Large Language Models (LLMs) have achieved impressive performance in text summarization and are increasingly deployed in real-world applications. However, these systems often inherit associative and framing biases from pre-training data, leading to inappropriate or unfair outputs in downstream tasks. In this work, we present AdvSumm (Adversarial Summarization), a domain-agnostic training framework designed to mitigate bias in text summarization through improved generalization. Inspired by adversarial robustness, AdvSumm introduces a novel Perturber component that applies gradient-guided perturbations at the embedding level of Sequence-to-Sequence models, enhancing the model's robustness to input variations. We empirically demonstrate that AdvSumm effectively reduces different types of bias in summarization-specifically, name-nationality bias and political framing bias-without compromising summarization quality. Compared to standard transformers and data augmentation techniques like back-translation, AdvSumm achieves stronger bias mitigation performance across benchmark datasets.