Chemical imaging enables label-free visualization of cells, tissues and living systems while providing direct biochemical information that is difficult to obtain with conventional fluorescence microscopy. Despite its promise in applications ranging from intraoperative diagnosis to drug-response analysis, its broader use remains limited by slow data acquisition, particularly for three-dimensional imaging. In practice, imaging large volumes or many samples at high spatial resolution is often prohibitively slow, creating a major throughput bottleneck for biomedical studies. Computational super-resolution is a promising approach to break the tradeoff between resolution and image volume. Although many methods have been developed for microscopy image restoration and enhancement, the problem of recovering high-resolution 3D structure from throughput-optimized low-resolution chemical imaging measurements has remained largely unexplored. Here we present MicroDiffuse3D, a pretrained foundation model for 3D microscopy image restoration that recovers high-quality volumetric structure from degraded low-resolution measurements acquired at substantially higher throughput. Built on large-scale pretraining over a curated corpus of 2.55 million microscopy images, MicroDiffuse3D combines broad biological and spatial structural priors learned from the data with strong generative capabilities of diffusion-based reconstruction. By restoring volumes jointly rather than slice by slice, the model better recovers sharp cellular structures in 3D while preserving consistency with the measured signal. We evaluated MicroDiffuse3D across three challenging restoration settings, including 3D super-resolution under 16-fold volumetric sparsity, joint degradation in resolution and noise, and 3D denoising in the low signal-to-noise ratio (SNR) regime. The model delivered clear gains over strong baselines in the two super-resolution-related settings, while remaining competitive in 3D denoising against methods specifically engineered for that task. Under the sparse 3D super-resolution setting, MicroDiffuse3D produced clearer continuity across depth with fewer artifacts and improved segmentation quality by 10.58% and line-profile concordance by 15.59%. Together, our results establish pretrained 3D restoration as a broadly applicable strategy for overcoming the throughput and SNR limitations in volumetric chemical imaging, enabling high-resolution analysis at scales and speeds that were previously difficult to achieve.