The continued success and ubiquity of machine learning techniques, particularly Deep Learning, have necessitated research in robust model training to enhance generalization capabilities and security against incomplete data, distributional shifts, and adversarial attacks. This thesis presents two primary sets of contributions to robust modeling in machine learning through the use of causal priors and data purification with generative models such as the Variational Autoencoder (VAE), Energy-Based Model (EBM), and Denoising Diffusion Probabilistic Model (DDPM), focusing on image datasets. In the first set of contributions, we use structural causal priors in the latent spaces of VAEs. Initially, we demonstrate counterfactual synthetic data generation outside the training data distribution. This technique allows for the creation of diverse and novel data points, which is critical to enhancing model robustness and generalization capabilities. We utilize a similar VAE architecture to compare causal structural (graphical) hypotheses, showing that the fit of generated data from various hypotheses on distributionally shifted test data is an effective method for hypothesis comparison. Additionally, we explore using augmentations in the latent space of a VAE as an efficient and effective way to generate realistic augmented data. The second set of contributions focuses on data purification using EBMs and DDPMs. We propose a framework of universal data purification methods to defend against train-time data poisoning attacks. This framework utilizes stochastic transforms realized via iterative Langevin dynamics of EBMs, DDPMs, or both, to purify poisoned data with minimal impact on classifier generalization. Our specially trained EBMs and DDPMs provide state-of-the-art defense against various poisoning attacks while preserving natural accuracy. Preprocessing data with these techniques pushes poisoned images into the natural, clean image manifold, effectively neutralizing adversarial perturbations. The framework achieves state-of-the-art performance without needing attack or classifier-specific information, even when the generative models are trained on poisoned or distributionally shifted data. Beyond defense against data poisoning, our framework also shows promise in applications such as the degradation and removal of unwanted intellectual property. The flexibility and generality of these data purification techniques represent a significant step forward in the adversarial model training paradigm. All of these methods enable new perspectives and approaches to robust machine learning, advancing an essential field in artificial intelligence research.