\section{Conclusion}\label{sec:conclusion}
In summary, we introduced NRFlow, which augments traditional flow-based generative models by the second-order term. Our theoretical results demonstrate that these higher-order terms act as an effective regularizer, providing improved noise robustness and smoother trajectories under bounded perturbations. A discrete Gronwall analysis further shows that error propagation remains controlled, reinforcing the framework’s stability. These findings highlight the promise of second-order methods for robust generative modeling.
 
