Introduction: Research interest in exoskeleton assistance strategies that incorporate the user's torque capacity is growing rapidly. However, the predicted torque capacity from users often includes uncertainty from various sources, which can have a significant impact on the safety of the exoskeleton-user interface. Methods: To address this challenge, this paper proposes an adaptive control framework for a knee exoskeleton that uses muscle electromyography (EMG) signals and joint kinematics. The framework predicted the user's knee flexion/extension torque with confidence bounds to quantify the uncertainty based on a neuromusculoskeletal (NMS) solver-informed Bayesian Neural Network (NMS-BNN). The predicted torque, with a specified confidence level, controlled the assistive torque provided by the exoskeleton through a TCP/IP stream. The performance of the NMS-BNN model was also compared to that of the Gaussian process (NMS-GP) model. Results: Our findings showed that both the NMS-BNN and NMS-GP models accurately predicted knee joint torque with low error, surpassing traditional NMS models. High uncertainties were observed at the beginning of each movement, and at terminal stance and terminal swing in self-selected speed walking in both NMS-BNN and NMS-GP models. The knee exoskeleton provided the desired assistive torque with a low error, although lower torque was observed during terminal stance of fast walking compared to self-selected walking speed. Discussion: The framework developed in this study was able to predict knee flexion/extension torque with quantifiable uncertainty and to provide adaptive assistive torque to the user. This holds significant potential for the development of exoskeletons that provide assistance as needed, with a focus on the safety of the exoskeleton-user interface.