Automatic diagnosis is a significant application of AI in healthcare, where diagnoses are generated based on the symptom description of patients. Previous works have approached this task directly by modeling the relationship between the normalized symptoms and all possible diseases. However, in the clinical diagnostic process, patients are initially consulted by a general practitioner and, if necessary, referred to specialists in specific domains for a more comprehensive evaluation. The final diagnosis often emerges from a collaborative consultation among medical specialist groups. Recently, large language models have shown impressive capabilities in natural language understanding. In this study, we adopt tuning-free LLM-based agents as medical practitioners and propose the Agent-derived Multi-Specialist Consultation (AMSC) framework to model the diagnosis process in the real world by adaptively fusing probability distributions of agents over potential diseases. Experimental results demonstrate the superiority of our approach compared with baselines. Notably, our approach requires significantly less parameter updating and training time, enhancing efficiency and practical utility. Furthermore, we delve into a novel perspective on the role of implicit symptoms within the context of automatic diagnosis.