generative AI in depth: A survey of recent advances, model variants, and real-world applications. Journal of Big Data, 12(1), 230. https://doi.org/10.1186/s40537-025-01247-x
[7] Song, W., Ma, W., Zhang, M., Zhang, Y., & Zhao, X. (2024). Lightweight diffusion models: A survey. Artificial Intelligence Review, 57(6), 161. https://doi.org/10.1007/s10462-024-10800-8
[8] Li, Z., Li, W., Zhang, X., Duan, J., & Bai, L. (2025). DMMP-Net: Diffusion model-based missing part patching network for station air quality data generation completion. International Journal of Machine Learning and Cybernetics, 16(5), 3601–3612. https://doi.org/10.1007/s13042-024-02468-x
[9] Zhang, C., et al. (2025). Multi-objective aerial collaborative secure communication optimization via generative diffusion model-enabled deep reinforcement learning. IEEE Transactions on Mobile Computing, 24(4), 3041–3058. https://doi.org/10.1109/TMC.2024.3502685
[10] Sordo, Z., et al. (2025). Synthetic scientific image generation with VAE, GAN, and diffusion model architectures. Journal of Imaging, 11(8), 252. https://doi.org/10.3390/jimaging11080252
[11] Kumar, P. (2025). Diffusion models and generative artificial intelligence: Frameworks, applications and challenges. Archives of Computational Methods in Engineering, 32(7), 4049–4092. https://doi.org/10.1007/s11831-025-10266-z
[12] Li, S., Xiong, H., & Chen, Y. (2024). DiffCharge: Generating EV charging scenarios via a denoising diffusion model. IEEE Transactions on Smart Grid, 15(4), 3936–3949. https://doi.org/10.1109/TSG.2024.3360874
[13] Dai, W. (2024). Stochastic differential games and a unified forward–backward coupled stochastic partial differential equation with Lévy jumps. Mathematics, 12(18), 2891. https://doi.org/10.3390/math12182891
[14] Cao, H., et al. (2024). A survey on generative diffusion models. IEEE Transactions on Knowledge and Data Engineering, 36(7), 2814–2830. https://doi.org/10.1109/TKDE.2024.3361474
[15] Cui, Z.-X., et al. (2025). SPIRiT-Diffusion: Self-consistency driven diffusion model for accelerated MRI. IEEE Transactions on Medical Imaging, 44(2), 1019–1031. https://doi.org/10.1109/TMI.2024.3473009
[16] Liang, R., et al. (2025). Diffusion models as network optimizers: Explorations and analysis. IEEE Internet of Things Journal, 12(10), 13183–13193. https://doi.org/10.1109/JIOT.2025.3528955
[17] Po, R., et al. (2024). State of the art on diffusion models for visual computing. Computer Graphics Forum, 43(2), e15063. https://doi.org/10.1111/cgf.15063
[18] Wang, Z., & Zhang, H. (2024). Customized load profiles synthesis for electricity customers based on conditional diffusion models. IEEE Transactions on Smart Grid, 15(4), 4259–4270. https://doi.org/10.1109/TSG.2024.3366212
[19] Babazadeh Darabi, A., & Coleri, S. (2025). Diffusion model based resource allocation strategy in ultra-reliable wireless networked control systems. IEEE Communications Letters, 29(1), 85–89. https://doi.org/10.1109/LCOMM.2024.3499745
[20] Cheng, Z., et al. (2024). Information cascade popularity prediction via probabilistic diffusion. IEEE Transactions on Knowledge and Data Engineering, 36(12), 8541–8555. https://doi.org/10.1109/TKDE.2024.3465241
[21] Luo, J., et al. (2025). Review of diffusion models and its applications in biomedical informatics. BMC Medical Informatics and Decision Making, 25(1), 390. https://doi.org/10.1186/s12911-025-03210-5
[22] Lee, Y. (2025). Enhancing plant health classification via diffusion model-based data augmentation. Multimedia Systems, 31(2), 143. https://doi.org/10.1007/s00530-025-01745-1
[23] Parigi, M., Martina, S., & Caruso, F. (2025). Quantum-noise-driven generative diffusion models. Advanced Quantum Technologies, 8(12), 2300401. https://doi.org/10.1002/qute.202300401
[24] Croitoru, F.-A., Hondru, V., Ionescu, R. T., & Shah, M. (2023). Diffusion models in vision: A survey. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(9), 10850–10869. https://doi.org/10.1109/TPAMI.2023.3261988
