Robust and Controllable Generative Models by Leveraging Physics-Based, Probabilistic, and Geometric Methods

Generative models are deep neural network-based models trained to learn the underlying distribution of a dataset. Once trained, these models can be used to sample novel data points from this distribution. Their impressive capabilities have been manifested in various generative tasks, encompassing areas like image-to-image translation, style transfer, image editing, and more. One notable application of generative models is data augmentation, aimed at expanding and diversifying the training dataset to augment the performance of deep learning models for a downstream task. Generative models can be used to create new samples similar to the original data but with different variations and properties that are difficult to capture with traditional data augmentation techniques. However, the quality, diversity, and controllability of the shape and structure of the generated samples from these models are often directly proportional to the size and diversity of the training dataset. A more extensive and diverse training dataset allows the generative model to capture overall structures present in the data and generate more diverse and realistic-looking samples. In this dissertation, I present innovative methods designed to enhance the robustness and controllability of generative models, drawing upon physics-based, probabilistic, and geometric techniques. These methods help improve the generalization and controllability of the generative model without necessarily relying on large training datasets. I enhance the robustness of generative models by integrating classical geometric moments for shape awareness and minimizing trainable parameters. Additionally, I employ non-parametric priors for the generative model's latent space through basic probability and optimization methods to improve the fidelity of interpolated images. I adopt a hybrid approach to address domain-specific challenges with limited data and controllability, combining physics-based rendering with generative models for more realistic results. These approaches are particularly relevant in industrial settings, where the training datasets are small and class imbalance is common. Through extensive experiments on various datasets, I demonstrate the effectiveness of the proposed methods over conventional approaches.