Analyzing microscopy images to extract biological object properties (e.g., their morphological organization, temporal dynamics, and population density) is fundamental to various biomedical research. Yet conducting this manually is costly and time-consuming. Though deep learning-based approaches have been explored to automate this process, the substantial diversity of microscopy analysis settings in practice (including variations of biological object types, sample processing protocols, imaging equipment, and analysis tasks, etc.) often renders them ineffective. As a result, these approaches typically require extensive adaptation for different settings, which, however, can impose burdens that are often practically unsustainable for laboratories, forcing biomedical researchers to still commonly rely on manual analysis, thereby severely bottlenecking the pace of biomedical research progress. This situation has created a pressing and long-standing need for a reliable and broadly applicable microscopy image analysis tool, yet such a tool is still missing. To address this gap, we present the first ready-to-use microscopy image analysis framework, MicroscopyMatching, that can reliably perform key analysis tasks (including segmentation, tracking, and counting) across diverse microscopy analysis settings. From a fundamentally different perspective, MicroscopyMatching reformulates diverse microscopy image analysis tasks as a unified matching problem, effectively handling this problem by exploiting the robust matching capability from pre-trained latent diffusion models.