Year: 2026
Type: dissertation
Abstract: Continuous Normalizing Flows (CNFs) and Flow Matching have emerged as powerful simulation-free paradigms for generative modeling. While the widely adopted linear Optimal Transport (OT) parameterization enables ultra-efficient inference with a low Number of Function Evaluations (NFE), it fundamentally forces generative trajectories into straight geometric crossfades, discarding the true intermediate physical dynamics of sequential data. Conversely, methods utilizing higher-order splines successfully capture non-linear temporal dynamics but reintroduce significant computational burdens during ODE integration. This thesis proposes a novel framework, Tangent-Augmented Post-Hoc Hermite Interpolation, to bridge this operational gap. By introducing a decoupled, dual-head architecture, our method retains the highly stable linear OT objective for the primary velocity field while employing a lightweight, shared-context tangent prediction head to extract and estimate local boundary momentums. During inference, intermediate physical states are synthesized analytically via cubic Hermite splines, entirely bypassing the neural ODE solver. This allows the model to accurately recover complex, non-linear intermediate trajectories with high fidelity while maintaining the state-of-the-art computational efficiency of standard linear FlowMatching. Ultimately, this approach offers a highly scalable and mathematicallyrigorous solution for physically grounded continuous sequence generation
Source: Aaltodoc (Aalto University)
Author: Chauvet, Mael
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204017810