MUSE: Mixture-to-Substructure Elucidation via Disentangled Set Prediction

Infrared (IR) spectroscopy is a crucial technique for molecular characterization in chemistry and materials science. Existing deep learning-based IR spectral analysis methods are largely confined to the idealized single-compound scenario, with limited exploration of more realistic multi-component mixtures. This challenge stems from two main issues: signal coupling and attribution ambiguity caused by overlapping absorption peaks, and the entanglement between a component's chemical structure and its concentration in the spectral features. To overcome these challenges, we introduce **MUSE**, an end-to-end framework that reformulates **M**ixt**u**re-to-**S**ubstructure **E**lucidation as a one-shot set prediction problem. By formulating a permutation-equivariant decoding scheme via learnable slot queries and cross-attention, the model simultaneously captures the physical additivity and global competition among components in a single forward pass. This joint modeling significantly mitigates the error accumulation that plagues traditional single-target methods. To overcome the intrinsic entanglement between chemical identity and abundance, MUSE partitions each slot embedding into structural and concentration subspaces, penalizing their empirical cross-covariance to encourage linear decorrelation. Building upon this latent disentanglement, it incorporates conditional flow matching during the generative process to provide physically interpretable supervision through generative reconstruction. Extensive experiments on real and simulated datasets demonstrate that MUSE significantly outperforms existing methods, establishing its effectiveness and robustness in complex mixture analysis. Our code can be found at https://anonymous.4open.science/r/MUSE-7716.