Tabular data are central to biomedical research, from liquid biopsy and bulk and single-cell transcriptomics to electronic health records and phenotypic profiling. Unlike images or sequences, however, tabular datasets lack intrinsic spatial organization: features are treated as unordered dimensions, and their relationships must be inferred implicitly by the model. This limits the ability of vision architectures to exploit local structure and higher-order feature interactions in non-spatial biomedical data. Here we introduce Dynamic Feature Mapping (Dynomap), an end-to-end deep learning framework that learns a task-optimized spatial topology of features directly from data. Dynomap jointly optimizes feature placement and prediction through a fully differentiable rendering mechanism, without relying on heuristics, predefined groupings, or external priors. By transforming high-dimensional tabular vectors into learned feature maps, Dynomap enables vision-based models to operate effectively on unordered biomedical inputs. Across multiple clinical and biological datasets, Dynomap consistently outperformed classical machine learning, modern deep tabular models, and existing vector-to-image approaches. In liquid biopsy data, Dynomap organized clinically relevant gene signatures into coherent spatial patterns and improved multiclass cancer subtype prediction accuracy by up to 18%. In a Parkinson disease voice dataset, it clustered disease-associated acoustic descriptors and improved accuracy by up to 8%. Similar gains and interpretable feature organization were observed in additional biomedical datasets. These results establish Dynomap as a general strategy for bridging tabular and vision-based deep learning and for uncovering structured, clinically relevant patterns in high-dimensional biomedical data.