Automated program repair aims to automate bug correction and alleviate the burden of manual debugging, which plays a crucial role in software development and maintenance. Recent studies reveal that learning-based approaches have outperformed conventional APR techniques (e.g., search-based APR). Existing learning-based APR techniques mainly center on treating program repair either as a translation task or a cloze task. The former primarily emphasizes statement-level repair, while the latter concentrates on token-level repair, as per our observations. In practice, however, patches may manifest at various repair granularity, including statement, expression, or token levels. Consequently, merely generating patches from a single granularity would be ineffective to tackle real-world defects. Motivated by this observation, we propose Mulpor, a multi-granularity patch generation approach designed to address the diverse nature of real-world bugs. Mulpor comprises three components: statement-level, expression-level, and token-level generator, each is pre-trained to generate correct patches at its respective granularity. The approach involves generating candidate patches from various granularities, followed by a re-ranking process based on a heuristic to prioritize patches. Experimental results on the Defects4J dataset demonstrate that Mulpor correctly repair 92 bugs on Defects4J-v1.2, which achieves 27.0% (20 bugs) and 12.2% (10 bugs) improvement over the previous state-of-the-art NMT-style Rap-Gen and Cloze-style GAMMA. We also studied the generalizability of Mulpor in repairing vulnerabilities, revealing a notable 51% increase in the number of correctly-fixed patches compared with state-of-the-art vulnerability repair approaches. This paper underscores the importance of considering multiple granularities in program repair techniques for a comprehensive strategy to address the diverse nature of real-world software defects. Mulpor, as proposed herein, exhibits promising results in achieving effective and diverse bug fixes across various program repair scenarios.