Abstract
<title>Abstract</title> <p>Reliable multi-modal odometry requires the estimator to reduce confidence before degraded measurements dominate the state update. This paper introduces PUD–DIKF, a prediction-uncertainty-driven Diffusion-Informed Kalman Filter for LiDAR–RGB-D–IMU odometry. Its core mechanism is a Prediction Uncertainty Tensor (PUT) that converts retrospective denoising uncertainty and short-horizon reliability prediction into positive-semidefinite, state-dependent process and measurement covariance increments. Bidirectional diffusion synchronization , reliability-aware LiDAR–camera calibration, and SE(3)-consistent feature extraction are treated as supporting front-end elements that populate the PUT and form reliable residuals; the predictive occupancy field is a downstream consumer of the estimated state and uncertainty rather than a separate estimation contribution. A monotonicity result shows that increasing predicted uncertainty cannot increase measurement information and cannot reduce the propagated covariance below the fixed-noise baseline. We collect three campus sequences totaling 1,135 m and 25.4 min; all trajectory metrics are computed over a 438.58 m synchronized evaluation window drawn from these sequences. On public HILTI–Oxford and KITTI odometry benchmarks, and on auxiliary M2UD uncertainty data, PUD–DIKF is evaluated using dataset-specific protocols. Under the campus evaluation protocol, PUD–DIKF achieves a trajectory RMSE of 0.034 m, an RPE of 0.008 m, and a median point-cloud alignment error of 0.008 m at 42 ms per LiDAR frame. Controlled ablations increase trajectory RMSE by 21% without proactive prediction and by 32% without retrospective denoising, directly supporting the central covariance-adaptation hypothesis.</p>