Due to variations in imaging modalities and protocols across institutions, medical image segmentation models often encounter challenges related to domain shift. Source-Free Domain Adaptation (SFDA) address this issue by adapting pre-trained source models to target domains without accessing source data. In recent research, self-training methods based on the MT architecture have achieved good results. However, such self-training methods still face two critical challenges: severe domain shift and the problem of performance degradation in the MT architecture during self-training. This paper presents Diakd, a SFDA framework integrating Domain-Aware Indicator and Adaptive Knowledge Distillation. In the domain discrepancy perception stage, Diakd fuses a domain-aware indicator with the target domain image to estimate a source domain image and optimizes the indicator via statistical alignment loss minimization, enabling the source model to recognize the fused image as a source domain image. In the domain adaptation phase, Diakd introduces the Adaptive Knowledge Distillation Module (AKDM) based on the Mean Teacher framework. AKDM uses a dynamic data enhancement strategy related to domain-aware indicators, allowing teacher and student models to adaptively adjust bidirectional knowledge transfer according to the student model’s evolution. Through the stages of the Diakd method, we mitigate domain shift and effectively mitigate performance degradation during self-training. Experiments on a fundus multicenter dataset confirm its efficacy, achieving 89.13% Dice in optic cup (OC) segmentation, 3.64% higher than the benchmark ProSFDA and outperforming methods like FSM and AdaEnt.