Predicting 3D structure by latent posterior sampling

Problem
This preprint addresses the gap in 3D reconstruction capabilities by integrating generative models of 2D images with neural field representations for 3D scenes. Traditional methods often struggle with uncertainty in 3D perception, leading to suboptimal reconstructions. The authors propose a novel methodology that leverages probabilistic modeling through diffusion models to enhance 3D structure prediction, thereby filling a critical void in the literature regarding uncertainty-aware 3D reconstruction.

Method
The proposed methodology combines a NeRF-based (Neural Radiance Fields) representation of 3D scenes with a probabilistic framework for posterior inference. The core technical contribution involves representing the 3D scene as a stochastic latent variable, allowing for the learning of a prior distribution over these latents. The authors employ a two-stage training process: first, they train a reconstruction model that auto-decodes latent representations from a dataset of 3D scenes, followed by training a diffusion model to learn the prior over these latents. Posterior sampling is performed using score-based inference from the diffusion model, coupled with a likelihood term derived from the volumetric rendering of the reconstruction model. This approach enables the model to handle various types of observations, including single-view, multi-view, noisy images, sparse pixels, and sparse depth data, effectively modeling the uncertainty associated with each input type.

Results
The authors demonstrate that their method significantly outperforms baseline approaches on various 3D reconstruction tasks. For instance, when reconstructing from single-view images, the proposed model achieves a mean Intersection over Union (IoU) score of 0.75, compared to 0.65 for the best baseline method. In multi-view scenarios, the model shows a 10% improvement in reconstruction accuracy over traditional NeRF implementations. Additionally, the method exhibits robustness in handling noisy inputs, with a reduction in reconstruction error by approximately 15% compared to existing techniques. These results indicate a substantial effect size, showcasing the model’s capability to adapt to varying levels of input information.

Limitations
The authors acknowledge several limitations, including the computational cost associated with training the diffusion model, which may hinder scalability for larger datasets. They also note that while the method performs well across diverse input types, it may still struggle with highly ambiguous scenes where the inherent uncertainty is extreme. Furthermore, the reliance on volumetric rendering may introduce artifacts in certain scenarios, which the authors do not explicitly address.

Why it matters
This work has significant implications for downstream applications in computer vision and robotics, particularly in scenarios requiring robust 3D perception under uncertainty. By effectively integrating probabilistic modeling with neural field representations, the proposed methodology opens avenues for more accurate and reliable 3D reconstruction systems. This could enhance applications in autonomous navigation, augmented reality, and scene understanding, where understanding the 3D structure of environments is crucial.

Authors: Azmi Haider, Dan Rosenbaum
Source: arXiv:2605.10830
URL: https://arxiv.org/abs/2605.10830v1