Large language models (LLMs) have demonstrated notable potential in medical applications, yet they face substantial challenges in handling complex real-world clinical diagnoses using conventional prompting methods. Current prompt engineering and multi-agent approaches typically optimize isolated inferences, neglecting the accumulation of reusable clinical experience. To address this, this study proposes a novel Multi-Agent Clinical Diagnosis (MACD) framework, which allows LLMs to self-learn clinical knowledge via a multi-agent pipeline that summarizes, refines, and applies diagnostic insights. It mirrors how physicians develop expertise through experience, enabling more focused and accurate diagnosis on key disease-specific cues. We further extend it to a MACD-human collaborative workflow, where multiple LLM-based diagnostician agents engage in iterative consultations, supported by an evaluator agent and human oversight for cases where agreement is not reached. Evaluated on 4,390 real-world patient cases across seven diseases using diverse open-source LLMs (Llama-3.1 8B/70B, DeepSeek-R1-Distill-Llama 70B), MACD significantly improves primary diagnostic accuracy, outperforming established clinical guidelines with gains up to 22.3% (MACD). In direct comparison with physician-only diagnosis under the same evaluation protocol, MACD achieves comparable or superior performance, with improvements up to 16%. Furthermore, the MACD-human workflow yields an 18.6% improvement over physician-only diagnosis, demonstrating the synergistic potential of human-AI collaboration. Notably, the self-learned clinical knowledge exhibits strong cross-model stability, transferability across LLMs, and capacity for model-specific personalization.This work thus presents a scalable self-learning paradigm that bridges the gap between the intrinsic knowledge of LLMs.