Equivariant Diffusion for The Inverse Radar Problem

Reconstructing 3D geometries from their radar signal is a complex inverse problem, often involving unique domain expertise and manual steps. Although deep learning approaches have emerged to address the automation challenges of this problem, there are still significant performance gaps due to noisy radar signals and partial observability. In this work, we propose symmetry-aware modeling to reduce uncertainty over potential 3D shape distributions measured via radar signals. We present a radar-conditioned equivariant latent diffusion model that uses a two-stage training approach. The first stage learns shape representations in latent space and the second stage uses an equivariant diffusion model to denosie the latent representation, conditioned on radar signal to generate the 3D shape. We introduce an equivariant FiLM layer that enables conditioning of our diffusion model while ensuring rotational equivariance throughout the generation process. Finally, we ensure equivariant latent representations of the conditioning radar signal by using a spherical CNN model. We show that our model predicts 3D geometries consistent with the observed radar signatures. In addition, we demonstrate improved performance over other competitive baselines in reconstruction and sample diversity.