Beyond KLD: A Symmetric Statistical Loss for Distribution-Aligned Detection

Existing regression losses for rotated object detection often suffer from asymmetry and numerical instability, especially for high aspect ratio or extremely rotated objects. We propose a novel Symmetric Gaussian Divergence (SGD) loss, which models each rotated bounding box as a 2D Gaussian distribution and measures prediction error via a closed-form, parameter-free divergence. Unlike KL divergence or Wasserstein-based losses, SGD is fully symmetric, scale-invariant, and free from cross-terms or tunable hyperparameters, ensuring stable gradients and balanced optimization of positional and angular parameters. We further derive its analytic formulation using box parameters and theoretically prove its self-consistency and robustness under degeneracy. Integrated into mainstream rotated detectors, SGD consistently improves localization accuracy and training stability on benchmarks like DOTA-v1.0 and DOTA-v1.5. Codes are publicly available.