# Reprojection-Guided 3D Gaussian Splatting Diffusion for Weakly Supervised Single-Image Normal Estimation

arXiv: https://arxiv.org/abs/2508.05950 · HTML: https://mlsanity.com/paper/2508.05950/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 31 references that are in the map.
- First posted on arXiv 8 Aug 2025.

## Builds on (most cited first, 22 of 22)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Objaverse: A Universe of Annotated 3D Objects](https://mlsanity.com/paper/2212.08051/) (2022)
- [Zero-1-to-3: Zero-shot One Image to 3D Object](https://mlsanity.com/paper/2303.11328/) (2023)
- [Magic3D: High-Resolution Text-to-3D Content Creation](https://mlsanity.com/paper/2211.10440/) (2022)
- [Wonder3D: Single Image to 3D using Cross-Domain Diffusion](https://mlsanity.com/paper/2310.15008/) (2023)
- [SuGaR: Surface-Aligned Gaussian Splatting for Efficient 3D Mesh Reconstruction and High-Quality Mesh Rendering](https://mlsanity.com/paper/2311.12775/) (2023)
- [Google Scanned Objects: A High-Quality Dataset of 3D Scanned Household Items](https://mlsanity.com/paper/2204.11918/) (2022)
- [Predicting Depth, Surface Normals and Semantic Labels with a Common Multi-Scale Convolutional Architecture](https://mlsanity.com/paper/1411.4734/) (2014)
- [Metric3Dv2: A Versatile Monocular Geometric Foundation Model for Zero-shot Metric Depth and Surface Normal Estimation](https://mlsanity.com/paper/2404.15506/) (2024)
- [OmniObject3D: Large-Vocabulary 3D Object Dataset for Realistic Perception, Reconstruction and Generation](https://mlsanity.com/paper/2301.07525/) (2023)
- [RealFusion: 360deg Reconstruction of Any Object from a Single Image](https://mlsanity.com/paper/2302.10663/) (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)
- [Enforcing geometric constraints of virtual normal for depth prediction](https://mlsanity.com/paper/1907.12209/) (2019)
- [StableNormal: Reducing Diffusion Variance for Stable and Sharp Normal](https://mlsanity.com/paper/2406.16864/) (2024)
- [Rethinking Inductive Biases for Surface Normal Estimation](https://mlsanity.com/paper/2403.00712/) (2024)
- [What Matters When Repurposing Diffusion Models for General Dense Perception Tasks?](https://mlsanity.com/paper/2403.06090/) (2024)
- [Designing Deep Networks for Surface Normal Estimation](https://mlsanity.com/paper/1411.4958/) (2014)
- [GeoSplatting: Towards Geometry Guided Gaussian Splatting for Physically-based Inverse Rendering](https://mlsanity.com/paper/2410.24204/) (2024)
- [Neural LightRig: Unlocking Accurate Object Normal and Material Estimation with Multi-Light Diffusion](https://mlsanity.com/paper/2412.09593/) (2024)
- [Normal-GS: 3D Gaussian Splatting with Normal-Involved Rendering](https://mlsanity.com/paper/2410.20593/) (2024)

## Abstract (arXiv)

We propose CLONE, a Continuous Latent Optimization framework for Normal Estimation via 3D Gaussian splatting. The core idea is to construct an image-geometry-image consistency strategy that unifies explicit geometric representation with differentiable rendering, thereby enabling weakly supervised learning without normal ground truth. Specifically, CLONE comprises four components. First, by introducing a differentiable light interaction model with a learnable modulation kernel, we perform a unified reparameterization of the 3DGS parameter space. Second, the conditional single-step deterministic refinement network integrates denoising architectures with differentiable reprojection constraints to refine the initial normals, thereby adaptively recovering the high-frequency details erased by the inherently smooth Gaussian primitives. Third, the cross-domain gating fusion mechanism adaptively combines the two complementary normal estimates, reconciling the geometrically consistent yet over-smooth 3DGS estimate with the detailed yet potentially geometry-inconsistent refinement. Finally, all components are jointly optimized under a unified photometric reprojection objective with geometric consistency regularizations in a fully differentiable pathway, achieving an end-to-end optimization closed loop without relying on external normal labels.