BioFlow: Conditional Flow Matching for Patient-Specific 3D Medical Image Forecasting from Irregular Histories

Given sparse 3D scans acquired at irregular clinical intervals, we forecast a patient's 3D volume at a specified future acquisition time. Repeated scans capture largely shared anatomy, so temporal changes are often small relative to the overall voxel content, making persistence a strong whole-volume baseline. Yet the latest scan alone cannot reveal the patient-specific rate or direction of change. Longitudinal volumetric imaging is costly, and our clinical cohorts contain only 45--92 training patients. Existing continuous-time methods do not preserve the full visit history as a separate, fixed condition. CRONOS, our closest multi-scan flow-matching baseline, makes the entire scan stack its evolving state and interpolates acquisition timestamps with the same numerical flow variable. This entangles clinical intervals with integration progress, implicitly aligning heterogeneous patient trajectories on a shared normalized coordinate. We introduce BioFlow, which, to our knowledge, is the first multi-scan 3D medical conditional flow-matching framework to separate a single evolving prediction state from a fixed, visit-resolved history. Target-relative intervals guide retrieval from this history and weight a blend of observed scans that initializes the state. Each velocity evaluation uses global cross-attention over all visit-patch tokens, followed by aligned-local cross-attention over corresponding spatial locations. Numerical flow time conditions only the evolving state pathway. Across three controlled benchmarks and three clinical MRI/CT cohorts, BioFlow outperforms all evaluated baselines on SSIM, PSNR, NRMSE, and MSE.