Nonlinear Diffusion

Nonlinear diffusion models are extending the capabilities of diffusion-based generative modeling and other applications by moving beyond the limitations of linear processes. Current research focuses on developing tractable methods for training and estimating scores in these nonlinear systems, often employing neural networks and techniques like score matching and Schrödinger bridges to learn the diffusion processes. These advancements are improving the performance of generative models, enhancing graph neural networks by mitigating over-smoothing, and providing more efficient solutions for tasks such as image restoration and time-series data generation. The resulting models offer improved accuracy and efficiency across diverse fields, from statistical physics to machine learning.