# PC2: Projection-Conditioned Point Cloud Diffusion for Single-Image 3D Reconstruction

arXiv: https://arxiv.org/abs/2302.10668 · HTML: https://mlsanity.com/paper/2302.10668/

## Key facts

- Cited by 84 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 55 references that are in the map.
- First posted on arXiv 21 Feb 2023.

## Builds on (most cited first, 30 of 46)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [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)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [Common Objects in 3D: Large-Scale Learning and Evaluation of Real-life 3D Category Reconstruction](https://mlsanity.com/paper/2109.00512/) (2021)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [Soft Rasterizer: A Differentiable Renderer for Image-based 3D Reasoning](https://mlsanity.com/paper/1904.01786/) (2019)
- [Point-Voxel CNN for Efficient 3D Deep Learning](https://mlsanity.com/paper/1907.03739/) (2019)

## Built on by (most cited first, 30 of 84)

- [One-2-3-45: Any Single Image to 3D Mesh in 45 Seconds without Per-Shape Optimization](https://mlsanity.com/paper/2306.16928/) (2023)
- [InstantMesh: Efficient 3D Mesh Generation from a Single Image with Sparse-view Large Reconstruction Models](https://mlsanity.com/paper/2404.07191/) (2024)
- [Splatter Image: Ultra-Fast Single-View 3D Reconstruction](https://mlsanity.com/paper/2312.13150/) (2023)
- [One-2-3-45++: Fast Single Image to 3D Objects with Consistent Multi-View Generation and 3D Diffusion](https://mlsanity.com/paper/2311.07885/) (2023)
- [Triplane Meets Gaussian Splatting: Fast and Generalizable Single-View 3D Reconstruction with Transformers](https://mlsanity.com/paper/2312.09147/) (2023)
- [PoseDiffusion: Solving Pose Estimation via Diffusion-aided Bundle Adjustment](https://mlsanity.com/paper/2306.15667/) (2023)
- [latentSplat: Autoencoding Variational Gaussians for Fast Generalizable 3D Reconstruction](https://mlsanity.com/paper/2403.16292/) (2024)
- [Consistent-1-to-3: Consistent Image to 3D View Synthesis via Geometry-aware Diffusion Models](https://mlsanity.com/paper/2310.03020/) (2023)
- [SparseFlex: High-Resolution and Arbitrary-Topology 3D Shape Modeling](https://mlsanity.com/paper/2503.21732/) (2025)
- [Free3D: Consistent Novel View Synthesis without 3D Representation](https://mlsanity.com/paper/2312.04551/) (2023)
- [Towards Realistic Scene Generation with LiDAR Diffusion Models](https://mlsanity.com/paper/2404.00815/) (2024)
- [PartGen: Part-level 3D Generation and Reconstruction with Multi-View Diffusion Models](https://mlsanity.com/paper/2412.18608/) (2024)
- [Amodal3R: Amodal 3D Reconstruction from Occluded 2D Images](https://mlsanity.com/paper/2503.13439/) (2025)
- [GVGEN: Text-to-3D Generation with Volumetric Representation](https://mlsanity.com/paper/2403.12957/) (2024)
- [Parameter-Efficient Fine-Tuning in Spectral Domain for Point Cloud Learning](https://mlsanity.com/paper/2410.08114/) (2024)
- [ShapeGPT: 3D Shape Generation with A Unified Multi-modal Language Model](https://mlsanity.com/paper/2311.17618/) (2023)
- [Template Free Reconstruction of Human-object Interaction with Procedural Interaction Generation](https://mlsanity.com/paper/2312.07063/) (2023)
- [GeoLRM: Geometry-Aware Large Reconstruction Model for High-Quality 3D Gaussian Generation](https://mlsanity.com/paper/2406.15333/) (2024)
- [Query2CAD: Generating CAD models using natural language queries](https://mlsanity.com/paper/2406.00144/) (2024)
- [A Conditional Denoising Diffusion Probabilistic Model for Point Cloud Upsampling](https://mlsanity.com/paper/2312.02719/) (2023)
- [HarmonyView: Harmonizing Consistency and Diversity in One-Image-to-3D](https://mlsanity.com/paper/2312.15980/) (2023)
- [Recent Trends in 3D Reconstruction of General Non-Rigid Scenes](https://mlsanity.com/paper/2403.15064/) (2024)
- [Diffusion Models Meet Remote Sensing: Principles, Methods, and Perspectives](https://mlsanity.com/paper/2404.08926/) (2024)
- [DRiVE: Diffusion-based Rigging Empowers Generation of Versatile and Expressive Characters](https://mlsanity.com/paper/2411.17423/) (2024)
- [InterTrack: Tracking Human Object Interaction without Object Templates](https://mlsanity.com/paper/2408.13953/) (2024)
- [Neuro-3D: Towards 3D Visual Decoding from EEG Signals](https://mlsanity.com/paper/2411.12248/) (2024)
- [SuperPC: A Single Diffusion Model for Point Cloud Completion, Upsampling, Denoising, and Colorization](https://mlsanity.com/paper/2503.14558/) (2025)
- [Bayesian Diffusion Models for 3D Shape Reconstruction](https://mlsanity.com/paper/2403.06973/) (2024)
- [InstructP2P: Learning to Edit 3D Point Clouds with Text Instructions](https://mlsanity.com/paper/2306.07154/) (2023)
- [EMIE-MAP: Large-Scale Road Surface Reconstruction Based on Explicit Mesh and Implicit Encoding](https://mlsanity.com/paper/2403.11789/) (2024)

## Abstract (arXiv)

Reconstructing the 3D shape of an object from a single RGB image is a long-standing and highly challenging problem in computer vision. In this paper, we propose a novel method for single-image 3D reconstruction which generates a sparse point cloud via a conditional denoising diffusion process. Our method takes as input a single RGB image along with its camera pose and gradually denoises a set of 3D points, whose positions are initially sampled randomly from a three-dimensional Gaussian distribution, into the shape of an object. The key to our method is a geometrically-consistent conditioning process which we call projection conditioning: at each step in the diffusion process, we project local image features onto the partially-denoised point cloud from the given camera pose. This projection conditioning process enables us to generate high-resolution sparse geometries that are well-aligned with the input image, and can additionally be used to predict point colors after shape reconstruction. Moreover, due to the probabilistic nature of the diffusion process, our method is naturally capable of generating multiple different shapes consistent with a single input image. In contrast to prior work, our approach not only performs well on synthetic benchmarks, but also gives large qualitative improvements on complex real-world data.