[25] Cheng, S., Osman, N., Qu, S., & Ballan, L. (2024). FastSTI: A fast conditional pseudo numerical diffusion model for spatio-temporal traffic data imputation. IEEE Transactions on Intelligent Transportation Systems, 25(12), 20547–20560. https://doi.org/10.1109/TITS.2024.3469240
[26] Ye, D., Luo, H., Winstein, C., & Schweighofer, N. (2025). Towards AI-based precision rehabilitation via contextual model-based reinforcement learning. Journal of NeuroEngineering and Rehabilitation, 22(1), 263. https://doi.org/10.1186/s12984-025-01771-0
[27] Zach, M., Kobler, E., Chambolle, A., & Pock, T. (2024). Product of Gaussian mixture diffusion models. Journal of Mathematical Imaging and Vision, 66(4), 504–528. https://doi.org/10.1007/s10851-024-01180-3
[28] Lin, L., Li, Z., Li, R., Li, X., & Gao, J. (2024). Diffusion models for time-series applications: A survey. Frontiers of Information Technology & Electronic Engineering, 25(1), 19–41. https://doi.org/10.1631/FITEE.2300310
[29] Lu, Y., & Xu, W. (2024). Generative downscaling of PDE solvers with physics-guided diffusion models. Journal of Scientific Computing, 101(3), 71. https://doi.org/10.1007/s10915-024-02709-9
[30] Cao, J., et al. (2025). Spiking diffusion models. IEEE Transactions on Artificial Intelligence, 6(1), 132–143. https://doi.org/10.1109/TAI.2024.3453229
[31] Du, H., et al. (2024). Enhancing deep reinforcement learning: A tutorial on generative diffusion models in network optimization. IEEE Communications Surveys & Tutorials, 26(4), 2611–2646. https://doi.org/10.1109/COMST.2024.3400011
[32] Li, S., & Sung, Y. (2023). MelodyDiffusion: Chord-conditioned melody generation using a transformer-based diffusion model. Mathematics, 11(8), 1915. https://doi.org/10.3390/math11081915
[33] Panda, S., & Nayak, M. M. (2025). Incorporating fuzzy stochastic differential equations into agricultural growth models: A comprehensive overview. Research in Mathematics, 12(1), 2572194. https://doi.org/10.1080/27684830.2025.2572194
[34] Moser, B. B., Shanbhag, A. S., Raue, F., Frolov, S., Palacio, S., & Dengel, A. (2025). Diffusion models, image super-resolution, and everything: A survey. IEEE Transactions on Neural Networks and Learning Systems, 36(7), 11793–11813. https://doi.org/10.1109/TNNLS.2024.3476671
[35] Wang, X., Du, H., Feng, L., Zhou, F., & Li, W. (2025). Effective throughput maximization for NOMA-enabled URLLC transmission in industrial IoT systems: A generative AI-based approach. IEEE Internet of Things Journal, 12(10), 13327–13339. https://doi.org/10.1109/JIOT.2025.3533570
[36] Sun, K., Chen, Z., Lin, X., Sun, X., Liu, H., & Ji, R. (2025). Conditional diffusion models for camouflaged and salient object detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 47(4), 2833–2848. https://doi.org/10.1109/TPAMI.2025.3527469
[37] Wu, Y., Li, Z., & Huang, H. (2025). SGM-EMA: Speech enhancement method score-based diffusion model and EMA mechanism. Applied Sciences, 15(10), 5243. https://doi.org/10.3390/app15105243
[38] Li, Y., et al. (2024). Zero-shot medical image translation via frequency-guided diffusion models. IEEE Transactions on Medical Imaging, 43(3), 980–993. https://doi.org/10.1109/TMI.2023.3325703
[39] Krizhevsky, A., Nair, V., & Hinton, G. (2009). The CIFAR-10 dataset. University of Toronto. https://www.cs.toronto.edu/~kriz/cifar.html
[40] Ho, J., Jain, A., & Abbeel, P. (2020). Denoising diffusion probabilistic models. arXiv preprint arXiv:2006.11239. https://doi.org/10.48550/arXiv.2006.11239
[41] Song, J., Meng, C., & Ermon, S. (2022). Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502. https://doi.org/10.48550/arXiv.2010.02502
[42] Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S., & Poole, B. (2021). Score-based generative modeling through stochastic differential equations. arXiv preprint arXiv:2006.11239. https://doi.org/10.48550/arXiv.2006.11239
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