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

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.