Jump diffusions is a class of stochastic processes designed to model dynamical systems subject to both continuous fluctuations and discrete, sudden changes. They represent an extension of standard diffusion processes by incorporating random jump components. This framework is particularly relevant for systems where the driving noise is discontinuous, heavy-tailed, or too intensive to be adequately represented by Brownian motion alone. Applications span diverse domains such as financial markets, physical phenomena like polymerization, and advanced generative models, enabling the capture of dynamics characterized by abrupt events alongside gradual evolution.