Image Difference Captioning (IDC) aims to generate natural language descriptions that highlight subtle differences between two visually similar images. While recent advances leverage pre-trained vision-language models to align fine-grained visual differences with textual semantics, existing supervised approaches often overfit to dataset-specific language patterns and fail to capture accurate preferences on IDC, which often indicates fine-grained and context-aware distinctions. To address these limitations, we propose an adversarial direct preference optimization (ADPO) framework for IDC, which formulates IDC as a preference optimization problem under the Bradley-Terry-Luce model, directly aligning the captioning policy with pairwise difference preferences via Direct Preference Optimization (DPO). To model more accurate and diverse IDC preferences, we introduce an adversarially trained hard negative retriever that selects counterfactual captions, This results in a minimax optimization problem, which we solve via policy-gradient reinforcement learning, enabling the policy and retriever to improve jointly. Experiments on benchmark IDC datasets show that our approach outperforms existing baselines, especially in generating fine-grained and accurate difference descriptions.