Optical volumetric imaging grapples with inherent noise problems arising from photon budget constraints, light scattering, and space-bandwidth product bottlenecks, all of which degrade structural fidelity and become even more pronounced than in planar imaging. While deep learning presents potential for denoising, supervised methods are hindered by the impracticality of paired datasets, and existing self-supervised approaches fail to fully exploit the intrinsic volumetric structural redundancy inherent to optical imaging. Here, we present a self-supervised volumetric biomedical imaging denoiser (VALID) that leverages intrinsic three-dimensional spatial coherence for highly efficient volumetric denoising through a self-supervised orthogonal learning framework. VALID demonstrates robust denoising performance across diverse imaging modalities, including two- and three-photon microscopy, light-field microscopy, and optical coherence tomography, substantially enhancing structural fidelity in deep-tissue, multimodal, and dynamic imaging scenarios. By combining computational efficiency with zero-shot adaptability, VALID establishes a transformative approach to volumetric image enhancement with structure-aware precision.