Accelerated dynamic volumetric magnetic resonance imaging (4DMRI) is essential for applications relying on motion resolution. Existing 4DMRI produces acceptable artifacts of averaged breathing phases, which can blur and misrepresent instantaneous dynamic information. Recovery of such information requires a new paradigm to reconstruct extremely undersampled non-Cartesian k-space data. We propose B-FIRE, a binning-free diffusion implicit neural representation framework for hyper-accelerated MR reconstruction capable of reflecting instantaneous 3D abdominal anatomy. B-FIRE employs a CNN-INR encoder-decoder backbone optimized using diffusion with a comprehensive loss that enforces image-domain fidelity and frequency-aware constraints. Motion binned image pairs were used as training references, while inference was performed on binning-free undersampled data. Experiments were conducted on a T1-weighted StarVIBE liver MRI cohort, with accelerations ranging from 8 spokes per frame (RV8) to RV1. B-FIRE was compared against direct NuFFT, GRASP-CS, and an unrolled CNN method. Reconstruction fidelity, motion trajectory consistency, and inference latency were evaluated.