Solving LiDAR Inverse Problems using LiDAR Diffusion Models

Inverse problems are widely studied across imaging domains, but formulations for LiDAR under real-world corruptions remain underexplored. LiDAR is frequently corrupted by adverse weather, which we cast as a LiDAR inverse problem with explicit measurement operators. However, when 2D inverse problem frameworks are naively applied to LiDAR range views, they struggle to handle the strong spatial correlations inherent in 2.5D data. This is because they typically rely on an unrealistic assumption of pixel independence. To address this limitation, we present a new diffusion model guidance mechanism, termed correlative guidance, explicitly designed to model these missing spatial dependencies. Our framework augments the standard L2 guidance, which assumes pixel independence, with our proposed correlative term. This new guidance is implemented as a tractable, robust patch-wise Earth Mover's Distance (EMD) that compares local depth histograms. By operating on local distributions, our correlative guidance enforces local geometric consistency, a property ignored by standard L2 guidance. Extensive experiments across eight distinct corruption types demonstrate the effectiveness of our method and establish a new state-of-the-art for solving LiDAR inverse problems.