Modeling Uncertainty Propagation in 3D Morphable Models

A correctly reconstructed distant point appears uncertain even when a frozen 3D model processes equivalent inputs because its output frame rotates fractionally. This exposes a weakness of trainingfree perturbation uncertainty: when outputs contain an unobserved symmetry, run-to-run variation potentially reflects symmetry rather than error. Existing alternatives have trade-offs: built-in confidence is outperformed in most evaluated conditions, while trained evidential heads require modelspecific supervision. For point maps, this research derives a closed-form, error-independent variance term that grows with scene extent and potentially overwhelms the desired signal. Simulation reproduces the effect; all 30 real VGGT view-sets tested exhibit its predicted $\|x_p\|^2$ signature. ReVar3R robustly registers predictions to a common similarity frame before computing per-point variance, without retraining or modifying the frozen model. Optional calibration and fusion use a held-out split. Across VGGT, π3, and MASt3R on six datasets, the same estimator on every backbone lowers AUSE below built-in confidence in 15 of 18 conditions. The staged evaluation yields 11 of 18 wins for the label-free core, 12/18 for label-free equal-weight fusion, 14/18 with held-out weights, and 15/18 when the built-in signal is included. Against a trained evidential head, the result is a trade-off: the head calibrates magnitude better and leads in its training domain, whereas ReVar3R transfers across backbones without adaptation. Its ranking improves point filtering, but it does not detect stable systematic bias, aid novel-view synthesis, or transfer calibration across domains.

Human mesh recovery from single images remains challenging due to inherent depth ambiguity and limited generalization across domains. While recent methods combine regression and optimization approaches, they struggle with poor initialization for test-time refinement and inefficient parameter updates during optimization. We propose a novel meta-learning framework that trains models to produce optimization-friendly initializations while incorporating uncertainty-aware adaptive updates during test-time refinement. Our approach introduces three key innovations: (1) a meta-learning strategy that simulates test-time optimization during training to learn better parameter initializations, (2) a selective parameter caching mechanism that identifies and freezes converged joints to reduce computational overhead, and (3) distribution-based adaptive updates that sample parameter changes from learned distributions, enabling robust exploration while quantifying uncertainty. Additionally, we employ stochastic approximation techniques to handle intractable gradients in complex loss landscapes. Extensive experiments on standard benchmarks demonstrate that our method achieves state-of-the-art performance, reducing MPJPE by 10.3 on 3DPW and 8.0 on Human3.6M compared to strong baselines. Our approach shows superior domain adaptation capabilities with minimal performance degradation across different environmental conditions, while providing meaningful uncertainty estimates that correlate with actual prediction errors. Combining meta-learning and adaptive optimization enables accurate mesh recovery and robust generalization to challenging scenarios.

Geometric foundation models hold promise for unconstrained dense geometry prediction from uncalibrated images. However, in current feed-forward designs, their predicted confidence scores are heuristic, lack probabilistic interpretation, and often fail to indicate where and how much the predicted geometry can be trusted. To address this gap, we present Trust3R, a lightweight evidential uncertainty framework for feed-forward 3D reconstruction. Trust3R combines gated residual mean refinement with a Normal-Inverse-Wishart evidential head, yielding a closed-form multivariate Student-t distribution for per-point geometric uncertainty. This design provides probabilistically grounded pointmap uncertainty estimates while adding moderate inference overhead. We evaluate on diverse indoor and outdoor benchmarks and compare against MASt3R's built-in confidence map as well as common uncertainty-aware baselines spanning single-pass heteroscedastic regression and sampling-based methods such as MC dropout and deep ensembles. Experimental results show that Trust3R consistently improves risk-coverage and sparsification, and generally improves geometric accuracy. These gains are reflected in stronger uncertainty ranking across benchmarks, with 25% lower AURC and 41% lower AUSE on ScanNet++, providing a practical reliability signal for uncertainty-aware weighting in downstream geometry pipelines. The project page and code are available at https://trust3r-z.github.io/.