# Adaptive 3D Reconstruction via Diffusion Priors and Forward Curvature-Matching Likelihood Updates

arXiv: https://arxiv.org/abs/2511.06310 · HTML: https://mlsanity.com/paper/2511.06310/

## Key facts

- Cited by 1 papers in the map (data through 7 Oct 2026).
- Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models.
- Builds on 29 of its 42 references that are in the map.
- First posted on arXiv 9 Nov 2025.

## 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, 29 of 29)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [LRM: Large Reconstruction Model for Single Image to 3D](https://mlsanity.com/paper/2311.04400/) (2023)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [LGM: Large Multi-View Gaussian Model for High-Resolution 3D Content Creation](https://mlsanity.com/paper/2402.05054/) (2024)
- [Point-E: A System for Generating 3D Point Clouds from Complex Prompts](https://mlsanity.com/paper/2212.08751/) (2022)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Splatter Image: Ultra-Fast Single-View 3D Reconstruction](https://mlsanity.com/paper/2312.13150/) (2023)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [DiffRF: Rendering-Guided 3D Radiance Field Diffusion](https://mlsanity.com/paper/2212.01206/) (2022)
- [Single-Stage Diffusion NeRF: A Unified Approach to 3D Generation and Reconstruction](https://mlsanity.com/paper/2304.06714/) (2023)
- [NerfDiff: Single-image View Synthesis with NeRF-guided Distillation from 3D-aware Diffusion](https://mlsanity.com/paper/2302.10109/) (2023)
- [3D Point Cloud Generative Adversarial Network Based on Tree Structured Graph Convolutions](https://mlsanity.com/paper/1905.06292/) (2019)
- [DiT-3D: Exploring Plain Diffusion Transformers for 3D Shape Generation](https://mlsanity.com/paper/2307.01831/) (2023)
- [PC2: Projection-Conditioned Point Cloud Diffusion for Single-Image 3D Reconstruction](https://mlsanity.com/paper/2302.10668/) (2023)
- [KeypointNet: A Large-scale 3D Keypoint Dataset Aggregated from Numerous Human Annotations](https://mlsanity.com/paper/2002.12687/) (2020)
- [Bayesian Diffusion Models for 3D Shape Reconstruction](https://mlsanity.com/paper/2403.06973/) (2024)
- [GSD: View-Guided Gaussian Splatting Diffusion for 3D Reconstruction](https://mlsanity.com/paper/2407.04237/) (2024)
- [RGB2Point: 3D Point Cloud Generation from Single RGB Images](https://mlsanity.com/paper/2407.14979/) (2024)
- [LIST: Learning Implicitly from Spatial Transformers for Single-View 3D Reconstruction](https://mlsanity.com/paper/2307.12194/) (2023)
- [Enhancing Diffusion-based Point Cloud Generation with Smoothness Constraint](https://mlsanity.com/paper/2404.02396/) (2024)
- [DiffPoint: Single and Multi-view Point Cloud Reconstruction with ViT Based Diffusion Model](https://mlsanity.com/paper/2402.11241/) (2024)

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

- [Point-MF: Stabilizing One-Step Mean Flows for Single-Image Point Cloud Reconstruction](https://mlsanity.com/paper/2604.24586/) (2026)

## Abstract (arXiv)

Reconstructing high-quality point clouds from images remains challenging in computer vision. Existing generative-model-based approaches, particularly diffusion-model approaches that directly learn the posterior, may suffer from inflexibility -- they require conditioning signals during training, support only a fixed number of input views, and need complete retraining for different measurements. Recent diffusion-based methods have attempted to address this by combining prior models with likelihood updates, but they rely on heuristic fixed step sizes for the likelihood update that lead to slow convergence and suboptimal reconstruction quality. We advance this line of approach by integrating our novel Forward Curvature-Matching (FCM) update method with diffusion sampling. Our method dynamically determines optimal step sizes using only forward automatic differentiation and finite-difference curvature estimates, enabling precise optimization of the likelihood update. This formulation enables high-fidelity reconstruction from both single-view and multi-view inputs, and supports various input modalities through simple operator substitution -- all without retraining. Experiments on ShapeNet and CO3D datasets demonstrate that our method achieves superior reconstruction quality at matched or lower NFEs, yielding higher F-score and lower CD and EMD, validating its efficiency and adaptability for practical applications. Code is available at https://github.com/Seunghyeok0715/FCM