Title: Equivariant Diffusion for The Inverse Radar Problem
Primary area: applications to computer vision, audio, language, and other modalities
Keywords: radar, diffusion, autonomous driving, aerospace, modelnet40, sampling, computer vision, Equivariance, Geometric

Abstract: 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 non-unique solutions and partial
observability. In this work, we explore the role of equivariant modeling in helping
reduce uncertainty over potential 3D shape distributions measured via partial radar
signals. We present a radar-conditioned equivariant latent diffusion model that
uses a two-stage training approach. In the first stage, we learn equivariant latent
representations of 3D shapes by training a SO(3)-equivariant encoder-decoder
model using vector neuron architectures. During the second stage, we train an
SO(3)-equivariant denoising diffusion model that operates over the learned latent
geometry representations. We introduce an equivariant FiLM layer that enables
conditioning of our diffusion model in Irreps space and thus ensures 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 plausible 3D geometries consistent with
the observed radar signatures. In addition, we demonstrate improved performance
over other competitive non-equivariant baseline methods with respect to one of the reconstruction quality metrics and a sample diversity metric under full
observability settings.

TL;DR: This paper introduces an Equivariant Diffusion model for generating 3D geometries from radar signals and evaluate the model on partial radar observations.