L3DR: 3D-aware LiDAR Diffusion and Rectification

based LiDAR diffusion has recently made huge strides towards 2D photo-realism. However, it neglects 3D geometry realism and often generates various RV artifacts such as depth bleeding and wavy surfaces. We design L3DR, a 3D-aware LiDAR Diffusion and Rectification framework that can regress and cancel RV artifacts in 3D space and restore local geometry accurately. Our theoretical and empirical analysis reveals that 3D models are inherently superior to 2D models in generating sharp and authentic boundaries. Leveraging such analysis, we design a 3D residual regression network that rectifies RV artifacts and achieves superb geometry realism by predicting pointlevel offsets in 3D space. On top of that, we design a Welsch Loss that helps focus on local geometry and ignore anomalous regions effectively. Extensive experiments over multiple benchmarks including KITTI, KITTI360, nuScenes and

Reverse sampling process. The goal is to learn a reverse process p θ (x t-1 | x t ) that reconstructs clean samples starting from Gaussian noise:

Typically, a model is trained to predict the added noise ϵ, and then restore the image using Equation 2.

We provide Theorem 1 where a constant bound can be derived for the image gradient in DDIM-sampled images. We then provide a proof sketch, while the full proof is placed in Appendix Sec. A.2.