Four-dimensional MRI (4D-MRI) is an promising technique for capturing respiratory-induced motion in radiation therapy planning and delivery. Conventional 4D reconstruction methods, which typically rely on phase binning or separate template scans, struggle to capture temporal variability, complicate workflows, and impose heavy computational loads. We introduce a neural representation framework that considers respiratory motion as a smooth, continuous deformation steered by a 1D surrogate signal, completely replacing the conventional discrete sorting approach. The new method fuses motion modeling with image reconstruction through two synergistic networks: the Spatial Anatomy Network (SAN) encodes a continuous 3D anatomical representation, while a Temporal Motion Network (TMN), guided by Transformer-derived respiratory signals, produces temporally consistent deformation fields. Evaluation using a free-breathing dataset of 19 volunteers demonstrates that our template- and phase-free method accurately captures both regular and irregular respiratory patterns, while preserving vessel and bronchial continuity with high anatomical fidelity. The proposed method significantly improves efficiency, reducing the total processing time from approximately five hours required by conventional discrete sorting methods to just 15 minutes of training. Furthermore, it enables inference of each 3D volume in under one second. The framework accurately reconstructs 3D images at any respiratory state, achieves superior performance compared to conventional methods, and demonstrates strong potential for application in 4D radiation therapy planning and real-time adaptive treatment.