Learning Patient-Specific Disease Dynamics With Latent Flow Matching For Longitudinal Imaging Generation

Understanding disease progression is a central clinical challenge with direct implications for early diagnosis and personalized treatment. While recent generative approaches have attempted to model progression, key mismatches remain: disease dynamics are inherently continuous and monotonic, yet latent representations are often scattered, lacking semantic structure, and diffusion-based models disrupt continuity through the random denoising process. In this work, we propose treating disease dynamics as a velocity field and leveraging Flow Matching (FM) to align the temporal evolution of patient data. Unlike prior methods, our approach captures the intrinsic dynamics of disease, making progression more interpretable. However, a key challenge remains: in latent space, Autoencoders (AEs) do not guarantee alignment across patients or correlation with clinical severity (e.g., age and disease conditions). To address this, we propose learning patient-specific latent alignment, which enforces patient trajectories to lie along a specific axis, with magnitudes increasing monotonically with disease severity. This leads to a consistent and semantically meaningful latent space. Together, we present ∆-LFM, a framework for modeling patient-specific latent progression with flow matching. Across three longitudinal MRI benchmarks, ∆-LFM demonstrates strong empirical performance and, more importantly, establishes a new framework for interpreting and visualizing disease dynamics.