On the Shape of Latent Variables in a Denoising VAE-MoG: A Posterior Sampling-Based Study

Abstract: In this work, we explore the latent space of a denoising variational autoencoder with a mixture-of-Gaussians prior (VAE-MoG), trained on gravitational wave data from event GW150914. To evaluate how well the model captures the underlying structure, we use Hamiltonian Monte Carlo (HMC) to draw posterior samples conditioned on clean inputs, and compare them to the encoder's outputs from noisy data. Although the model reconstructs signals accurately, statistical comparisons reveal a clear mismatch in the latent space. This shows that strong denoising performance doesn't necessarily mean the latent representations are reliable highlighting the importance of using posterior-based validation when evaluating generative models.