Hematoxylin and eosin (H&E)-stained slides are central to cancer diagnosis and monitoring, visualizing tissue architecture and cellular morphology. However, H&E lacks the molecular specificity needed to distinguish cell states and functional activation. Antibody-based stains, such as immunohistochemistry (IHC), are therefore required to identify specific phenotypes (e.g., CD3$^+$ T cells or HER2-positive tumor cells) but are costly, time-consuming, and not universally available. Deep learning-based image translation methods, often termed virtual staining, offer a complementary alternative by generating virtual immunostains directly from H&E images. Most existing virtual staining methods are patch-based and operate at fixed resolutions, often requiring large datasets and additional post-hoc super-resolution models to generate high-resolution images. Furthermore, GAN- and diffusion-based approaches introduce stochasticity into generated stains which, although beneficial for visual realism in natural images, can lead to hallucinations and structural distortions that affect the accuracy and reliability required for clinical use. We propose IMPLICITSTAINER, a deterministic framework that reformulates virtual staining as a continuous pixel-level translation problem. In contrast to existing patch-based approaches, IMPLICITSTAINER formulates image translation as a continuous spatial mapping using neural implicit deep learning models. Each target-domain (IHC) pixel is predicted from a high-dimensional embedding of the corresponding source-domain H&E pixel, its local spatial neighborhood, and explicit coordinate information. IMPLICITSTAINER enables resolution-agnostic inference, improves robustness in low-data regimes, and yields deterministic, reproducible outputs. Across more than twenty baselines, IMPLICITSTAINER achieves SOTA performance on virtual staining tasks, including IHC and mIF.