Multi-Energy Quasi-Symplectic Langevin Inference for Latent Disentangled Learning

The variational autoencoder-based method has been widely used for modeling massive datasets. However, for 3D images, simultaneously achieving disentangled representations, low-variance Evidence Lower Bounds (ELBO), and a lightweight model remains a challenging task. In this work, we propose a Langevin dynamics-based inference framework that integrates target data information for efficient likelihood inference and disentangles appearance and morphology features via multi-scale energy-level encoding that enables unsupervised disentanglement. We adopt a quasi-symplectic integrator to handle the Hessian-related computational bottleneck that often arises in Langevin-based flow inference. We demonstrate both theoretical and empirical effectiveness of our approach compared to other methods. Experiments on public benchmarks and clinical 3D imaging datasets show that our Langevin-VAE achieves high-quality generation and learns disentangled shape and appearance representations with a model size of only 1.7M parameters. The code will be available at: https://github.com/LaplaceCenter/LangevinVAE.