Understanding the structure of complex, nonstationary, high-dimensional time-evolving signals is a central challenge in scientific data analysis. In many domains, such as speech and biomedical signal processing, the ability to learn disentangled and interpretable representations is critical for uncovering latent generative mechanisms. Traditional approaches to unsupervised representation learning, including variational autoencoders (VAEs), often struggle to capture the temporal and spectral diversity inherent in such data. Here we introduce variational decomposition autoencoding (VDA), a framework that incorporates a strong structural bias toward signal decomposition into variational representation learning. VDA is instantiated through variational decomposition autoencoders (DecVAEs), i.e., encoder-only neural networks that perform latent autoencoding at the level of distributions to learn multiple latent subspaces aligned with time-frequency characteristics. We evaluate DecVAEs on simulated data and three publicly available scientific datasets, spanning speech recognition, dysarthric speech evaluation, and emotional speech classification. DecVAEs improve on VAE-based methods in disentanglement quality and robustness, and their latent subspaces become factor-specific when the generative factors have distinct spectral signatures. These findings position decomposition-aware architectures as potential tools for extracting structured representations from speech, and potentially from other dynamic signals with factors exhibiting distinct spectral signatures, with applications in clinical diagnostics, human-computer interaction, and adaptive neurotechnologies.

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