# Predicting 3D structure by latent posterior sampling

arXiv: https://arxiv.org/abs/2605.10830 · HTML: https://mlsanity.com/paper/2605.10830/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models.
- Builds on 28 of its 32 references that are in the map.
- First posted on arXiv 11 May 2026.

## Placed in

- Diffusion models / [3D, point cloud and scene generation](https://mlsanity.com/diffusion/3d-point-cloud-and-scene-generation/)

## Builds on (most cited first, 28 of 28)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [Objaverse: A Universe of Annotated 3D Objects](https://mlsanity.com/paper/2212.08051/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [IBRNet: Learning Multi-View Image-Based Rendering](https://mlsanity.com/paper/2102.13090/) (2021)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [3D Neural Field Generation using Triplane Diffusion](https://mlsanity.com/paper/2211.16677/) (2022)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [From data to functa: Your data point is a function and you can treat it like one](https://mlsanity.com/paper/2201.12204/) (2022)
- [Single-Stage Diffusion NeRF: A Unified Approach to 3D Generation and Reconstruction](https://mlsanity.com/paper/2304.06714/) (2023)
- [Optimizing the Latent Space of Generative Networks](https://mlsanity.com/paper/1707.05776/) (2017)
- [HyperDiffusion: Generating Implicit Neural Fields with Weight-Space Diffusion](https://mlsanity.com/paper/2303.17015/) (2023)
- [NeRF-VAE: A Geometry Aware 3D Scene Generative Model](https://mlsanity.com/paper/2104.00587/) (2021)
- [Bayes' Rays: Uncertainty Quantification for Neural Radiance Fields](https://mlsanity.com/paper/2309.03185/) (2023)
- [Conditional-Flow NeRF: Accurate 3D Modelling with Reliable Uncertainty Quantification](https://mlsanity.com/paper/2203.10192/) (2022)
- [Density-aware NeRF Ensembles: Quantifying Predictive Uncertainty in Neural Radiance Fields](https://mlsanity.com/paper/2209.08718/) (2022)
- [GaussianCube: A Structured and Explicit Radiance Representation for 3D Generative Modeling](https://mlsanity.com/paper/2403.19655/) (2024)
- [Deceptive-NeRF/3DGS: Diffusion-Generated Pseudo-Observations for High-Quality Sparse-View Reconstruction](https://mlsanity.com/paper/2305.15171/) (2023)
- [Learning a Diffusion Prior for NeRFs](https://mlsanity.com/paper/2304.14473/) (2023)
- [Robust Inverse Graphics via Probabilistic Inference](https://mlsanity.com/paper/2402.01915/) (2024)

## Built on by (most cited first, 1 of 1)

- [Learning Spherical Occupancy Profiles for Multi-View 3D Reconstruction and Generation](https://mlsanity.com/paper/2608.23206/) (2026)

## Abstract (arXiv)

The remarkable achievements of both generative models of 2D images and neural field representations for 3D scenes present a compelling opportunity to integrate the strengths of both approaches. In this work, we propose a methodology that combines a NeRF-based representation of 3D scenes with probabilistic modeling and reasoning using diffusion models. We view 3D reconstruction as a perception problem with inherent uncertainty that can thereby benefit from probabilistic inference methods. The core idea is to represent the 3D scene as a stochastic latent variable for which we can learn a prior and use it to perform posterior inference given a set of observations. We formulate posterior sampling using the score-based inference method of diffusion models in conjunction with a likelihood term computed from a reconstruction model that includes volumetric rendering. We train the model using a two-stage process: first we train the reconstruction model while auto-decoding the latent representations for a dataset of 3D scenes, and then we train the prior over the latents using a diffusion model. By using the model to generate samples from the posterior we demonstrate that various 3D reconstruction tasks can be performed, differing by the type of observation used as inputs. We showcase reconstruction from single-view, multi-view, noisy images, sparse pixels, and sparse depth data. These observations vary in the amount of information they provide for the scene and we show that our method can model the varying levels of inherent uncertainty associated with each task. Our experiments illustrate that this approach yields a comprehensive method capable of accurately predicting 3D structure from diverse types of observations.