This paper extends latent ODE-based time series models to include finite numbers of finite jumps, effectively incorporating Hawkes-process-like ideas into the framework. This breaks the determinism of latent ODE-based methods. Overall I feel that this work deserves to get in. However, I beseech the authors to change the name of the method to something that doesn't include the phrase "Stochastic Differential Equations". While this method does have differential equations as well as stochastic events, in my understanding SDEs already refer exclusively to processes driven by infinitesimal noise. Calling this model an SDE is a misleading and inaccurate. How about just "Neural ODEs with Jumps"?