High-dimensional partial differential equations (PDEs) pose substantial challenges to mesh-based methods, especially when dealing with large gradients or unknown concentration fields. Although mesh-free methods exhibit inherent advantages in such scenarios, they often become computationally infeasible for long-time simulations. In this talk, I will present the latest advancements in stochastic interacting particle field (SIPF) methods, which are derived from the Lagrangian framework. These methods are designed for the computation of parabolic-parabolic Keller-Segel chemotaxis systems and haptotaxis advection-diffusion systems, the latter of which are used to model cancer cell invasion. Building on the training data generated by the SIPF methods, we propose DeepParticle, a novel framework that synergistically integrates deep learning (DL), mini-batch optimal transport (OT), and particle methods. This framework is dedicated to learning and generating aggregation patterns in multi-dimensional Keller–Segel chemotaxis systems. Additionally, I will discuss the implications of these results and their interactions with the field of generative modeling.