ANGLE: Angular Neural Generative Learning via Engression

Generative Astrodynamics is advanced in this work by extending generative modelling to an orbit determination problem in the cislunar environment. The task is formulated as conditional density estimation, aiming to infer the probability distribution of the initial state from angles-only measurements over short observation arcs. A normalising flow is trained on perturbed topocentric observations from Near Rectilinear Halo Orbits, enabling a flexible and potentially multimodal posterior representation. Given new measurements, the learned density is sampled to generate statistically consistent and physics-informed state hypotheses. These estimates are refined via nonlinear least-squares minimisation, providing a competitive warm start for classical algorithms.

In many real-world systems, including articulated robots and biomechanical models, rotations are defined in joint space and naturally parameterized by Euler angles with bounded ranges. Yet regressing Euler angles remains challenging, as their discontinuities and singularities often destabilize training. In this work, we revisit Euler-angle regression and show that its effectiveness depends critically on the interaction between rotation representation, regression architecture, and domain constraints. We introduce a new framework that combines range-aware Euler modeling with Kolmogorov-Arnold Networks (KAN), which replace fixed node-wise activations with learnable univariate functions on edges. We further provide theoretical analysis indicating that bounded Euler ranges motivate a near-additive structure in the regression function, which favors the additive functional form of KAN, and we confirm this trend empirically. Extensive experiments on controlled rotation regression, object pose estimation, and robotic and human inverse kinematics demonstrate consistent improvements in accuracy, convergence, and efficiency. The code will be publicly available.

Angular radio maps describe the received-power distribution over the angle of arrival and underpin beam selection and receiver localization in sixth-generation (6G) networks. Predicting the angular power spectrum (APS) from geometry is difficult, because the mapping is ill-posed in non-line-of-sight (NLOS) conditions and must generalize to unseen environments. Distortion-minimizing regressors return the conditional mean, which over-smooths the spectrum and erases the multipath structure that downstream tasks need. We cast the task as a perception-distortion problem and propose RadioDiff-v2, a dual-branch one-dimensional diffusion transformer trained with flow matching. It couples periodic angular encoding, adaptive layer-normalization conditioning, a Fourier angular mixer, and joint velocity and clean-signal heads. A per-metric estimator portfolio reads every deployment quantity from this single model, so that samples carry the distribution, the clean-signal head supplies a regression-grade point estimate, Bayes-optimal rules select beams, and the conditional likelihood localizes the receiver. We prove that a concentrated conditional yields a straight probability-flow trajectory that one step integrates exactly, identifying deterministic transport as the correct inductive bias. On a zero-shot test of 99 environments and one million links, RadioDiff-v2 leads every baseline on every metric, with a 0.39 dB Wasserstein-1 distance, per-bin error below the regression baseline, a 2.43 dB eight-beam NLOS sweep loss, and a 20.6-pixel localization error with four base stations. Code is available at https://github.com/UNIC-Lab/RadioDiff-v2.