InertialBridge: Efficient Structure-Aware Denoising of IMU Trajectories via Variational Autoencoder Conditional Bridge Matching

Dense inertial motion estimation requires accurate per-sample predictions at a manageable computational cost. We present InertialBridge (IB), a conditional bridge-matching (BM) framework that predicts 100 samples of 3D velocity v and angular rate ω after observing a complete one-second IMU window, using a single network evaluation. Conditioning the drift on the source window makes every interior bridge target algebraically identifiable. A boundary-weighted scheduler πρ = ρ δ0 + (1 − ρ) U [0, 1] allocates training mass to the deployed query at t = 0. Our population analysis establishes one-step exactness of the optimal field and characterizes the boundary drift that determines its prediction. A matched ten-epoch, single-seed sweep yields 2.7–3.9 times higher position ATE under uniform scheduling than under the evaluated positive-boundary-mass schedules. IB parameterizes the drift with a Mamba3 state-space network conditioned on a frozen variational autoencoder (VAE), and uses a structured kinematic loss. Under our common RoNIN protocol, IB achieves the lowest mean position ATE and RTE among the evaluated methods on both subject splits; paired ATE tests do not detect a significant difference from EqNIO. IB uses 1.95 M parameters and 0.87 GFLOPs per window, compared with 5.03 M and 0.84 GFLOPs for EqNIO, while returning an estimate at every input sample. These results support efficient dense reconstruction of observed IMU windows.