Seeing Through Spectral Overlap: Recovering Mixture Composition as a Measure on a Learned Infrared Spectral Manifold

Infrared mixture analysis seeks to recover component spectra and their abundances from a single observation, but spectral overlap allows different compositions to produce similar signals, making reconstruction alone insufficient for identification. We introduce SpecMUSE, which represents mixture composition as a finitely supported probability measure on a learned spectral manifold. Its support locations specify component spectra, while its masses encode their abundances. Masked reconstruction and coordinate alignment establish the manifold from pure spectra. A set estimator jointly predicts component coordinates, presence probabilities, and abundances from the observed mixture. A differentiable realization field and discrete projection connect coordinates to individual component spectra, while a straight-through surrogate carries spectral-loss gradients to the continuous selection queries. This formulation couples component recovery with spectral reconstruction while accommodating unknown component counts at inference. Experiments on mixtures constructed from simulated QM9S spectra and measured NIST spectra demonstrate improved recovery across mixture complexities and generalization to unseen mixtures. Anonymous code is available at https://anonymous.4open.science/r/SpecMUSE-9F68.